Quizbank/University Physics Semester 2/T11

University Physics Semester 2/T11 ID153341821922

For more information visit Quizbank/University Physics Semester 2

Exams: A0 A1 A2 B0 B1 B2 C0 C1 C2 D0 D1 D2 E0 E1 E2 F0 F1 F2 G0 G1 G2 H0 H1 H2 I0 I1 I2 J0 J1 J2 K0 K1 K2 L0 L1 L2 M0 M1 M2 N0 N1 N2 O0 O1 O2 P0 P1 P2 Q0 Q1 Q2 R0 R1 R2 S0 S1 S2 T0 T1 T2 U0 U1 U2 V0 V1 V2 W0 W1 W2 X0 X1 X2 Y0 Y1 Y2 Z0 Z1 Z2

Answers: A0 A1 A2 B0 B1 B2 C0 C1 C2 D0 D1 D2 E0 E1 E2 F0 F1 F2 G0 G1 G2 H0 H1 H2 I0 I1 I2 J0 J1 J2 K0 K1 K2 L0 L1 L2 M0 M1 M2 N0 N1 N2 O0 O1 O2 P0 P1 P2 Q0 Q1 Q2 R0 R1 R2 S0 S1 S2 T0 T1 T2 U0 U1 U2 V0 V1 V2 W0 W1 W2 X0 X1 X2 Y0 Y1 Y2 Z0 Z1 Z2

78 Tests = 3 versions x 26 variations: Each of the 26 variations (A, B, ...) represents a different random selection of questions taken from the study guide.The 3 versions (0,1,..) all have the same questions but in different order and with different numerical inputs. Unless all students take version "0" it is best to reserve it for the instructor because the questions are grouped according to the order in which they appear on the study guide.

Links: Quizbank/Instructions Study guide file:QB-University Physics Semester 2-T11.pdf

Contact me at User talk:Guy vandegrift if you need any help.

T11 A0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$ .

a) 1.606E+00 V/m²

b) 1.767E+00 V/m²

c) 1.943E+00 V/m²

d) 2.138E+00 V/m²

e) 2.351E+00 V/m²

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}$

a) 2.067E+03 V·m

b) 2.274E+03 V·m

c) 2.501E+03 V·m

d) 2.752E+03 V·m

e) 3.027E+03 V·m

3)

A diploe has a charge magnitude of q=4 nC and a separation distance of d=3.79 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.2 cm, y=1.9 cm)? Note that following the textbook's example, the y-value of the field point at 1.9 cm matches the disance of the positive charge above the x-axis.

a) 2.731E+02 V

b) 3.004E+02 V

c) 3.304E+02 V

d) 3.634E+02 V

e) 3.998E+02 V

4)

In the figure shown C₁=16.0 μF, C₂=2.27 μF, and C₃=4.4 μF. The voltage source provides ε=7.11 V. What is the charge on C₁?

a) 2.515E+01 μC

b) 2.766E+01 μC

c) 3.043E+01 μC

d) 3.347E+01 μC

e) 3.682E+01 μC

5) What is the average current involved when a truck battery sets in motion 537 C of charge in 5.08 s while starting an engine?

a) 8.736E+01 A

b) 9.610E+01 A

c) 1.057E+02 A

d) 1.163E+02 A

e) 1.279E+02 A

6)

The resistances in the figure shown are R₁= 1.6 Ω, R₂= 1.3 Ω, and R₂= 2.22 Ω. V₁ and V₃ are text 0.55 V and 3.18 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.743 V. What is the absolute value of the current through R₁?

a) 1.721E-01 A

b) 1.893E-01 A

c) 2.082E-01 A

d) 2.291E-01 A

e) 2.520E-01 A

7) A circular current loop of radius 1.67 cm carries a current of 3.81 mA. What is the magnitude of the torque if the dipole is oriented at 40 ° to a uniform magnetic fied of 0.884 T?

a) 1.568E-06 N m

b) 1.724E-06 N m

c) 1.897E-06 N m

d) 2.087E-06 N m

e) 2.295E-06 N m

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.51 m and $B_{max}=\,$ 0.649 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.376 m that is centered on the axis with its plane perpendicular to the axis?

a) 9.388E+05 A

b) 1.033E+06 A

c) 1.136E+06 A

d) 1.249E+06 A

e) 1.374E+06 A

9) A square coil has sides that are L= 0.727 m long and is tightly wound with N=376 turns of wire. The resistance of the coil is R=5.59 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0485 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.567E+00 A

b) 1.724E+00 A

c) 1.897E+00 A

d) 2.086E+00 A

e) 2.295E+00 A

10) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.856E-04 s

b) 4.242E-04 s

c) 4.666E-04 s

d) 5.133E-04 s

e) 5.646E-04 s

11) The output of an ac generator connected to an RLC series combination has a frequency of 280 Hz and an amplitude of 0.35 V;. If R =5 Ω, L= 9.50E-03H , and C=6.90E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

a) 8.646E-01 &rad;

b) 9.511E-01 &rad;

c) 1.046E+00 &rad;

d) 1.151E+00 &rad;

e) 1.266E+00 &rad;

12) What is the radiation force on an object that is 4.70E+11 m away from the sun and has cross-sectional area of 0.098 m²? The average power output of the Sun is 3.80E+26 W.

a) 7.396E-08 N

b) 8.136E-08 N

c) 8.950E-08 N

d) 9.845E-08 N

e) 1.083E-07 N

T11 A1

1)

The resistances in the figure shown are R₁= 1.81 Ω, R₂= 1.18 Ω, and R₂= 2.62 Ω. V₁ and V₃ are text 0.628 V and 2.54 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.748 V. What is the absolute value of the current through R₁?

a) 1.552E-01 A

b) 1.707E-01 A

c) 1.878E-01 A

d) 2.065E-01 A

e) 2.272E-01 A

2) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m²? The average power output of the Sun is 3.80E+26 W.

a) 5.275E-07 N

b) 5.803E-07 N

c) 6.383E-07 N

d) 7.021E-07 N

e) 7.723E-07 N

3) What is the average current involved when a truck battery sets in motion 631 C of charge in 3.8 s while starting an engine?

a) 1.661E+02 A

b) 1.827E+02 A

c) 2.009E+02 A

d) 2.210E+02 A

e) 2.431E+02 A

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.407 m and $B_{max}=\,$ 0.605 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.196 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.583E+05 A

b) 3.941E+05 A

c) 4.335E+05 A

d) 4.769E+05 A

e) 5.246E+05 A

5) A square coil has sides that are L= 0.738 m long and is tightly wound with N=717 turns of wire. The resistance of the coil is R=5.25 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0655 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.660E+00 A

b) 4.027E+00 A

c) 4.429E+00 A

d) 4.872E+00 A

e) 5.359E+00 A

6)

In the figure shown C₁=19.2 μF, C₂=2.86 μF, and C₃=5.03 μF. The voltage source provides ε=9.46 V. What is the charge on C₁?

a) 4.809E+01 μC

b) 5.290E+01 μC

c) 5.819E+01 μC

d) 6.401E+01 μC

e) 7.041E+01 μC

7) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?

a) 6.230E-04 s

b) 6.853E-04 s

c) 7.538E-04 s

d) 8.292E-04 s

e) 9.121E-04 s

8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}$

a) 1.997E+03 V·m

b) 2.197E+03 V·m

c) 2.417E+03 V·m

d) 2.659E+03 V·m

e) 2.924E+03 V·m

9) The output of an ac generator connected to an RLC series combination has a frequency of 320 Hz and an amplitude of 0.69 V;. If R =6 Ω, L= 6.80E-03H , and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

a) 1.143E+00 &rad;

b) 1.257E+00 &rad;

c) 1.382E+00 &rad;

d) 1.521E+00 &rad;

e) 1.673E+00 &rad;

10) A circular current loop of radius 1.63 cm carries a current of 2.38 mA. What is the magnitude of the torque if the dipole is oriented at 54 ° to a uniform magnetic fied of 0.125 T?

a) 2.009E-07 N m

b) 2.210E-07 N m

c) 2.431E-07 N m

d) 2.674E-07 N m

e) 2.941E-07 N m

11) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=4.2{\text{ m}}$ .

a) 5.134E-01 V/m²

b) 5.648E-01 V/m²

c) 6.212E-01 V/m²

d) 6.834E-01 V/m²

e) 7.517E-01 V/m²

12)

A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.17 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.

a) 5.261E+02 V

b) 5.787E+02 V

c) 6.365E+02 V

d) 7.002E+02 V

e) 7.702E+02 V

T11 A2

1) A circular current loop of radius 1.11 cm carries a current of 4.0 mA. What is the magnitude of the torque if the dipole is oriented at 68 ° to a uniform magnetic fied of 0.173 T?

a) 1.866E-07 N m

b) 2.052E-07 N m

c) 2.258E-07 N m

d) 2.484E-07 N m

e) 2.732E-07 N m

2) What is the average current involved when a truck battery sets in motion 572 C of charge in 3.33 s while starting an engine?

a) 1.173E+02 A

b) 1.291E+02 A

c) 1.420E+02 A

d) 1.562E+02 A

e) 1.718E+02 A

3)

The resistances in the figure shown are R₁= 2.38 Ω, R₂= 1.87 Ω, and R₂= 2.32 Ω. V₁ and V₃ are text 0.605 V and 3.8 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.67 V. What is the absolute value of the current through R₁?

a) 8.147E-02 A

b) 8.962E-02 A

c) 9.858E-02 A

d) 1.084E-01 A

e) 1.193E-01 A

4)

In the figure shown C₁=17.1 μF, C₂=2.87 μF, and C₃=4.74 μF. The voltage source provides ε=6.63 V. What is the charge on C₁?

a) 2.385E+01 μC

b) 2.623E+01 μC

c) 2.886E+01 μC

d) 3.174E+01 μC

e) 3.492E+01 μC

5) What is the radiation force on an object that is 3.60E+11 m away from the sun and has cross-sectional area of 0.069 m²? The average power output of the Sun is 3.80E+26 W.

a) 7.336E-08 N

b) 8.069E-08 N

c) 8.876E-08 N

d) 9.764E-08 N

e) 1.074E-07 N

6) In an LC circuit, the self-inductance is 0.0815 H and the capacitance is 6.520E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.410E-05 C. How long does it take for the capacitor to become completely discharged?

a) 7.821E-04 s

b) 8.603E-04 s

c) 9.463E-04 s

d) 1.041E-03 s

e) 1.145E-03 s

7) The output of an ac generator connected to an RLC series combination has a frequency of 510 Hz and an amplitude of 0.24 V;. If R =7 Ω, L= 2.90E-03H , and C=9.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

a) 7.495E-01 &rad;

b) 8.244E-01 &rad;

c) 9.068E-01 &rad;

d) 9.975E-01 &rad;

e) 1.097E+00 &rad;

8) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$ .

a) 8.253E-01 V/m²

b) 9.079E-01 V/m²

c) 9.987E-01 V/m²

d) 1.099E+00 V/m²

e) 1.208E+00 V/m²

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}$

a) 8.545E+01 V·m

b) 9.400E+01 V·m

c) 1.034E+02 V·m

d) 1.137E+02 V·m

e) 1.251E+02 V·m

10) A square coil has sides that are L= 0.219 m long and is tightly wound with N=508 turns of wire. The resistance of the coil is R=8.42 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0619 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.791E-01 A

b) 1.970E-01 A

c) 2.167E-01 A

d) 2.384E-01 A

e) 2.622E-01 A

11) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.736 m and $B_{max}=\,$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.532 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.764E+05 A

b) 4.140E+05 A

c) 4.554E+05 A

d) 5.010E+05 A

e) 5.510E+05 A

12)

A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.29 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.33 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.

a) 4.324E+02 V

b) 4.757E+02 V

c) 5.232E+02 V

d) 5.755E+02 V

e) 6.331E+02 V

T11 B0

1)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate

f(x,y)

at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 6.311E+00 V/m²

b) 6.943E+00 V/m²

c) 7.637E+00 V/m²

d) 8.401E+00 V/m²

e) 9.241E+00 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.6 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.4 m, z=z₀=1.4 m, and z=z₁=5.6 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 9.6m² ,and those in the zx plane have area 11.0m². An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 8.921E+01 N·m²/C

b) 9.813E+01 N·m²/C

c) 1.079E+02 N·m²/C

d) 1.187E+02 N·m²/C

e) 1.306E+02 N·m²/C

3) If a 28 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=77 V is x² + y² + z² = R², where R=

a) 2.701E+00 m

b) 2.971E+00 m

c) 3.268E+00 m

d) 3.595E+00 m

e) 3.955E+00 m

4)

What is the net capacitance if C₁=3.56 μF, C₂=4.23 μF, and C₃=2.61 μF in the configuration shown?

a) 3.755E+00 μF

b) 4.130E+00 μF

c) 4.543E+00 μF

d) 4.997E+00 μF

e) 5.497E+00 μF

5) Calculate the drift speed of electrons in a copper wire with a diameter of 2.17 mm carrying a 19.4 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

a) 3.569E-04 m/s

b) 3.926E-04 m/s

c) 4.319E-04 m/s

d) 4.750E-04 m/s

e) 5.226E-04 m/s

6) Three resistors, R₁ = 0.855 Ω, and R₂ = R₂ = 1.91 Ω, are connected in parallel to a 6.97 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 5.682E+01 W

b) 6.250E+01 W

c) 6.875E+01 W

d) 7.563E+01 W

e) 8.319E+01 W

7) A charged particle in a magnetic field of 5.500E-04 T is moving perpendicular to the magnetic field with a speed of 2.930E+05 m/s. What is the period of orbit if orbital radius is 0.787 m?

a) 1.688E-05 s

b) 1.856E-05 s

c) 2.042E-05 s

d) 2.246E-05 s

e) 2.471E-05 s

8) Two loops of wire carry the same current of 44 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.678 m while the other has a radius of 1.14 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.508 m from the first (smaller) loopif the disance between the loops is 1.16 m?

a) 3.342E-02 T

b) 3.676E-02 T

c) 4.044E-02 T

d) 4.448E-02 T

e) 4.893E-02 T

9) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.609E+00 A

b) 2.870E+00 A

c) 3.157E+00 A

d) 3.473E+00 A

e) 3.820E+00 A

10) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?

a) 2.549E-01 H

b) 2.804E-01 H

c) 3.084E-01 H

d) 3.392E-01 H

e) 3.732E-01 H

11) An ac generator produces an emf of amplitude 66 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a 97 mF inductor?

a) 4.972E-01 A

b) 5.469E-01 A

c) 6.016E-01 A

d) 6.618E-01 A

e) 7.280E-01 A

12) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.016 m²? The average power output of the Sun is 3.80E+26 W.

a) 6.669E-07 N/m²

b) 7.336E-07 N/m²

c) 8.069E-07 N/m²

d) 8.876E-07 N/m²

e) 9.764E-07 N/m²

T11 B1

1) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.052 m²? The average power output of the Sun is 3.80E+26 W.

a) 2.392E-06 N/m²

b) 2.631E-06 N/m²

c) 2.894E-06 N/m²

d) 3.184E-06 N/m²

e) 3.502E-06 N/m²

2) Three resistors, R₁ = 1.82 Ω, and R₂ = R₂ = 4.14 Ω, are connected in parallel to a 5.65 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 1.754E+01 W

b) 1.929E+01 W

c) 2.122E+01 W

d) 2.335E+01 W

e) 2.568E+01 W

3)

What is the net capacitance if C₁=2.96 μF, C₂=3.95 μF, and C₃=3.74 μF in the configuration shown?

a) 4.489E+00 μF

b) 4.938E+00 μF

c) 5.432E+00 μF

d) 5.975E+00 μF

e) 6.573E+00 μF

4)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate

f(x,y)

at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 8.690E+00 V/m²

b) 9.559E+00 V/m²

c) 1.051E+01 V/m²

d) 1.157E+01 V/m²

e) 1.272E+01 V/m²

5) An induced emf of 6.29V is measured across a coil of 85 closely wound turns while the current throuth it increases uniformly from 0.0 to 2.15A in 0.913s. What is the self-inductance of the coil?

a) 2.428E+00 H

b) 2.671E+00 H

c) 2.938E+00 H

d) 3.232E+00 H

e) 3.555E+00 H

6) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=43 V is x² + y² + z² = R², where R=

a) 2.299E+00 m

b) 2.529E+00 m

c) 2.782E+00 m

d) 3.060E+00 m

e) 3.366E+00 m

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.9 m, y=y₁=5.3 m, z=z₀=1.4 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 14.0m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 9.8m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.270E+01 N·m²/C

b) 6.897E+01 N·m²/C

c) 7.586E+01 N·m²/C

d) 8.345E+01 N·m²/C

e) 9.179E+01 N·m²/C

8) Calculate the drift speed of electrons in a copper wire with a diameter of 3.17 mm carrying a 12.0 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

a) 1.138E-04 m/s

b) 1.252E-04 m/s

c) 1.377E-04 m/s

d) 1.515E-04 m/s

e) 1.666E-04 m/s

9) Two loops of wire carry the same current of 85 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.854 m while the other has a radius of 1.18 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.5 m from the first (smaller) loopif the disance between the loops is 1.66 m?

a) 4.253E-02 T

b) 4.678E-02 T

c) 5.146E-02 T

d) 5.661E-02 T

e) 6.227E-02 T

10) An ac generator produces an emf of amplitude 58 V at a frequency of 99 Hz. What is the maximum amplitude of the current if the generator is connected to a 35 mF inductor?

a) 2.422E+00 A

b) 2.664E+00 A

c) 2.930E+00 A

d) 3.224E+00 A

e) 3.546E+00 A

11) A square coil has sides that are L= 0.308 m long and is tightly wound with N=969 turns of wire. The resistance of the coil is R=8.64 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0498 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 4.817E-01 A

b) 5.298E-01 A

c) 5.828E-01 A

d) 6.411E-01 A

e) 7.052E-01 A

12) A charged particle in a magnetic field of 3.330E-04 T is moving perpendicular to the magnetic field with a speed of 4.800E+05 m/s. What is the period of orbit if orbital radius is 0.402 m?

a) 4.784E-06 s

b) 5.262E-06 s

c) 5.788E-06 s

d) 6.367E-06 s

e) 7.004E-06 s

T11 B2

1) An ac generator produces an emf of amplitude 97 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 55 mF inductor?

a) 4.386E+00 A

b) 4.824E+00 A

c) 5.307E+00 A

d) 5.838E+00 A

e) 6.421E+00 A

2) What is the radiation pressure on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.098 m²? The average power output of the Sun is 3.80E+26 W.

a) 2.144E-07 N/m²

b) 2.358E-07 N/m²

c) 2.594E-07 N/m²

d) 2.854E-07 N/m²

e) 3.139E-07 N/m²

3) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=43 V is x² + y² + z² = R², where R=

a) 2.299E+00 m

b) 2.529E+00 m

c) 2.782E+00 m

d) 3.060E+00 m

e) 3.366E+00 m

4) A square coil has sides that are L= 0.727 m long and is tightly wound with N=376 turns of wire. The resistance of the coil is R=5.59 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0485 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.567E+00 A

b) 1.724E+00 A

c) 1.897E+00 A

d) 2.086E+00 A

e) 2.295E+00 A

5)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate

f(x,y)

at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

a) 3.610E+00 V/m²

b) 3.971E+00 V/m²

c) 4.368E+00 V/m²

d) 4.804E+00 V/m²

e) 5.285E+00 V/m²

6) A charged particle in a magnetic field of 3.350E-04 T is moving perpendicular to the magnetic field with a speed of 4.350E+05 m/s. What is the period of orbit if orbital radius is 0.841 m?

a) 1.004E-05 s

b) 1.104E-05 s

c) 1.215E-05 s

d) 1.336E-05 s

e) 1.470E-05 s

7) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.838 m while the other has a radius of 1.17 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?

a) 3.863E-02 T

b) 4.249E-02 T

c) 4.674E-02 T

d) 5.141E-02 T

e) 5.655E-02 T

8) Three resistors, R₁ = 1.52 Ω, and R₂ = R₂ = 3.38 Ω, are connected in parallel to a 5.82 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 1.842E+01 W

b) 2.026E+01 W

c) 2.228E+01 W

d) 2.451E+01 W

e) 2.696E+01 W

9) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?

a) 2.549E-01 H

b) 2.804E-01 H

c) 3.084E-01 H

d) 3.392E-01 H

e) 3.732E-01 H

10)

What is the net capacitance if C₁=2.55 μF, C₂=4.13 μF, and C₃=2.5 μF in the configuration shown?

a) 4.077E+00 μF

b) 4.484E+00 μF

c) 4.933E+00 μF

d) 5.426E+00 μF

e) 5.969E+00 μF

11)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.6 m, z=z₀=1.4 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 9.0m². Those in the xy plane have area 6.4m² ,and those in the zx plane have area 6.8m². An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.959E+01 N·m²/C

b) 4.354E+01 N·m²/C

c) 4.790E+01 N·m²/C

d) 5.269E+01 N·m²/C

e) 5.796E+01 N·m²/C

12) Calculate the drift speed of electrons in a copper wire with a diameter of 3.3 mm carrying a 18.5 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

a) 1.472E-04 m/s

b) 1.619E-04 m/s

c) 1.781E-04 m/s

d) 1.959E-04 m/s

e) 2.155E-04 m/s

T11 C0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.3{\text{ m}}$ and the surface charge density is $\sigma =5{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=5.3{\text{ m}}$ .

a) 1.022E+00 V/m²

b) 1.125E+00 V/m²

c) 1.237E+00 V/m²

d) 1.361E+00 V/m²

e) 1.497E+00 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.3 m, z=z₀=1.5 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 8.3m². Those in the xy plane have area 5.7m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.408E+01 N·m²/C

b) 5.949E+01 N·m²/C

c) 6.544E+01 N·m²/C

d) 7.198E+01 N·m²/C

e) 7.918E+01 N·m²/C

3)

An electron gun has parallel plates separated by 5.38 cm and gives electrons 54 keV of energy. What force would the field between the plates exert on a 0.427 μC charge that gets between the plates?

a) 3.542E-01 N

b) 3.896E-01 N

c) 4.286E-01 N

d) 4.714E-01 N

e) 5.186E-01 N

4)

In the figure shown C₁=16.5 μF, C₂=2.7 μF, and C₃=4.82 μF. The voltage source provides ε=15.7 V. What is the energy stored in C₂?

a) 2.188E+01 μJ

b) 2.407E+01 μJ

c) 2.647E+01 μJ

d) 2.912E+01 μJ

e) 3.203E+01 μJ

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =78 C and $\tau =$ 0.0244 s. What is the current at $t=$ 0.0225 s?

a) 1.271E+03 A

b) 1.398E+03 A

c) 1.538E+03 A

d) 1.692E+03 A

e) 1.861E+03 A

6) A given battery has a 12 V emf and an internal resistance of 0.0984 Ω. If it is connected to a 0.485 Ω resistor what is the power dissipated by that load?

a) 2.052E+02 W

b) 2.257E+02 W

c) 2.483E+02 W

d) 2.731E+02 W

e) 3.004E+02 W

7) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.44 m and a magneticfield of 1.31 T. What is their maximum kinetic energy?

a) 1.323E+01 MeV

b) 1.456E+01 MeV

c) 1.601E+01 MeV

d) 1.761E+01 MeV

e) 1.937E+01 MeV

8) Two parallel wires each carry a 9.08 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.17 cm, 1.32 cm), while the other is located at (5.72 cm, 4.47 cm). What is the force per unit length between the wires?

a) 3.882E-10 N/m

b) 4.270E-10 N/m

c) 4.697E-10 N/m

d) 5.167E-10 N/m

e) 5.683E-10 N/m

9) A recangular coil with an area of 0.449 m² and 20 turns is placed in a uniform magnetic field of 3.58 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.990E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 66 s?

a) 7.734E+04 V

b) 8.507E+04 V

c) 9.358E+04 V

d) 1.029E+05 V

e) 1.132E+05 V

10) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.28mm$ , and $n=2.4$ . What is the volume of the washer?

a) 1.097E+00 cm³

b) 1.207E+00 cm³

c) 1.328E+00 cm³

d) 1.460E+00 cm³

e) 1.606E+00 cm³

11) A step-down transformer steps 6 kV down to 190 V. The high-voltage input is provided by a 130 Ω power line that carries 6 A of currentWhat is the output current (at the 190 V side ?)

a) 1.424E+02 A

b) 1.566E+02 A

c) 1.722E+02 A

d) 1.895E+02 A

e) 2.084E+02 A

12) What is the radiation force on an object that is 2.50E+11 m away from the sun and has cross-sectional area of 0.045 m²? The average power output of the Sun is 3.80E+26 W.

a) 1.200E-07 N

b) 1.320E-07 N

c) 1.452E-07 N

d) 1.598E-07 N

e) 1.757E-07 N

T11 C1

1) Two parallel wires each carry a 8.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.66 cm, 1.4 cm), while the other is located at (5.64 cm, 5.66 cm). What is the force per unit length between the wires?

a) 2.449E-10 N/m

b) 2.694E-10 N/m

c) 2.963E-10 N/m

d) 3.260E-10 N/m

e) 3.586E-10 N/m

2) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.14mm$ , and $n=2.86$ . What is the volume of the washer?

a) 1.071E+00 cm³

b) 1.178E+00 cm³

c) 1.296E+00 cm³

d) 1.425E+00 cm³

e) 1.568E+00 cm³

3)

In the figure shown C₁=20.7 μF, C₂=2.79 μF, and C₃=5.18 μF. The voltage source provides ε=15.0 V. What is the energy stored in C₂?

a) 2.064E+01 μJ

b) 2.270E+01 μJ

c) 2.497E+01 μJ

d) 2.747E+01 μJ

e) 3.022E+01 μJ

4) A given battery has a 13 V emf and an internal resistance of 0.159 Ω. If it is connected to a 0.617 Ω resistor what is the power dissipated by that load?

a) 1.301E+02 W

b) 1.431E+02 W

c) 1.574E+02 W

d) 1.732E+02 W

e) 1.905E+02 W

5) What is the radiation force on an object that is 1.70E+11 m away from the sun and has cross-sectional area of 0.033 m²? The average power output of the Sun is 3.80E+26 W.

a) 1.904E-07 N

b) 2.094E-07 N

c) 2.303E-07 N

d) 2.534E-07 N

e) 2.787E-07 N

6) A recangular coil with an area of 0.137 m² and 18 turns is placed in a uniform magnetic field of 1.18 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.120E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 47 s?

a) 1.086E+04 V

b) 1.195E+04 V

c) 1.314E+04 V

d) 1.446E+04 V

e) 1.590E+04 V

7) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =91 C and $\tau =$ 0.0156 s. What is the current at $t=$ 0.0131 s?

a) 2.082E+03 A

b) 2.290E+03 A

c) 2.519E+03 A

d) 2.771E+03 A

e) 3.048E+03 A

8)

An electron gun has parallel plates separated by 2.98 cm and gives electrons 11 keV of energy. What force would the field between the plates exert on a 0.685 μC charge that gets between the plates?

a) 1.900E-01 N

b) 2.090E-01 N

c) 2.299E-01 N

d) 2.529E-01 N

e) 2.781E-01 N

9) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$ .

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

10) A step-down transformer steps 15 kV down to 250 V. The high-voltage input is provided by a 130 Ω power line that carries 4 A of currentWhat is the output current (at the 250 V side ?)

a) 1.983E+02 A

b) 2.182E+02 A

c) 2.400E+02 A

d) 2.640E+02 A

e) 2.904E+02 A

11)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.6 m, z=z₀=1.4 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 9.0m². Those in the xy plane have area 6.4m² ,and those in the zx plane have area 6.8m². An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.959E+01 N·m²/C

b) 4.354E+01 N·m²/C

c) 4.790E+01 N·m²/C

d) 5.269E+01 N·m²/C

e) 5.796E+01 N·m²/C

12) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.413 m and a magneticfield of 0.988 T. What is their maximum kinetic energy?

a) 6.029E+00 MeV

b) 6.631E+00 MeV

c) 7.295E+00 MeV

d) 8.024E+00 MeV

e) 8.827E+00 MeV

T11 C2

1) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.28mm$ , and $n=2.4$ . What is the volume of the washer?

a) 1.097E+00 cm³

b) 1.207E+00 cm³

c) 1.328E+00 cm³

d) 1.460E+00 cm³

e) 1.606E+00 cm³

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.8 m. The other four surfaces are rectangles in y=y₀=1.2 m, y=y₁=5.9 m, z=z₀=1.3 m, and z=z₁=5.2 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 8.5m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 4.777E+01 N·m²/C

b) 5.254E+01 N·m²/C

c) 5.780E+01 N·m²/C

d) 6.358E+01 N·m²/C

e) 6.993E+01 N·m²/C

3) A recangular coil with an area of 0.39 m² and 16 turns is placed in a uniform magnetic field of 3.07 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.320E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 44 s?

a) 3.792E+04 V

b) 4.172E+04 V

c) 4.589E+04 V

d) 5.048E+04 V

e) 5.552E+04 V

4) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=1.2{\text{ m}}$ .

a) 8.933E+00 V/m²

b) 9.826E+00 V/m²

c) 1.081E+01 V/m²

d) 1.189E+01 V/m²

e) 1.308E+01 V/m²

5)

In the figure shown C₁=15.7 μF, C₂=2.87 μF, and C₃=5.46 μF. The voltage source provides ε=5.38 V. What is the energy stored in C₂?

a) 6.890E+00 μJ

b) 7.579E+00 μJ

c) 8.337E+00 μJ

d) 9.171E+00 μJ

e) 1.009E+01 μJ

6) A given battery has a 9 V emf and an internal resistance of 0.16 Ω. If it is connected to a 0.45 Ω resistor what is the power dissipated by that load?

a) 6.691E+01 W

b) 7.360E+01 W

c) 8.096E+01 W

d) 8.905E+01 W

e) 9.796E+01 W

7) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =18 C and $\tau =$ 0.0169 s. What is the current at $t=$ 0.0137 s?

a) 3.913E+02 A

b) 4.305E+02 A

c) 4.735E+02 A

d) 5.209E+02 A

e) 5.729E+02 A

8) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.145 m and a magneticfield of 1.03 T. What is their maximum kinetic energy?

a) 7.342E-01 MeV

b) 8.076E-01 MeV

c) 8.884E-01 MeV

d) 9.772E-01 MeV

e) 1.075E+00 MeV

9)

An electron gun has parallel plates separated by 3.68 cm and gives electrons 54 keV of energy. What force would the field between the plates exert on a 0.181 μC charge that gets between the plates?

a) 2.656E-01 N

b) 2.922E-01 N

c) 3.214E-01 N

d) 3.535E-01 N

e) 3.889E-01 N

10) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?

a) 1.283E-10 N/m

b) 1.411E-10 N/m

c) 1.552E-10 N/m

d) 1.708E-10 N/m

e) 1.878E-10 N/m

11) A step-down transformer steps 8 kV down to 220 V. The high-voltage input is provided by a 110 Ω power line that carries 8 A of currentWhat is the output current (at the 220 V side ?)

a) 2.404E+02 A

b) 2.645E+02 A

c) 2.909E+02 A

d) 3.200E+02 A

e) 3.520E+02 A

12) What is the radiation force on an object that is 9.90E+11 m away from the sun and has cross-sectional area of 0.083 m²? The average power output of the Sun is 3.80E+26 W.

a) 1.167E-08 N

b) 1.284E-08 N

c) 1.412E-08 N

d) 1.553E-08 N

e) 1.708E-08 N

T11 D0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$ .

a) 1.606E+00 V/m²

b) 1.767E+00 V/m²

c) 1.943E+00 V/m²

d) 2.138E+00 V/m²

e) 2.351E+00 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.8 m, y=y₁=5.3 m, z=z₀=1.2 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 15.0m². Those in the xy plane have area 7.7m² ,and those in the zx plane have area 9.5m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.989E+01 N·m²/C

b) 6.588E+01 N·m²/C

c) 7.247E+01 N·m²/C

d) 7.971E+01 N·m²/C

e) 8.769E+01 N·m²/C

3) When a 6.03 V battery operates a 1.56 W bulb, how many electrons pass through it each second?

a) 1.615E+18 electrons

b) 1.776E+18 electrons

c) 1.954E+18 electrons

d) 2.149E+18 electrons

e) 2.364E+18 electrons

4) An empty parallel-plate capacitor with metal plates has an area of 2.02 m², separated by 1.44 mm. How much charge does it store if the voltage is 2.170E+03 V?

a) 2.450E+01 μC

b) 2.695E+01 μC

c) 2.965E+01 μC

d) 3.261E+01 μC

e) 3.587E+01 μC

5) Calculate the electric field in a 12-gauge copper wire that is 84 m long and carries a current of 48 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 1.664E-04 V/m

b) 1.830E-04 V/m

c) 2.013E-04 V/m

d) 2.215E-04 V/m

e) 2.436E-04 V/m

6)

Two sources of emf ε₁=26.2 V, and ε₂=8.29 V are oriented as shownin the circuit. The resistances are R₁=3.43 kΩ and R₂=1.16 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=4.09 mA and I₄=1.06 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 6.720E+00 V

b) 7.392E+00 V

c) 8.131E+00 V

d) 8.944E+00 V

e) 9.838E+00 V

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 5.75 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(1.81 i + 2.05 j + 4.49 k) x 10⁴ m/s?

a) 2.576E-14 N

b) 2.834E-14 N

c) 3.117E-14 N

d) 3.429E-14 N

e) 3.772E-14 N

8)

Three wires sit at the corners of a square of length 0.716 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.94 A, 2.04 A, 2.41 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 6.833E-05 T

b) B_y= 7.517E-05 T

c) B_y= 8.268E-05 T

d) B_y= 9.095E-05 T

e) B_y= 1.000E-04 T

9) Calculate the motional emf induced along a 48.8 km conductor moving at an orbital speed of 7.88 km/s perpendicular to Earth's 4.660E-05 Tesla magnetic field.

a) 1.224E+04 V

b) 1.346E+04 V

c) 1.481E+04 V

d) 1.629E+04 V

e) 1.792E+04 V

10) An induced emf of 7.94V is measured across a coil of 94 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.65A in 0.478s. What is the self-inductance of the coil?

a) 5.047E-01 H

b) 5.552E-01 H

c) 6.107E-01 H

d) 6.717E-01 H

e) 7.389E-01 H

11) An ac generator produces an emf of amplitude 71 V at a frequency of 68 Hz. What is the maximum amplitude of the current if the generator is connected to a 35 mF capacitor?

a) 7.252E-01 A

b) 7.977E-01 A

c) 8.775E-01 A

d) 9.652E-01 A

e) 1.062E+00 A

12) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?

a) 1.753E+02 km

b) 1.928E+02 km

c) 2.121E+02 km

d) 2.333E+02 km

e) 2.567E+02 km

T11 D1

1) Calculate the electric field in a 12-gauge copper wire that is 48 m long and carries a current of 63 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 3.198E-04 V/m

b) 3.517E-04 V/m

c) 3.869E-04 V/m

d) 4.256E-04 V/m

e) 4.682E-04 V/m

2) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.13 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(5.64 i + 1.93 j + 8.71 k) x 10⁴ m/s?

a) 1.757E-14 N

b) 1.933E-14 N

c) 2.126E-14 N

d) 2.339E-14 N

e) 2.573E-14 N

3) An empty parallel-plate capacitor with metal plates has an area of 2.1 m², separated by 1.13 mm. How much charge does it store if the voltage is 1.680E+03 V?

a) 2.764E+01 μC

b) 3.041E+01 μC

c) 3.345E+01 μC

d) 3.679E+01 μC

e) 4.047E+01 μC

4) An ac generator produces an emf of amplitude 54 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 7 mF capacitor?

a) 2.850E-01 A

b) 3.135E-01 A

c) 3.449E-01 A

d) 3.793E-01 A

e) 4.173E-01 A

5) When a 2.59 V battery operates a 2.89 W bulb, how many electrons pass through it each second?

a) 5.756E+18 electrons

b) 6.331E+18 electrons

c) 6.964E+18 electrons

d) 7.661E+18 electrons

e) 8.427E+18 electrons

6) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?

a) 2.094E+02 km

b) 2.304E+02 km

c) 2.534E+02 km

d) 2.788E+02 km

e) 3.066E+02 km

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.7 m, z=z₀=1.8 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 9.2m² ,and those in the zx plane have area 8.1m². An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 2.134E+01 N·m²/C

b) 2.347E+01 N·m²/C

c) 2.582E+01 N·m²/C

d) 2.840E+01 N·m²/C

e) 3.124E+01 N·m²/C

8)

Two sources of emf ε₁=38.8 V, and ε₂=14.9 V are oriented as shownin the circuit. The resistances are R₁=5.83 kΩ and R₂=1.77 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.57 mA and I₄=1.19 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 1.013E+01 V

b) 1.115E+01 V

c) 1.226E+01 V

d) 1.349E+01 V

e) 1.484E+01 V

9)

Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 7.035E-05 T

b) B_y= 7.739E-05 T

c) B_y= 8.512E-05 T

d) B_y= 9.364E-05 T

e) B_y= 1.030E-04 T

10) An induced emf of 1.92V is measured across a coil of 74 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.38A in 0.69s. What is the self-inductance of the coil?

a) 1.560E-01 H

b) 1.716E-01 H

c) 1.888E-01 H

d) 2.076E-01 H

e) 2.284E-01 H

11) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$ .

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

12) Calculate the motional emf induced along a 46.2 km conductor moving at an orbital speed of 7.9 km/s perpendicular to Earth's 4.630E-05 Tesla magnetic field.

a) 1.536E+04 V

b) 1.690E+04 V

c) 1.859E+04 V

d) 2.045E+04 V

e) 2.249E+04 V

T11 D2

1) Calculate the electric field in a 12-gauge copper wire that is 99 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 3.604E-04 V/m

b) 3.964E-04 V/m

c) 4.360E-04 V/m

d) 4.796E-04 V/m

e) 5.276E-04 V/m

2) An ac generator produces an emf of amplitude 17 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 6 mF capacitor?

a) 5.253E-02 A

b) 5.778E-02 A

c) 6.356E-02 A

d) 6.991E-02 A

e) 7.691E-02 A

3) An empty parallel-plate capacitor with metal plates has an area of 2.21 m², separated by 1.25 mm. How much charge does it store if the voltage is 1.580E+03 V?

a) 2.249E+01 μC

b) 2.473E+01 μC

c) 2.721E+01 μC

d) 2.993E+01 μC

e) 3.292E+01 μC

4)

Three wires sit at the corners of a square of length 0.702 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 7.576E-05 T

b) B_y= 8.333E-05 T

c) B_y= 9.167E-05 T

d) B_y= 1.008E-04 T

e) B_y= 1.109E-04 T

5) When a 4.21 V battery operates a 2.17 W bulb, how many electrons pass through it each second?

a) 2.659E+18 electrons

b) 2.925E+18 electrons

c) 3.217E+18 electrons

d) 3.539E+18 electrons

e) 3.893E+18 electrons

6) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?

a) 2.549E-01 H

b) 2.804E-01 H

c) 3.084E-01 H

d) 3.392E-01 H

e) 3.732E-01 H

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.3 m. The other four surfaces are rectangles in y=y₀=1.1 m, y=y₁=5.7 m, z=z₀=1.8 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 12.0m². Those in the xy plane have area 6.0m² ,and those in the zx plane have area 3.5m². An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 9.823E+00 N·m²/C

b) 1.080E+01 N·m²/C

c) 1.189E+01 N·m²/C

d) 1.307E+01 N·m²/C

e) 1.438E+01 N·m²/C

8) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3{\text{ m}}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$ .

a) 6.877E+00 V/m²

b) 7.565E+00 V/m²

c) 8.321E+00 V/m²

d) 9.153E+00 V/m²

e) 1.007E+01 V/m²

9) Calculate the motional emf induced along a 49.5 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.310E-05 Tesla magnetic field.

a) 1.395E+04 V

b) 1.534E+04 V

c) 1.688E+04 V

d) 1.857E+04 V

e) 2.042E+04 V

10)

Two sources of emf ε₁=30.6 V, and ε₂=12.0 V are oriented as shownin the circuit. The resistances are R₁=3.46 kΩ and R₂=2.77 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.97 mA and I₄=0.643 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 4.986E+00 V

b) 5.484E+00 V

c) 6.033E+00 V

d) 6.636E+00 V

e) 7.299E+00 V

11) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 4.69 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(8.9 i + 4.27 j + 7.52 k) x 10⁴ m/s?

a) 5.296E-14 N

b) 5.826E-14 N

c) 6.408E-14 N

d) 7.049E-14 N

e) 7.754E-14 N

12) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?

a) 1.003E+02 km

b) 1.103E+02 km

c) 1.213E+02 km

d) 1.335E+02 km

e) 1.468E+02 km

T11 E0

1) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 9.412E+01 N/C

b) 1.035E+02 N/C

c) 1.139E+02 N/C

d) 1.253E+02 N/C

e) 1.378E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\vec {E}}=4y^{2.0}{\hat {i}}+3x^{2.0}{\hat {j}}+3y^{3.0}{\hat {k}}$

a) 4.820E+03 V·m

b) 5.302E+03 V·m

c) 5.832E+03 V·m

d) 6.415E+03 V·m

e) 7.057E+03 V·m

3) If a 14 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=26 V is x² + y² + z² = R², where R=

a) 3.636E+00 m

b) 4.000E+00 m

c) 4.399E+00 m

d) 4.839E+00 m

e) 5.323E+00 m

4)

In the figure shown C₁=16.9 μF, C₂=2.86 μF, and C₃=5.1 μF. The voltage source provides ε=9.98 V. What is the energy stored in C₂?

a) 1.764E+01 μJ

b) 1.940E+01 μJ

c) 2.134E+01 μJ

d) 2.348E+01 μJ

e) 2.583E+01 μJ

5) Calculate the electric field in a 12-gauge copper wire that is 21 m long and carries a current of 42 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 1.602E-04 V/m

b) 1.762E-04 V/m

c) 1.938E-04 V/m

d) 2.132E-04 V/m

e) 2.345E-04 V/m

6) A given battery has a 13 V emf and an internal resistance of 0.113 Ω. If it is connected to a 0.686 Ω resistor what is the power dissipated by that load?

a) 1.501E+02 W

b) 1.651E+02 W

c) 1.816E+02 W

d) 1.998E+02 W

e) 2.197E+02 W

7) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.83 T magnetic field is directed 22° away from the wire?

a) 1.062E+00 N/m

b) 1.168E+00 N/m

c) 1.285E+00 N/m

d) 1.413E+00 N/m

e) 1.555E+00 N/m

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.253 m and $B_{max}=\,$ 0.489 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.112 m that is centered on the axis with its plane perpendicular to the axis?

a) 1.289E+05 A

b) 1.418E+05 A

c) 1.560E+05 A

d) 1.716E+05 A

e) 1.888E+05 A

9) A long solenoid has a radius of 0.413 m and 17 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 1 A and $\alpha =$ 21 s⁻¹.What is the induced electric fied at a distance 2.25 m from the axis at time t=0.0689 s ?

a) 3.006E-06 V/m

b) 3.307E-06 V/m

c) 3.637E-06 V/m

d) 4.001E-06 V/m

e) 4.401E-06 V/m

10)

A long solenoid has a length 0.777 meters, radius 3.45 cm, and 557 turns. It surrounds coil of radius 6.01 meters and 10turns. If the current in the solenoid is changing at a rate of 184 A/s, what is the emf induced in the surounding coil?

a) 1.463E-02 V

b) 1.609E-02 V

c) 1.770E-02 V

d) 1.947E-02 V

e) 2.142E-02 V

11) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.43 V;. If R =7 Ω, L= 7.40E-03H , and C=6.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

a) 9.380E-01 &rad;

b) 1.032E+00 &rad;

c) 1.135E+00 &rad;

d) 1.248E+00 &rad;

e) 1.373E+00 &rad;

12)

A parallel plate capacitor with a capicatnce C=6.50E-06 F whose plates have an area A=4.50E+03 m² and separation d=6.10E-03 m is connected via a swith to a 4 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.70E-05?

a) 1.456E+00 V

b) 1.602E+00 V

c) 1.762E+00 V

d) 1.938E+00 V

e) 2.132E+00 V

T11 E1

1) Calculate the electric field in a 12-gauge copper wire that is 99 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 3.604E-04 V/m

b) 3.964E-04 V/m

c) 4.360E-04 V/m

d) 4.796E-04 V/m

e) 5.276E-04 V/m

2) A given battery has a 12 V emf and an internal resistance of 0.107 Ω. If it is connected to a 0.814 Ω resistor what is the power dissipated by that load?

a) 1.382E+02 W

b) 1.520E+02 W

c) 1.672E+02 W

d) 1.839E+02 W

e) 2.023E+02 W

3)

A parallel plate capacitor with a capicatnce C=7.10E-06 F whose plates have an area A=5.10E+03 m² and separation d=6.40E-03 m is connected via a swith to a 54 Ω resistor and a battery of voltage V₀=83 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-03?

a) 6.111E+01 V

b) 6.722E+01 V

c) 7.395E+01 V

d) 8.134E+01 V

e) 8.947E+01 V

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.547 m and $B_{max}=\,$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.158 m that is centered on the axis with its plane perpendicular to the axis?

a) 1.751E+05 A

b) 1.927E+05 A

c) 2.119E+05 A

d) 2.331E+05 A

e) 2.564E+05 A

5) A long solenoid has a radius of 0.757 m and 90 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 30 s⁻¹.What is the induced electric fied at a distance 2.08 m from the axis at time t=0.0442 s ?

a) 6.527E-04 V/m

b) 7.180E-04 V/m

c) 7.898E-04 V/m

d) 8.688E-04 V/m

e) 9.556E-04 V/m

6) If a 26 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=21 V is x² + y² + z² = R², where R=

a) 8.360E+00 m

b) 9.196E+00 m

c) 1.012E+01 m

d) 1.113E+01 m

e) 1.224E+01 m

7) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}$

a) 7.054E+03 V·m

b) 7.759E+03 V·m

c) 8.535E+03 V·m

d) 9.388E+03 V·m

e) 1.033E+04 V·m

9) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.355 T magnetic field is directed 53° away from the wire?

a) 8.520E-01 N/m

b) 9.372E-01 N/m

c) 1.031E+00 N/m

d) 1.134E+00 N/m

e) 1.247E+00 N/m

10)

In the figure shown C₁=19.2 μF, C₂=2.24 μF, and C₃=4.93 μF. The voltage source provides ε=11.7 V. What is the energy stored in C₂?

a) 1.303E+01 μJ

b) 1.434E+01 μJ

c) 1.577E+01 μJ

d) 1.735E+01 μJ

e) 1.908E+01 μJ

11)

A long solenoid has a length 0.805 meters, radius 4.24 cm, and 536 turns. It surrounds coil of radius 8.5 meters and 16turns. If the current in the solenoid is changing at a rate of 278 A/s, what is the emf induced in the surounding coil?

a) 6.604E-02 V

b) 7.264E-02 V

c) 7.990E-02 V

d) 8.789E-02 V

e) 9.668E-02 V

12) The output of an ac generator connected to an RLC series combination has a frequency of 200 Hz and an amplitude of 0.14 V;. If R =3 Ω, L= 1.70E-03H , and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

a) 3.691E-01 &rad;

b) 4.060E-01 &rad;

c) 4.466E-01 &rad;

d) 4.913E-01 &rad;

e) 5.404E-01 &rad;

T11 E2

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.736 m and $B_{max}=\,$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.532 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.764E+05 A

b) 4.140E+05 A

c) 4.554E+05 A

d) 5.010E+05 A

e) 5.510E+05 A

2) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.761 T magnetic field is directed 44° away from the wire?

a) 2.527E+00 N/m

b) 2.780E+00 N/m

c) 3.058E+00 N/m

d) 3.364E+00 N/m

e) 3.700E+00 N/m

3) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

4) If a 21 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=94 V is x² + y² + z² = R², where R=

a) 1.371E+00 m

b) 1.509E+00 m

c) 1.659E+00 m

d) 1.825E+00 m

e) 2.008E+00 m

5) A given battery has a 12 V emf and an internal resistance of 0.107 Ω. If it is connected to a 0.814 Ω resistor what is the power dissipated by that load?

a) 1.382E+02 W

b) 1.520E+02 W

c) 1.672E+02 W

d) 1.839E+02 W

e) 2.023E+02 W

6) The output of an ac generator connected to an RLC series combination has a frequency of 480 Hz and an amplitude of 0.63 V;. If R =7 Ω, L= 3.80E-03H , and C=5.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

a) 9.972E-01 &rad;

b) 1.097E+00 &rad;

c) 1.207E+00 &rad;

d) 1.327E+00 &rad;

e) 1.460E+00 &rad;

7)

In the figure shown C₁=16.7 μF, C₂=2.26 μF, and C₃=4.53 μF. The voltage source provides ε=10.7 V. What is the energy stored in C₂?

a) 1.292E+01 μJ

b) 1.421E+01 μJ

c) 1.563E+01 μJ

d) 1.719E+01 μJ

e) 1.891E+01 μJ

8)

A parallel plate capacitor with a capicatnce C=7.50E-06 F whose plates have an area A=2.90E+03 m² and separation d=3.40E-03 m is connected via a swith to a 61 Ω resistor and a battery of voltage V₀=77 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.70E-03?

a) 5.131E+01 V

b) 5.644E+01 V

c) 6.209E+01 V

d) 6.830E+01 V

e) 7.513E+01 V

9) Calculate the electric field in a 12-gauge copper wire that is 18 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 1.117E-04 V/m

b) 1.228E-04 V/m

c) 1.351E-04 V/m

d) 1.486E-04 V/m

e) 1.635E-04 V/m

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}$

a) 1.997E+03 V·m

b) 2.197E+03 V·m

c) 2.417E+03 V·m

d) 2.659E+03 V·m

e) 2.924E+03 V·m

11)

A long solenoid has a length 0.89 meters, radius 3.01 cm, and 505 turns. It surrounds coil of radius 8.65 meters and 18turns. If the current in the solenoid is changing at a rate of 279 A/s, what is the emf induced in the surounding coil?

a) 2.646E-02 V

b) 2.911E-02 V

c) 3.202E-02 V

d) 3.522E-02 V

e) 3.874E-02 V

12) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 5 A and $\alpha =$ 28 s⁻¹.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?

a) 1.616E-04 V/m

b) 1.778E-04 V/m

c) 1.955E-04 V/m

d) 2.151E-04 V/m

e) 2.366E-04 V/m

T11 F0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=1e

,

q_{2}=-8e

, and

q_{3}=2e

?

a) 5.732E-15 N

b) 6.305E-15 N

c) 6.936E-15 N

d) 7.629E-15 N

e) 8.392E-15 N

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
${\vec {E}}=4y^{1.4}{\hat {i}}+2x^{2.3}{\hat {j}}+4y^{2.3}{\hat {k}}$

a) 2.694E+03 V·m

b) 2.963E+03 V·m

c) 3.259E+03 V·m

d) 3.585E+03 V·m

e) 3.944E+03 V·m

3)

An electron gun has parallel plates separated by 3.68 cm and gives electrons 54 keV of energy. What force would the field between the plates exert on a 0.181 μC charge that gets between the plates?

a) 2.656E-01 N

b) 2.922E-01 N

c) 3.214E-01 N

d) 3.535E-01 N

e) 3.889E-01 N

4)

What is the net capacitance if C₁=2.3 μF, C₂=2.84 μF, and C₃=3.41 μF in the configuration shown?

a) 4.255E+00 μF

b) 4.681E+00 μF

c) 5.149E+00 μF

d) 5.664E+00 μF

e) 6.230E+00 μF

5) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?

a) 2.240E+02 A

b) 2.464E+02 A

c) 2.711E+02 A

d) 2.982E+02 A

e) 3.280E+02 A

6)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 558 V. If the combined external and internal resistance is 198 &Omega and the capacitance is 80 mF, how long will it take for the capacitor's voltage to reach 345.0 V?

a) 1.146E+01 s

b) 1.261E+01 s

c) 1.387E+01 s

d) 1.525E+01 s

e) 1.678E+01 s

7) A circular current loop of radius 2.84 cm carries a current of 3.01 mA. What is the magnitude of the torque if the dipole is oriented at 63 ° to a uniform magnetic fied of 0.174 T?

a) 1.075E-06 N m

b) 1.182E-06 N m

c) 1.301E-06 N m

d) 1.431E-06 N m

e) 1.574E-06 N m

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.852 m and $B_{max}=\,$ 0.476 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.212 m that is centered on the axis with its plane perpendicular to the axis?

a) 1.502E+05 A

b) 1.652E+05 A

c) 1.817E+05 A

d) 1.999E+05 A

e) 2.199E+05 A

9) A long solenoid has a radius of 0.682 m and 38 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 2 A and $\alpha =$ 27 s⁻¹.What is the induced electric fied at a distance 0.16 m from the axis at time t=0.0736 s ?

a) 2.571E-05 V/m

b) 2.828E-05 V/m

c) 3.111E-05 V/m

d) 3.422E-05 V/m

e) 3.764E-05 V/m

10) A washer has an inner diameter of 2.3 cm and an outer diamter of 4.44 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.31mm$ , and $n=2.66$ . What is the volume of the washer?

a) 1.089E+00 cm³

b) 1.198E+00 cm³

c) 1.318E+00 cm³

d) 1.449E+00 cm³

e) 1.594E+00 cm³

11) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.88 V. The resistance, inductance, and capacitance are R =7 Ω, L= 8.00E-03H , and C=5.50E-04 F, respectively. What is the amplitude of the current?

a) 1.143E-01 A

b) 1.257E-01 A

c) 1.383E-01 A

d) 1.521E-01 A

e) 1.673E-01 A

12) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m²? The average power output of the Sun is 3.80E+26 W.

a) 2.673E-07 N

b) 2.940E-07 N

c) 3.234E-07 N

d) 3.558E-07 N

e) 3.913E-07 N

T11 F1

1) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.82 V. The resistance, inductance, and capacitance are R =8 Ω, L= 6.40E-03H , and C=5.70E-04 F, respectively. What is the amplitude of the current?

a) 7.701E-02 A

b) 8.471E-02 A

c) 9.318E-02 A

d) 1.025E-01 A

e) 1.128E-01 A

2) What is the average current involved when a truck battery sets in motion 659 C of charge in 5.48 s while starting an engine?

a) 8.214E+01 A

b) 9.035E+01 A

c) 9.938E+01 A

d) 1.093E+02 A

e) 1.203E+02 A

3)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=1e

,

q_{2}=-7e

, and

q_{3}=2e

?

a) 3.391E-14 N

b) 3.731E-14 N

c) 4.104E-14 N

d) 4.514E-14 N

e) 4.965E-14 N

4) A circular current loop of radius 3.04 cm carries a current of 1.94 mA. What is the magnitude of the torque if the dipole is oriented at 50 ° to a uniform magnetic fied of 0.193 T?

a) 6.257E-07 N m

b) 6.882E-07 N m

c) 7.570E-07 N m

d) 8.327E-07 N m

e) 9.160E-07 N m

5) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.407 m and $B_{max}=\,$ 0.605 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.196 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.583E+05 A

b) 3.941E+05 A

c) 4.335E+05 A

d) 4.769E+05 A

e) 5.246E+05 A

6) What is the radiation force on an object that is 2.50E+11 m away from the sun and has cross-sectional area of 0.045 m²? The average power output of the Sun is 3.80E+26 W.

a) 1.200E-07 N

b) 1.320E-07 N

c) 1.452E-07 N

d) 1.598E-07 N

e) 1.757E-07 N

7)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 543 V. If the combined external and internal resistance is 201 &Omega and the capacitance is 82 mF, how long will it take for the capacitor's voltage to reach 281.0 V?

a) 9.024E+00 s

b) 9.927E+00 s

c) 1.092E+01 s

d) 1.201E+01 s

e) 1.321E+01 s

8) A washer has an inner diameter of 2.62 cm and an outer diamter of 4.79 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.08mm$ , and $n=2.68$ . What is the volume of the washer?

a) 1.056E+00 cm³

b) 1.161E+00 cm³

c) 1.278E+00 cm³

d) 1.405E+00 cm³

e) 1.546E+00 cm³

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}$

a) 3.429E+03 V·m

b) 3.771E+03 V·m

c) 4.149E+03 V·m

d) 4.564E+03 V·m

e) 5.020E+03 V·m

10)

An electron gun has parallel plates separated by 3.35 cm and gives electrons 26 keV of energy. What force would the field between the plates exert on a 0.682 μC charge that gets between the plates?

a) 3.977E-01 N

b) 4.374E-01 N

c) 4.812E-01 N

d) 5.293E-01 N

e) 5.822E-01 N

11) A long solenoid has a radius of 0.749 m and 62 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 9 A and $\alpha =$ 25 s⁻¹.What is the induced electric fied at a distance 0.139 m from the axis at time t=0.071 s ?

a) 2.065E-04 V/m

b) 2.271E-04 V/m

c) 2.499E-04 V/m

d) 2.748E-04 V/m

e) 3.023E-04 V/m

12)

What is the net capacitance if C₁=2.3 μF, C₂=2.84 μF, and C₃=3.41 μF in the configuration shown?

a) 4.255E+00 μF

b) 4.681E+00 μF

c) 5.149E+00 μF

d) 5.664E+00 μF

e) 6.230E+00 μF

T11 F2

1) A long solenoid has a radius of 0.603 m and 51 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 2 A and $\alpha =$ 26 s⁻¹.What is the induced electric fied at a distance 0.105 m from the axis at time t=0.0659 s ?

a) 2.154E-05 V/m

b) 2.369E-05 V/m

c) 2.606E-05 V/m

d) 2.867E-05 V/m

e) 3.154E-05 V/m

2)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=3e

?

a) 1.473E-14 N

b) 1.620E-14 N

c) 1.782E-14 N

d) 1.960E-14 N

e) 2.156E-14 N

3)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 554 V. If the combined external and internal resistance is 228 &Omega and the capacitance is 93 mF, how long will it take for the capacitor's voltage to reach 450.0 V?

a) 3.224E+01 s

b) 3.547E+01 s

c) 3.902E+01 s

d) 4.292E+01 s

e) 4.721E+01 s

4) A circular current loop of radius 1.56 cm carries a current of 2.57 mA. What is the magnitude of the torque if the dipole is oriented at 38 ° to a uniform magnetic fied of 0.79 T?

a) 7.898E-07 N m

b) 8.688E-07 N m

c) 9.557E-07 N m

d) 1.051E-06 N m

e) 1.156E-06 N m

5)

What is the net capacitance if C₁=4.7 μF, C₂=4.82 μF, and C₃=3.61 μF in the configuration shown?

a) 5.445E+00 μF

b) 5.990E+00 μF

c) 6.589E+00 μF

d) 7.247E+00 μF

e) 7.972E+00 μF

6) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.096 m²? The average power output of the Sun is 3.80E+26 W.

a) 4.373E-08 N

b) 4.810E-08 N

c) 5.291E-08 N

d) 5.820E-08 N

e) 6.402E-08 N

7)

An electron gun has parallel plates separated by 5.31 cm and gives electrons 41 keV of energy. What force would the field between the plates exert on a 0.368 μC charge that gets between the plates?

a) 2.348E-01 N

b) 2.583E-01 N

c) 2.841E-01 N

d) 3.126E-01 N

e) 3.438E-01 N

8) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.75 V. The resistance, inductance, and capacitance are R =5 Ω, L= 9.90E-03H , and C=6.80E-04 F, respectively. What is the amplitude of the current?

a) 1.240E-01 A

b) 1.364E-01 A

c) 1.500E-01 A

d) 1.650E-01 A

e) 1.815E-01 A

9) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?

a) 2.240E+02 A

b) 2.464E+02 A

c) 2.711E+02 A

d) 2.982E+02 A

e) 3.280E+02 A

10) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.62 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.66mm$ , and $n=2.61$ . What is the volume of the washer?

a) 6.960E-01 cm³

b) 7.656E-01 cm³

c) 8.421E-01 cm³

d) 9.264E-01 cm³

e) 1.019E+00 cm³

11) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}$

a) 9.952E+03 V·m

b) 1.095E+04 V·m

c) 1.204E+04 V·m

d) 1.325E+04 V·m

e) 1.457E+04 V·m

12) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.619 m and $B_{max}=\,$ 0.215 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.351 m that is centered on the axis with its plane perpendicular to the axis?

a) 2.534E+05 A

b) 2.787E+05 A

c) 3.066E+05 A

d) 3.373E+05 A

e) 3.710E+05 A

T11 G0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-9e

, and

q_{3}=6e

?

a) 5.767E+01 degrees

b) 6.343E+01 degrees

c) 6.978E+01 degrees

d) 7.676E+01 degrees

e) 8.443E+01 degrees

2) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=2 nC·m^-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

a) 3.821E+02 N/C

b) 4.203E+02 N/C

c) 4.624E+02 N/C

d) 5.086E+02 N/C

e) 5.594E+02 N/C

3) If a 19 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=73 V is x² + y² + z² = R², where R=

a) 1.598E+00 m

b) 1.757E+00 m

c) 1.933E+00 m

d) 2.127E+00 m

e) 2.339E+00 m

4)

In the figure shown C₁=17.7 μF, C₂=2.48 μF, and C₃=4.68 μF. The voltage source provides ε=12.7 V. What is the energy stored in C₂?

a) 2.242E+01 μJ

b) 2.467E+01 μJ

c) 2.713E+01 μJ

d) 2.985E+01 μJ

e) 3.283E+01 μJ

5) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.58 Ω at a temperature of 24°C and that the temperature coefficient of expansion is 5.520E-03 (°C)⁻¹). What is the resistance at a temperature of 349 °C?

a) 9.526E+00 Ω

b) 1.000E+01 Ω

c) 1.050E+01 Ω

d) 1.103E+01 Ω

e) 1.158E+01 Ω

6)

Two sources of emf ε₁=31.0 V, and ε₂=10.0 V are oriented as shownin the circuit. The resistances are R₁=4.22 kΩ and R₂=1.37 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.32 mA and I₄=1.03 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

a) 2.290E+00 mA

b) 2.519E+00 mA

c) 2.771E+00 mA

d) 3.048E+00 mA

e) 3.353E+00 mA

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 8.55 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(1.96 i + 1.68 j + 6.92 k) x 10⁴ m/s?

a) 4.179E-14 N

b) 4.596E-14 N

c) 5.056E-14 N

d) 5.562E-14 N

e) 6.118E-14 N

8) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?

a) 1.283E-10 N/m

b) 1.411E-10 N/m

c) 1.552E-10 N/m

d) 1.708E-10 N/m

e) 1.878E-10 N/m

9) A recangular coil with an area of 0.449 m² and 20 turns is placed in a uniform magnetic field of 3.58 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.990E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 66 s?

a) 7.734E+04 V

b) 8.507E+04 V

c) 9.358E+04 V

d) 1.029E+05 V

e) 1.132E+05 V

10)

A long solenoid has a length 0.667 meters, radius 4.41 cm, and 517 turns. It surrounds coil of radius 9.18 meters and 9turns. If the current in the solenoid is changing at a rate of 296 A/s, what is the emf induced in the surounding coil?

a) 4.116E-02 V

b) 4.528E-02 V

c) 4.981E-02 V

d) 5.479E-02 V

e) 6.027E-02 V

11) The output of an ac generator connected to an RLC series combination has a frequency of 8.00E+04 Hz and an amplitude of 2 V. If R =7 Ω, L= 4.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

a) 1.047E-04 Watts

b) 1.151E-04 Watts

c) 1.267E-04 Watts

d) 1.393E-04 Watts

e) 1.533E-04 Watts

12)

A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=3.60E+03 m² and separation d=3.50E-03 m is connected via a swith to a 28 Ω resistor and a battery of voltage V₀=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.00E-04?

a) 3.751E+03 V/m

b) 4.126E+03 V/m

c) 4.539E+03 V/m

d) 4.993E+03 V/m

e) 5.492E+03 V/m

T11 G1

1)

Two sources of emf ε₁=20.6 V, and ε₂=9.53 V are oriented as shownin the circuit. The resistances are R₁=5.46 kΩ and R₂=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.5 mA and I₄=0.415 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

a) 1.085E+00 mA

b) 1.194E+00 mA

c) 1.313E+00 mA

d) 1.444E+00 mA

e) 1.589E+00 mA

2) The output of an ac generator connected to an RLC series combination has a frequency of 6.00E+04 Hz and an amplitude of 2 V. If R =3 Ω, L= 7.20E-03H , and C=6.50E-06 F, what is the rms power transferred to the resistor?

a) 2.222E-05 Watts

b) 2.444E-05 Watts

c) 2.689E-05 Watts

d) 2.958E-05 Watts

e) 3.253E-05 Watts

3) A recangular coil with an area of 0.412 m² and 18 turns is placed in a uniform magnetic field of 3.81 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 2.120E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 79 s?

a) 4.465E+04 V

b) 4.912E+04 V

c) 5.403E+04 V

d) 5.943E+04 V

e) 6.538E+04 V

4)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=1e

,

q_{2}=-8e

, and

q_{3}=3e

?

a) 3.629E+01 degrees

b) 3.992E+01 degrees

c) 4.391E+01 degrees

d) 4.830E+01 degrees

e) 5.313E+01 degrees

5) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=2 nC·m^-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.123E+02 N/C

b) 1.235E+02 N/C

c) 1.358E+02 N/C

d) 1.494E+02 N/C

e) 1.644E+02 N/C

6)

A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=4.80E+03 m² and separation d=5.80E-03 m is connected via a swith to a 93 Ω resistor and a battery of voltage V₀=48 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=9.00E-04?

a) 5.023E+03 V/m

b) 5.525E+03 V/m

c) 6.078E+03 V/m

d) 6.685E+03 V/m

e) 7.354E+03 V/m

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.61 Ω at a temperature of 92°C and that the temperature coefficient of expansion is 4.260E-03 (°C)⁻¹). What is the resistance at a temperature of 422 °C?

a) 6.279E+00 Ω

b) 6.593E+00 Ω

c) 6.923E+00 Ω

d) 7.269E+00 Ω

e) 7.632E+00 Ω

8)

A long solenoid has a length 0.864 meters, radius 3.37 cm, and 522 turns. It surrounds coil of radius 7.87 meters and 13turns. If the current in the solenoid is changing at a rate of 290 A/s, what is the emf induced in the surounding coil?

a) 2.917E-02 V

b) 3.208E-02 V

c) 3.529E-02 V

d) 3.882E-02 V

e) 4.270E-02 V

9) If a 26 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=21 V is x² + y² + z² = R², where R=

a) 8.360E+00 m

b) 9.196E+00 m

c) 1.012E+01 m

d) 1.113E+01 m

e) 1.224E+01 m

10) Two parallel wires each carry a 7.68 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.36 cm, 1.58 cm), while the other is located at (5.29 cm, 5.18 cm). What is the force per unit length between the wires?

a) 1.973E-10 N/m

b) 2.170E-10 N/m

c) 2.387E-10 N/m

d) 2.625E-10 N/m

e) 2.888E-10 N/m

11) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.13 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(5.64 i + 1.93 j + 8.71 k) x 10⁴ m/s?

a) 1.757E-14 N

b) 1.933E-14 N

c) 2.126E-14 N

d) 2.339E-14 N

e) 2.573E-14 N

12)

In the figure shown C₁=15.7 μF, C₂=2.87 μF, and C₃=5.46 μF. The voltage source provides ε=5.38 V. What is the energy stored in C₂?

a) 6.890E+00 μJ

b) 7.579E+00 μJ

c) 8.337E+00 μJ

d) 9.171E+00 μJ

e) 1.009E+01 μJ

T11 G2

1) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.89 Ω at a temperature of 89°C and that the temperature coefficient of expansion is 5.340E-03 (°C)⁻¹). What is the resistance at a temperature of 566 °C?

a) 9.763E+00 Ω

b) 1.025E+01 Ω

c) 1.076E+01 Ω

d) 1.130E+01 Ω

e) 1.187E+01 Ω

2)

Two sources of emf ε₁=31.0 V, and ε₂=10.0 V are oriented as shownin the circuit. The resistances are R₁=4.22 kΩ and R₂=1.37 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.32 mA and I₄=1.03 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

a) 2.290E+00 mA

b) 2.519E+00 mA

c) 2.771E+00 mA

d) 3.048E+00 mA

e) 3.353E+00 mA

3)

A long solenoid has a length 0.822 meters, radius 4.37 cm, and 515 turns. It surrounds coil of radius 6.12 meters and 14turns. If the current in the solenoid is changing at a rate of 118 A/s, what is the emf induced in the surounding coil?

a) 2.229E-02 V

b) 2.451E-02 V

c) 2.697E-02 V

d) 2.966E-02 V

e) 3.263E-02 V

4)

A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=5.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 98 Ω resistor and a battery of voltage V₀=67 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.80E-03?

a) 5.050E+03 V/m

b) 5.555E+03 V/m

c) 6.111E+03 V/m

d) 6.722E+03 V/m

e) 7.394E+03 V/m

5) Two parallel wires each carry a 2.58 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.79 cm, 1.03 cm), while the other is located at (5.64 cm, 5.12 cm). What is the force per unit length between the wires?

a) 2.634E-11 N/m

b) 2.897E-11 N/m

c) 3.187E-11 N/m

d) 3.506E-11 N/m

e) 3.856E-11 N/m

6) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 6.96 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(7.01 i + 5.35 j + 2.07 k) x 10⁴ m/s?

a) 1.192E-13 N

b) 1.311E-13 N

c) 1.442E-13 N

d) 1.586E-13 N

e) 1.745E-13 N

7) If a 20 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=70 V is x² + y² + z² = R², where R=

a) 1.754E+00 m

b) 1.929E+00 m

c) 2.122E+00 m

d) 2.334E+00 m

e) 2.568E+00 m

8) A recangular coil with an area of 0.178 m² and 17 turns is placed in a uniform magnetic field of 2.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.380E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 45 s?

a) 1.068E+04 V

b) 1.175E+04 V

c) 1.293E+04 V

d) 1.422E+04 V

e) 1.564E+04 V

9)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=5e

?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

10) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 6.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

a) 2.007E-03 Watts

b) 2.208E-03 Watts

c) 2.429E-03 Watts

d) 2.672E-03 Watts

e) 2.939E-03 Watts

11)

In the figure shown C₁=16.3 μF, C₂=2.17 μF, and C₃=4.67 μF. The voltage source provides ε=8.35 V. What is the energy stored in C₂?

a) 8.718E+00 μJ

b) 9.589E+00 μJ

c) 1.055E+01 μJ

d) 1.160E+01 μJ

e) 1.276E+01 μJ

12) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=2 nC·m^-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 6.411E+02 N/C

b) 7.052E+02 N/C

c) 7.757E+02 N/C

d) 8.533E+02 N/C

e) 9.386E+02 N/C

T11 H0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=4e

?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.7 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.3 m, z=z₀=1.8 m, and z=z₁=4.9 m. The surfaces in the yz plane each have area 8.1m². Those in the xy plane have area 7.0m² ,and those in the zx plane have area 8.4m². An electric field has the xyz components (0, 9.2, 7.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.364E+01 N·m²/C

b) 7.000E+01 N·m²/C

c) 7.700E+01 N·m²/C

d) 8.470E+01 N·m²/C

e) 9.317E+01 N·m²/C

3)

A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.29 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.33 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.

a) 4.324E+02 V

b) 4.757E+02 V

c) 5.232E+02 V

d) 5.755E+02 V

e) 6.331E+02 V

4)

What is the net capacitance if C₁=3.13 μF, C₂=2.28 μF, and C₃=2.59 μF in the configuration shown?

a) 3.231E+00 μF

b) 3.554E+00 μF

c) 3.909E+00 μF

d) 4.300E+00 μF

e) 4.730E+00 μF

5) Calculate the drift speed of electrons in a copper wire with a diameter of 5.33 mm carrying a 5.1 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

a) 1.711E-05 m/s

b) 1.882E-05 m/s

c) 2.070E-05 m/s

d) 2.277E-05 m/s

e) 2.505E-05 m/s

6)

The resistances in the figure shown are R₁= 2.73 Ω, R₂= 1.4 Ω, and R₂= 2.35 Ω. V₁ and V₃ are text 0.549 V and 1.27 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.584 V. What is the absolute value of the current through R₁?

a) 1.213E-01 A

b) 1.334E-01 A

c) 1.468E-01 A

d) 1.614E-01 A

e) 1.776E-01 A

7)

The silver ribbon shown are a=3.47 cm, b=2.98 cm, and c= 0.681 cm. The current carries a current of 289 A and it lies in a uniform magnetic field of 3.37 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

a) 1.375E-05 V

b) 1.513E-05 V

c) 1.664E-05 V

d) 1.831E-05 V

e) 2.014E-05 V

8) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 1.791E-05 T

b) 1.970E-05 T

c) 2.167E-05 T

d) 2.384E-05 T

e) 2.622E-05 T

9) A long solenoid has a radius of 0.521 m and 46 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 1 A and $\alpha =$ 30 s⁻¹.What is the induced electric fied at a distance 2.42 m from the axis at time t=0.0449 s ?

a) 2.529E-05 V/m

b) 2.782E-05 V/m

c) 3.060E-05 V/m

d) 3.366E-05 V/m

e) 3.703E-05 V/m

10)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =3.56 s if ε = 6.14 V , R = 7.96 Ω, and L = 6.65 H?

a) 5.281E-01 V

b) 6.337E-01 V

c) 7.605E-01 V

d) 9.126E-01 V

e) 1.095E+00 V

11) An ac generator produces an emf of amplitude 98 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a 2 mF capacitor?

a) 1.232E-01 A

b) 1.355E-01 A

c) 1.490E-01 A

d) 1.639E-01 A

e) 1.803E-01 A

12)

A parallel plate capacitor with a capicatnce C=8.90E-06 F whose plates have an area A=6.90E+03 m² and separation d=6.90E-03 m is connected via a swith to a 89 Ω resistor and a battery of voltage V₀=89 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-03?

a) 6.595E+01 V

b) 7.255E+01 V

c) 7.980E+01 V

d) 8.778E+01 V

e) 9.656E+01 V

T11 H1

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.26 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.494E-05 T

b) 1.644E-05 T

c) 1.808E-05 T

d) 1.989E-05 T

e) 2.188E-05 T

2)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =5.67 s if ε = 5.58 V , R = 3.81 Ω, and L = 3.85 H?

a) 7.037E-01 V

b) 8.444E-01 V

c) 1.013E+00 V

d) 1.216E+00 V

e) 1.459E+00 V

3)

The silver ribbon shown are a=3.68 cm, b=2.66 cm, and c= 0.505 cm. The current carries a current of 113 A and it lies in a uniform magnetic field of 3.12 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

a) 6.104E-06 V

b) 6.714E-06 V

c) 7.385E-06 V

d) 8.124E-06 V

e) 8.936E-06 V

4)

The resistances in the figure shown are R₁= 1.81 Ω, R₂= 1.18 Ω, and R₂= 2.62 Ω. V₁ and V₃ are text 0.628 V and 2.54 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.748 V. What is the absolute value of the current through R₁?

a) 1.552E-01 A

b) 1.707E-01 A

c) 1.878E-01 A

d) 2.065E-01 A

e) 2.272E-01 A

5)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=5e

?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

6)

A parallel plate capacitor with a capicatnce C=7.10E-06 F whose plates have an area A=5.10E+03 m² and separation d=6.40E-03 m is connected via a swith to a 54 Ω resistor and a battery of voltage V₀=83 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-03?

a) 6.111E+01 V

b) 6.722E+01 V

c) 7.395E+01 V

d) 8.134E+01 V

e) 8.947E+01 V

7)

A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.08 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.

a) 7.017E+02 V

b) 7.718E+02 V

c) 8.490E+02 V

d) 9.339E+02 V

e) 1.027E+03 V

8)

What is the net capacitance if C₁=3.13 μF, C₂=2.28 μF, and C₃=2.59 μF in the configuration shown?

a) 3.231E+00 μF

b) 3.554E+00 μF

c) 3.909E+00 μF

d) 4.300E+00 μF

e) 4.730E+00 μF

9) Calculate the drift speed of electrons in a copper wire with a diameter of 5.82 mm carrying a 9.11 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

a) 1.926E-05 m/s

b) 2.118E-05 m/s

c) 2.330E-05 m/s

d) 2.563E-05 m/s

e) 2.819E-05 m/s

10) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

a) 1.170E+00 A

b) 1.287E+00 A

c) 1.415E+00 A

d) 1.557E+00 A

e) 1.713E+00 A

11)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.1 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.2 m, z=z₀=1.1 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 8.5m². Those in the xy plane have area 2.8m² ,and those in the zx plane have area 3.7m². An electric field has the xyz components (0, 7.4, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 2.079E+01 N·m²/C

b) 2.287E+01 N·m²/C

c) 2.516E+01 N·m²/C

d) 2.768E+01 N·m²/C

e) 3.044E+01 N·m²/C

12) A long solenoid has a radius of 0.306 m and 98 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 6 A and $\alpha =$ 22 s⁻¹.What is the induced electric fied at a distance 2.52 m from the axis at time t=0.0246 s ?

a) 1.598E-04 V/m

b) 1.758E-04 V/m

c) 1.934E-04 V/m

d) 2.127E-04 V/m

e) 2.340E-04 V/m

T11 H2

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.03 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 1.720E-05 T

b) 1.892E-05 T

c) 2.081E-05 T

d) 2.289E-05 T

e) 2.518E-05 T

2) An ac generator produces an emf of amplitude 90 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 16 mF capacitor?

a) 4.351E-01 A

b) 4.786E-01 A

c) 5.264E-01 A

d) 5.791E-01 A

e) 6.370E-01 A

3)

What is the net capacitance if C₁=3.06 μF, C₂=3.09 μF, and C₃=2.48 μF in the configuration shown?

a) 3.018E+00 μF

b) 3.320E+00 μF

c) 3.652E+00 μF

d) 4.017E+00 μF

e) 4.419E+00 μF

4)

The silver ribbon shown are a=3.55 cm, b=2.99 cm, and c= 1.03 cm. The current carries a current of 135 A and it lies in a uniform magnetic field of 1.26 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

a) 1.193E-06 V

b) 1.313E-06 V

c) 1.444E-06 V

d) 1.588E-06 V

e) 1.747E-06 V

5) Calculate the drift speed of electrons in a copper wire with a diameter of 3.17 mm carrying a 12.0 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

a) 1.138E-04 m/s

b) 1.252E-04 m/s

c) 1.377E-04 m/s

d) 1.515E-04 m/s

e) 1.666E-04 m/s

6)

The resistances in the figure shown are R₁= 2.67 Ω, R₂= 1.78 Ω, and R₂= 3.63 Ω. V₁ and V₃ are text 0.448 V and 2.29 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.656 V. What is the absolute value of the current through R₁?

a) 9.287E-02 A

b) 1.022E-01 A

c) 1.124E-01 A

d) 1.236E-01 A

e) 1.360E-01 A

7)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 23 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?

a) 2.877E+00 V

b) 3.165E+00 V

c) 3.481E+00 V

d) 3.829E+00 V

e) 4.212E+00 V

8) A long solenoid has a radius of 0.306 m and 98 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 6 A and $\alpha =$ 22 s⁻¹.What is the induced electric fied at a distance 2.52 m from the axis at time t=0.0246 s ?

a) 1.598E-04 V/m

b) 1.758E-04 V/m

c) 1.934E-04 V/m

d) 2.127E-04 V/m

e) 2.340E-04 V/m

9)

A diploe has a charge magnitude of q=4 nC and a separation distance of d=4.16 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.

a) 3.070E+02 V

b) 3.377E+02 V

c) 3.715E+02 V

d) 4.086E+02 V

e) 4.495E+02 V

10)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.6 m. The other four surfaces are rectangles in y=y₀=1.6 m, y=y₁=5.6 m, z=z₀=1.8 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 10.0m². Those in the xy plane have area 6.4m² ,and those in the zx plane have area 4.2m². An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 1.891E+01 N·m²/C

b) 2.080E+01 N·m²/C

c) 2.288E+01 N·m²/C

d) 2.517E+01 N·m²/C

e) 2.768E+01 N·m²/C

11)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=5e

?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

12)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =20.1 s if ε = 5.77 V , R = 1.38 Ω, and L = 5.45 H?

a) 3.463E+00 V

b) 4.156E+00 V

c) 4.987E+00 V

d) 5.984E+00 V

e) 7.181E+00 V

T11 I0

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C

b) 3.771E+01 N/C

c) 4.148E+01 N/C

d) 4.563E+01 N/C

e) 5.020E+01 N/C

2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.7 (r≤R) where a=3 nC·m^-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 1.390E+03 N/C

b) 1.530E+03 N/C

c) 1.682E+03 N/C

d) 1.851E+03 N/C

e) 2.036E+03 N/C

3) Two large parallel conducting plates are separated by 6.67 mm. Equal and opposite surface charges of 7.080E-07 C/m² exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 60 V?

a) 6.525E-01 mm

b) 7.504E-01 mm

c) 8.629E-01 mm

d) 9.923E-01 mm

e) 1.141E+00 mm

4)

What is the net capacitance if C₁=2.25 μF, C₂=4.16 μF, and C₃=2.49 μF in the configuration shown?

a) 2.698E+00 μF

b) 2.968E+00 μF

c) 3.265E+00 μF

d) 3.591E+00 μF

e) 3.950E+00 μF

5) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 4.957E-02 Ω

b) 5.453E-02 Ω

c) 5.998E-02 Ω

d) 6.598E-02 Ω

e) 7.258E-02 Ω

6) A given battery has a 12 V emf and an internal resistance of 0.0984 Ω. If it is connected to a 0.485 Ω resistor what is the power dissipated by that load?

a) 2.052E+02 W

b) 2.257E+02 W

c) 2.483E+02 W

d) 2.731E+02 W

e) 3.004E+02 W

7) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.449 m and a magneticfield of 0.81 T. What is their maximum kinetic energy?

a) 5.795E+00 MeV

b) 6.374E+00 MeV

c) 7.012E+00 MeV

d) 7.713E+00 MeV

e) 8.484E+00 MeV

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.44 kA, I₂=1.1 kA, and I₃=1.99 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 1.017E-03 T-m

b) 1.118E-03 T-m

c) 1.230E-03 T-m

d) 1.353E-03 T-m

e) 1.489E-03 T-m

9) Calculate the motional emf induced along a 34.3 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.780E-05 Tesla magnetic field.

a) 8.802E+03 V

b) 9.682E+03 V

c) 1.065E+04 V

d) 1.172E+04 V

e) 1.289E+04 V

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.56% of its maximum value if ε = 4.22 V , R = 1.89 Ω, and L = 6.57 H?

a) -4.939E+00 s

b) -5.433E+00 s

c) -5.976E+00 s

d) -6.574E+00 s

e) -7.231E+00 s

11) An ac generator produces an emf of amplitude 5 V at a frequency of 52 Hz. What is the maximum amplitude of the current if the generator is connected to a 49 mF inductor?

a) 2.839E-01 A

b) 3.123E-01 A

c) 3.435E-01 A

d) 3.779E-01 A

e) 4.157E-01 A

12)

A parallel plate capacitor with a capicatnce C=6.20E-06 F whose plates have an area A=5.30E+03 m² and separation d=7.50E-03 m is connected via a swith to a 95 Ω resistor and a battery of voltage V₀=15 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=9.20E-04?

a) 8.097E+00 V

b) 8.906E+00 V

c) 9.797E+00 V

d) 1.078E+01 V

e) 1.185E+01 V

T11 I1

1) Calculate the resistance of a 12-gauge copper wire that is 59 m long and carries a current of 26 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 2.995E-01 Ω

b) 3.294E-01 Ω

c) 3.623E-01 Ω

d) 3.986E-01 Ω

e) 4.384E-01 Ω

2) Calculate the motional emf induced along a 30.3 km conductor moving at an orbital speed of 7.76 km/s perpendicular to Earth's 5.100E-05 Tesla magnetic field.

a) 1.090E+04 V

b) 1.199E+04 V

c) 1.319E+04 V

d) 1.451E+04 V

e) 1.596E+04 V

3)

A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m² and separation d=3.40E-03 m is connected via a swith to a 15 Ω resistor and a battery of voltage V₀=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?

a) 7.693E+01 V

b) 8.463E+01 V

c) 9.309E+01 V

d) 1.024E+02 V

e) 1.126E+02 V

4) A given battery has a 13 V emf and an internal resistance of 0.106 Ω. If it is connected to a 0.752 Ω resistor what is the power dissipated by that load?

a) 1.569E+02 W

b) 1.726E+02 W

c) 1.899E+02 W

d) 2.089E+02 W

e) 2.298E+02 W

5) Two large parallel conducting plates are separated by 7.93 mm. Equal and opposite surface charges of 7.720E-07 C/m² exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 77 V?

a) 6.678E-01 mm

b) 7.679E-01 mm

c) 8.831E-01 mm

d) 1.016E+00 mm

e) 1.168E+00 mm

6)

What is the net capacitance if C₁=3.97 μF, C₂=3.51 μF, and C₃=2.18 μF in the configuration shown?

a) 3.038E+00 μF

b) 3.341E+00 μF

c) 3.675E+00 μF

d) 4.043E+00 μF

e) 4.447E+00 μF

7)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.43% of its maximum value if ε = 1.64 V , R = 8.3 Ω, and L = 1.61 H?

a) -4.120E-01 s

b) -4.532E-01 s

c) -4.985E-01 s

d) -5.483E-01 s

e) -6.031E-01 s

8) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.8 (r≤R) where a=2 nC·m^-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.079E+02 N/C

b) 2.287E+02 N/C

c) 2.516E+02 N/C

d) 2.767E+02 N/C

e) 3.044E+02 N/C

9) An ac generator produces an emf of amplitude 40 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a 52 mF inductor?

a) 7.783E-01 A

b) 8.561E-01 A

c) 9.417E-01 A

d) 1.036E+00 A

e) 1.140E+00 A

10)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.48 kA, I₂=1.47 kA, and I₃=2.6 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 1.420E-03 T-m

b) 1.562E-03 T-m

c) 1.718E-03 T-m

d) 1.890E-03 T-m

e) 2.079E-03 T-m

11) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.409 m and a magneticfield of 1.27 T. What is their maximum kinetic energy?

a) 8.881E+00 MeV

b) 9.769E+00 MeV

c) 1.075E+01 MeV

d) 1.182E+01 MeV

e) 1.300E+01 MeV

12) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C

b) 3.771E+01 N/C

c) 4.148E+01 N/C

d) 4.563E+01 N/C

e) 5.020E+01 N/C

T11 I2

1) An ac generator produces an emf of amplitude 70 V at a frequency of 63 Hz. What is the maximum amplitude of the current if the generator is connected to a 34 mF inductor?

a) 3.908E+00 A

b) 4.298E+00 A

c) 4.728E+00 A

d) 5.201E+00 A

e) 5.721E+00 A

2)

What is the net capacitance if C₁=3.13 μF, C₂=2.28 μF, and C₃=2.59 μF in the configuration shown?

a) 3.231E+00 μF

b) 3.554E+00 μF

c) 3.909E+00 μF

d) 4.300E+00 μF

e) 4.730E+00 μF

3) Calculate the resistance of a 12-gauge copper wire that is 14 m long and carries a current of 38 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 5.873E-02 Ω

b) 6.460E-02 Ω

c) 7.106E-02 Ω

d) 7.816E-02 Ω

e) 8.598E-02 Ω

4)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=5.60E+03 m² and separation d=5.10E-03 m is connected via a swith to a 15 Ω resistor and a battery of voltage V₀=54 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.50E-04?

a) 3.015E+01 V

b) 3.316E+01 V

c) 3.648E+01 V

d) 4.013E+01 V

e) 4.414E+01 V

5)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 2.01% of its maximum value if ε = 1.45 V , R = 4.4 Ω, and L = 2.36 H?

a) -8.659E-01 s

b) -9.525E-01 s

c) -1.048E+00 s

d) -1.153E+00 s

e) -1.268E+00 s

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 7.000E+01 N/C

b) 7.701E+01 N/C

c) 8.471E+01 N/C

d) 9.318E+01 N/C

e) 1.025E+02 N/C

7) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=3 nC·m^-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C

b) 4.177E+01 N/C

c) 4.595E+01 N/C

d) 5.054E+01 N/C

e) 5.560E+01 N/C

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.31 kA, I₂=1.08 kA, and I₃=1.77 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 7.166E-04 T-m

b) 7.883E-04 T-m

c) 8.671E-04 T-m

d) 9.538E-04 T-m

e) 1.049E-03 T-m

9) Calculate the motional emf induced along a 24.6 km conductor moving at an orbital speed of 7.89 km/s perpendicular to Earth's 5.180E-05 Tesla magnetic field.

a) 9.140E+03 V

b) 1.005E+04 V

c) 1.106E+04 V

d) 1.217E+04 V

e) 1.338E+04 V

10) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.378 m and a magneticfield of 0.835 T. What is their maximum kinetic energy?

a) 4.365E+00 MeV

b) 4.801E+00 MeV

c) 5.281E+00 MeV

d) 5.809E+00 MeV

e) 6.390E+00 MeV

11) A given battery has a 15 V emf and an internal resistance of 0.177 Ω. If it is connected to a 0.824 Ω resistor what is the power dissipated by that load?

a) 1.682E+02 W

b) 1.850E+02 W

c) 2.035E+02 W

d) 2.239E+02 W

e) 2.463E+02 W

12) Two large parallel conducting plates are separated by 7.77 mm. Equal and opposite surface charges of 7.310E-07 C/m² exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 73 V?

a) 5.814E-01 mm

b) 6.686E-01 mm

c) 7.689E-01 mm

d) 8.842E-01 mm

e) 1.017E+00 mm

T11 J0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-7e

, and

q_{3}=4e

?

a) 5.914E+01 degrees

b) 6.506E+01 degrees

c) 7.157E+01 degrees

d) 7.872E+01 degrees

e) 8.659E+01 degrees

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.3 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.2 m, z=z₀=1.8 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 8.5m² ,and those in the zx plane have area 6.0m². An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 4.730E+01 N·m²/C

b) 5.203E+01 N·m²/C

c) 5.723E+01 N·m²/C

d) 6.295E+01 N·m²/C

e) 6.925E+01 N·m²/C

3) A 12.0 V battery can move 30,000 C of charge. How many Joules does it deliver?

a) 3.273E+05 J

b) 3.600E+05 J

c) 3.960E+05 J

d) 4.356E+05 J

e) 4.792E+05 J

4)

What is the net capacitance if C₁=3.25 μF, C₂=4.87 μF, and C₃=2.19 μF in the configuration shown?

a) 4.139E+00 μF

b) 4.553E+00 μF

c) 5.008E+00 μF

d) 5.509E+00 μF

e) 6.060E+00 μF

5) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.06 Ω at a temperature of 80°C and that the temperature coefficient of expansion is 4.290E-03 (°C)⁻¹). What is the resistance at a temperature of 330 °C?

a) 1.196E+01 Ω

b) 1.256E+01 Ω

c) 1.319E+01 Ω

d) 1.385E+01 Ω

e) 1.454E+01 Ω

6)

The resistances in the figure shown are R₁= 1.54 Ω, R₂= 0.927 Ω, and R₂= 2.46 Ω. V₁ and V₃ are text 0.632 V and 2.12 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.586 V. What is the absolute value of the current through R₁?

a) 1.770E-01 A

b) 1.947E-01 A

c) 2.141E-01 A

d) 2.355E-01 A

e) 2.591E-01 A

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.78 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(1.43 i + 8.8 j + 4.16 k) x 10⁴ m/s?

a) 1.064E-13 N

b) 1.171E-13 N

c) 1.288E-13 N

d) 1.417E-13 N

e) 1.558E-13 N

8) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.86 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 3.416E-05 T

b) 3.758E-05 T

c) 4.133E-05 T

d) 4.547E-05 T

e) 5.001E-05 T

9) A long solenoid has a radius of 0.793 m and 45 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 2 A and $\alpha =$ 29 s⁻¹.What is the induced electric fied at a distance 0.216 m from the axis at time t=0.0208 s ?

a) 1.456E-04 V/m

b) 1.601E-04 V/m

c) 1.762E-04 V/m

d) 1.938E-04 V/m

e) 2.132E-04 V/m

10)

A long solenoid has a length 0.841 meters, radius 3.81 cm, and 516 turns. It surrounds coil of radius 9.2 meters and 11turns. If the current in the solenoid is changing at a rate of 190 A/s, what is the emf induced in the surounding coil?

a) 1.735E-02 V

b) 1.908E-02 V

c) 2.099E-02 V

d) 2.309E-02 V

e) 2.540E-02 V

11) An ac generator produces an emf of amplitude 4 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 19 mF capacitor?

a) 6.946E-02 A

b) 7.640E-02 A

c) 8.404E-02 A

d) 9.245E-02 A

e) 1.017E-01 A

12)

A parallel plate capacitor with a capicatnce C=6.60E-06 F whose plates have an area A=4.90E+03 m² and separation d=6.60E-03 m is connected via a swith to a 20 Ω resistor and a battery of voltage V₀=59 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.70E-04?

a) 8.138E-01 A

b) 8.952E-01 A

c) 9.847E-01 A

d) 1.083E+00 A

e) 1.191E+00 A

T11 J1

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.6 m. The other four surfaces are rectangles in y=y₀=1.2 m, y=y₁=5.9 m, z=z₀=1.9 m, and z=z₁=5.0 m. The surfaces in the yz plane each have area 15.0m². Those in the xy plane have area 12.0m² ,and those in the zx plane have area 8.1m². An electric field has the xyz components (0, 8.1, 6.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.529E+01 N·m²/C

b) 7.181E+01 N·m²/C

c) 7.900E+01 N·m²/C

d) 8.690E+01 N·m²/C

e) 9.559E+01 N·m²/C

2)

What is the net capacitance if C₁=3.97 μF, C₂=3.51 μF, and C₃=2.18 μF in the configuration shown?

a) 3.038E+00 μF

b) 3.341E+00 μF

c) 3.675E+00 μF

d) 4.043E+00 μF

e) 4.447E+00 μF

3)

A parallel plate capacitor with a capicatnce C=4.40E-06 F whose plates have an area A=1.80E+03 m² and separation d=3.60E-03 m is connected via a swith to a 87 Ω resistor and a battery of voltage V₀=61 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.70E-04?

a) 8.320E-02 A

b) 9.152E-02 A

c) 1.007E-01 A

d) 1.107E-01 A

e) 1.218E-01 A

4) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.13 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(5.64 i + 1.93 j + 8.71 k) x 10⁴ m/s?

a) 1.757E-14 N

b) 1.933E-14 N

c) 2.126E-14 N

d) 2.339E-14 N

e) 2.573E-14 N

5) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.66 mm from the center of a wire of radius 4 mm if the current is 1A?

a) 3.325E-05 T

b) 3.658E-05 T

c) 4.023E-05 T

d) 4.426E-05 T

e) 4.868E-05 T

6) A long solenoid has a radius of 0.596 m and 19 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 5 A and $\alpha =$ 29 s⁻¹.What is the induced electric fied at a distance 0.209 m from the axis at time t=0.0604 s ?

a) 6.277E-05 V/m

b) 6.904E-05 V/m

c) 7.595E-05 V/m

d) 8.354E-05 V/m

e) 9.190E-05 V/m

7) A 12.0 V battery can move 29,000 C of charge. How many Joules does it deliver?

a) 2.615E+05 J

b) 2.876E+05 J

c) 3.164E+05 J

d) 3.480E+05 J

e) 3.828E+05 J

8) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a 99 mF capacitor?

a) 1.644E+00 A

b) 1.808E+00 A

c) 1.989E+00 A

d) 2.188E+00 A

e) 2.407E+00 A

9)

The resistances in the figure shown are R₁= 2.74 Ω, R₂= 1.63 Ω, and R₂= 2.75 Ω. V₁ and V₃ are text 0.485 V and 2.01 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.555 V. What is the absolute value of the current through R₁?

a) 1.114E-01 A

b) 1.225E-01 A

c) 1.348E-01 A

d) 1.483E-01 A

e) 1.631E-01 A

10)

A long solenoid has a length 0.974 meters, radius 4.72 cm, and 587 turns. It surrounds coil of radius 8.65 meters and 17turns. If the current in the solenoid is changing at a rate of 146 A/s, what is the emf induced in the surounding coil?

a) 2.823E-02 V

b) 3.105E-02 V

c) 3.416E-02 V

d) 3.757E-02 V

e) 4.133E-02 V

11) Imagine a substance could be made into a very hot filament. Suppose the resitance is 5.89 Ω at a temperature of 43°C and that the temperature coefficient of expansion is 4.400E-03 (°C)⁻¹). What is the resistance at a temperature of 398 °C?

a) 1.369E+01 Ω

b) 1.437E+01 Ω

c) 1.509E+01 Ω

d) 1.584E+01 Ω

e) 1.664E+01 Ω

12)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-9e

, and

q_{3}=6e

?

a) 5.767E+01 degrees

b) 6.343E+01 degrees

c) 6.978E+01 degrees

d) 7.676E+01 degrees

e) 8.443E+01 degrees

T11 J2

1) A long solenoid has a radius of 0.851 m and 12 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 3 A and $\alpha =$ 30 s⁻¹.What is the induced electric fied at a distance 0.14 m from the axis at time t=0.0531 s ?

a) 1.319E-05 V/m

b) 1.451E-05 V/m

c) 1.596E-05 V/m

d) 1.756E-05 V/m

e) 1.932E-05 V/m

2) A 12.0 V battery can move 11,000 C of charge. How many Joules does it deliver?

a) 9.016E+04 J

b) 9.917E+04 J

c) 1.091E+05 J

d) 1.200E+05 J

e) 1.320E+05 J

3)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.0 m, z=z₀=1.9 m, and z=z₁=4.3 m. The surfaces in the yz plane each have area 7.9m². Those in the xy plane have area 4.0m² ,and those in the zx plane have area 2.9m². An electric field has the xyz components (0, 5.3, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 1.388E+01 N·m²/C

b) 1.526E+01 N·m²/C

c) 1.679E+01 N·m²/C

d) 1.847E+01 N·m²/C

e) 2.032E+01 N·m²/C

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.03 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 1.720E-05 T

b) 1.892E-05 T

c) 2.081E-05 T

d) 2.289E-05 T

e) 2.518E-05 T

5)

The resistances in the figure shown are R₁= 1.18 Ω, R₂= 0.878 Ω, and R₂= 2.11 Ω. V₁ and V₃ are text 0.637 V and 3.51 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.547 V. What is the absolute value of the current through R₁?

a) 1.701E-01 A

b) 1.871E-01 A

c) 2.058E-01 A

d) 2.264E-01 A

e) 2.490E-01 A

6)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-7e

, and

q_{3}=6e

?

a) 6.343E+01 degrees

b) 6.978E+01 degrees

c) 7.676E+01 degrees

d) 8.443E+01 degrees

e) 9.288E+01 degrees

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.23 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(3.84 i + 8.79 j + 9.05 k) x 10⁴ m/s?

a) 7.509E-14 N

b) 8.259E-14 N

c) 9.085E-14 N

d) 9.994E-14 N

e) 1.099E-13 N

8)

What is the net capacitance if C₁=3.54 μF, C₂=3.53 μF, and C₃=3.65 μF in the configuration shown?

a) 3.700E+00 μF

b) 4.070E+00 μF

c) 4.477E+00 μF

d) 4.925E+00 μF

e) 5.417E+00 μF

9) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.64 Ω at a temperature of 82°C and that the temperature coefficient of expansion is 4.530E-03 (°C)⁻¹). What is the resistance at a temperature of 390 °C?

a) 7.532E+00 Ω

b) 7.908E+00 Ω

c) 8.303E+00 Ω

d) 8.719E+00 Ω

e) 9.155E+00 Ω

10)

A long solenoid has a length 0.89 meters, radius 3.01 cm, and 505 turns. It surrounds coil of radius 8.65 meters and 18turns. If the current in the solenoid is changing at a rate of 279 A/s, what is the emf induced in the surounding coil?

a) 2.646E-02 V

b) 2.911E-02 V

c) 3.202E-02 V

d) 3.522E-02 V

e) 3.874E-02 V

11) An ac generator produces an emf of amplitude 4 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 19 mF capacitor?

a) 6.946E-02 A

b) 7.640E-02 A

c) 8.404E-02 A

d) 9.245E-02 A

e) 1.017E-01 A

12)

A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=2.70E+03 m² and separation d=6.30E-03 m is connected via a swith to a 85 Ω resistor and a battery of voltage V₀=22 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.50E-03?

a) 2.058E-03 A

b) 2.263E-03 A

c) 2.490E-03 A

d) 2.739E-03 A

e) 3.013E-03 A

T11 K0

1)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

a) 5.352E+09 N/C²

b) 5.887E+09 N/C²

c) 6.476E+09 N/C²

d) 7.124E+09 N/C²

e) 7.836E+09 N/C²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.3 m, z=z₀=1.5 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 8.3m². Those in the xy plane have area 5.7m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.408E+01 N·m²/C

b) 5.949E+01 N·m²/C

c) 6.544E+01 N·m²/C

d) 7.198E+01 N·m²/C

e) 7.918E+01 N·m²/C

3) Assume that a 29 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P₁ and P₂ where the polar coordinates (r,φ) of P₁ are (6 cm, 0°) and P₂ is at (12 cm, 77°).

a) 1.483E+03 V

b) 1.632E+03 V

c) 1.795E+03 V

d) 1.975E+03 V

e) 2.172E+03 V

4)

What is the net capacitance if C₁=4.13 μF, C₂=3.56 μF, and C₃=3.57 μF in the configuration shown?

a) 5.482E+00 μF

b) 6.030E+00 μF

c) 6.633E+00 μF

d) 7.296E+00 μF

e) 8.026E+00 μF

5) A DC winch moter draws 19 amps at 175 volts as it lifts a 4.230E+03 N weight at a constant speed of 0.483 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

a) 3.551E+00 Ω

b) 3.906E+00 Ω

c) 4.297E+00 Ω

d) 4.726E+00 Ω

e) 5.199E+00 Ω

6) A battery with a terminal voltage of 7.82 V is connected to a circuit consisting of 2 19.3 Ω resistors and one 12.2 Ω resistor. What is the voltage drop across the 12.2 Ω resistor?

a) 1.552E+00 V

b) 1.707E+00 V

c) 1.878E+00 V

d) 2.066E+00 V

e) 2.272E+00 V

7) A circular current loop of radius 2.16 cm carries a current of 1.72 mA. What is the magnitude of the torque if the dipole is oriented at 52 ° to a uniform magnetic fied of 0.24 T?

a) 3.582E-07 N m

b) 3.940E-07 N m

c) 4.334E-07 N m

d) 4.768E-07 N m

e) 5.245E-07 N m

8) Two parallel wires each carry a 8.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.66 cm, 1.4 cm), while the other is located at (5.64 cm, 5.66 cm). What is the force per unit length between the wires?

a) 2.449E-10 N/m

b) 2.694E-10 N/m

c) 2.963E-10 N/m

d) 3.260E-10 N/m

e) 3.586E-10 N/m

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.419 m. The magnetic field is spatially uniform but decays in time according to $(2.48)e^{-\alpha t}$ , where $\alpha =$ 9.15 s. What is the current in the coil if the impedance of the coil is 67.8 Ω?

a) 1.240E-01 A

b) 1.364E-01 A

c) 1.500E-01 A

d) 1.650E-01 A

e) 1.815E-01 A

10)

A long solenoid has a length 0.794 meters, radius 4.45 cm, and 568 turns. It surrounds coil of radius 6.81 meters and 9turns. If the current in the solenoid is changing at a rate of 246 A/s, what is the emf induced in the surounding coil?

a) 3.890E-02 V

b) 4.279E-02 V

c) 4.707E-02 V

d) 5.177E-02 V

e) 5.695E-02 V

11) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

a) 1.170E+00 A

b) 1.287E+00 A

c) 1.415E+00 A

d) 1.557E+00 A

e) 1.713E+00 A

12)

A parallel plate capacitor with a capicatnce C=2.90E-06 F whose plates have an area A=1.60E+03 m² and separation d=5.00E-03 m is connected via a swith to a 41 Ω resistor and a battery of voltage V₀=92 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=4.50E-04?

a) 6.755E+01 V

b) 7.431E+01 V

c) 8.174E+01 V

d) 8.991E+01 V

e) 9.890E+01 V

T11 K1

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.7 m, z=z₀=1.8 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 9.2m² ,and those in the zx plane have area 8.1m². An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 2.134E+01 N·m²/C

b) 2.347E+01 N·m²/C

c) 2.582E+01 N·m²/C

d) 2.840E+01 N·m²/C

e) 3.124E+01 N·m²/C

2)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

3)

What is the net capacitance if C₁=4.12 μF, C₂=3.45 μF, and C₃=3.41 μF in the configuration shown?

a) 4.370E+00 μF

b) 4.807E+00 μF

c) 5.288E+00 μF

d) 5.816E+00 μF

e) 6.398E+00 μF

4)

A long solenoid has a length 0.605 meters, radius 4.26 cm, and 597 turns. It surrounds coil of radius 9.08 meters and 12turns. If the current in the solenoid is changing at a rate of 250 A/s, what is the emf induced in the surounding coil?

a) 4.551E-02 V

b) 5.006E-02 V

c) 5.507E-02 V

d) 6.057E-02 V

e) 6.663E-02 V

5) A battery with a terminal voltage of 8.14 V is connected to a circuit consisting of 2 21.5 Ω resistors and one 13.1 Ω resistor. What is the voltage drop across the 13.1 Ω resistor?

a) 1.298E+00 V

b) 1.428E+00 V

c) 1.571E+00 V

d) 1.728E+00 V

e) 1.901E+00 V

6)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 23 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?

a) 2.877E+00 V

b) 3.165E+00 V

c) 3.481E+00 V

d) 3.829E+00 V

e) 4.212E+00 V

7) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.419 m. The magnetic field is spatially uniform but decays in time according to $(2.48)e^{-\alpha t}$ , where $\alpha =$ 9.15 s. What is the current in the coil if the impedance of the coil is 67.8 Ω?

a) 1.240E-01 A

b) 1.364E-01 A

c) 1.500E-01 A

d) 1.650E-01 A

e) 1.815E-01 A

8) A circular current loop of radius 2.48 cm carries a current of 3.67 mA. What is the magnitude of the torque if the dipole is oriented at 21 ° to a uniform magnetic fied of 0.402 T?

a) 1.022E-06 N m

b) 1.124E-06 N m

c) 1.236E-06 N m

d) 1.360E-06 N m

e) 1.496E-06 N m

9) Assume that a 25 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P₁ and P₂ where the polar coordinates (r,φ) of P₁ are (5 cm, 0°) and P₂ is at (13 cm, 70°).

a) 2.285E+03 V

b) 2.514E+03 V

c) 2.765E+03 V

d) 3.042E+03 V

e) 3.346E+03 V

10) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?

a) 2.977E-11 N/m

b) 3.274E-11 N/m

c) 3.602E-11 N/m

d) 3.962E-11 N/m

e) 4.358E-11 N/m

11) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

a) 5.042E+00 A

b) 5.546E+00 A

c) 6.100E+00 A

d) 6.710E+00 A

e) 7.381E+00 A

12) A DC winch moter draws 20 amps at 175 volts as it lifts a 5.180E+03 N weight at a constant speed of 0.541 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

a) 1.744E+00 Ω

b) 1.918E+00 Ω

c) 2.110E+00 Ω

d) 2.321E+00 Ω

e) 2.553E+00 Ω

T11 K2

1)

A long solenoid has a length 0.822 meters, radius 4.37 cm, and 515 turns. It surrounds coil of radius 6.12 meters and 14turns. If the current in the solenoid is changing at a rate of 118 A/s, what is the emf induced in the surounding coil?

a) 2.229E-02 V

b) 2.451E-02 V

c) 2.697E-02 V

d) 2.966E-02 V

e) 3.263E-02 V

2) A DC winch moter draws 19 amps at 175 volts as it lifts a 4.230E+03 N weight at a constant speed of 0.483 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

a) 3.551E+00 Ω

b) 3.906E+00 Ω

c) 4.297E+00 Ω

d) 4.726E+00 Ω

e) 5.199E+00 Ω

3)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

4) A battery with a terminal voltage of 12.4 V is connected to a circuit consisting of 3 21.6 Ω resistors and one 12.1 Ω resistor. What is the voltage drop across the 12.1 Ω resistor?

a) 1.333E+00 V

b) 1.466E+00 V

c) 1.612E+00 V

d) 1.774E+00 V

e) 1.951E+00 V

5)

A parallel plate capacitor with a capicatnce C=7.40E-06 F whose plates have an area A=7.20E+03 m² and separation d=8.60E-03 m is connected via a swith to a 14 Ω resistor and a battery of voltage V₀=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-04?

a) 9.195E+00 V

b) 1.011E+01 V

c) 1.113E+01 V

d) 1.224E+01 V

e) 1.346E+01 V

6)

What is the net capacitance if C₁=4.55 μF, C₂=4.39 μF, and C₃=3.32 μF in the configuration shown?

a) 4.173E+00 μF

b) 4.590E+00 μF

c) 5.049E+00 μF

d) 5.554E+00 μF

e) 6.110E+00 μF

7) Two parallel wires each carry a 7.59 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.98 cm, 0.969 cm), while the other is located at (5.13 cm, 5.53 cm). What is the force per unit length between the wires?

a) 1.840E-10 N/m

b) 2.024E-10 N/m

c) 2.227E-10 N/m

d) 2.449E-10 N/m

e) 2.694E-10 N/m

8) Assume that a 29 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P₁ and P₂ where the polar coordinates (r,φ) of P₁ are (6 cm, 0°) and P₂ is at (12 cm, 77°).

a) 1.483E+03 V

b) 1.632E+03 V

c) 1.795E+03 V

d) 1.975E+03 V

e) 2.172E+03 V

9)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.5 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.3 m, z=z₀=1.2 m, and z=z₁=4.6 m. The surfaces in the yz plane each have area 9.9m². Those in the xy plane have area 4.3m² ,and those in the zx plane have area 5.1m². An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.750E+01 N·m²/C

b) 4.125E+01 N·m²/C

c) 4.537E+01 N·m²/C

d) 4.991E+01 N·m²/C

e) 5.490E+01 N·m²/C

10) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.419 m. The magnetic field is spatially uniform but decays in time according to $(2.48)e^{-\alpha t}$ , where $\alpha =$ 9.15 s. What is the current in the coil if the impedance of the coil is 67.8 Ω?

a) 1.240E-01 A

b) 1.364E-01 A

c) 1.500E-01 A

d) 1.650E-01 A

e) 1.815E-01 A

11) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a 99 mF capacitor?

a) 1.644E+00 A

b) 1.808E+00 A

c) 1.989E+00 A

d) 2.188E+00 A

e) 2.407E+00 A

12) A circular current loop of radius 1.94 cm carries a current of 1.83 mA. What is the magnitude of the torque if the dipole is oriented at 43 ° to a uniform magnetic fied of 0.156 T?

a) 1.903E-07 N m

b) 2.093E-07 N m

c) 2.302E-07 N m

d) 2.532E-07 N m

e) 2.785E-07 N m

T11 L0

1)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate

f(x,y)

at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

a) 6.804E+00 V/m²

b) 7.485E+00 V/m²

c) 8.233E+00 V/m²

d) 9.056E+00 V/m²

e) 9.962E+00 V/m²

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}$

a) 2.067E+03 V·m

b) 2.274E+03 V·m

c) 2.501E+03 V·m

d) 2.752E+03 V·m

e) 3.027E+03 V·m

3) A 12.0 V battery can move 12,000 C of charge. How many Joules does it deliver?

a) 1.190E+05 J

b) 1.309E+05 J

c) 1.440E+05 J

d) 1.584E+05 J

e) 1.742E+05 J

4) An empty parallel-plate capacitor with metal plates has an area of 1.94 m², separated by 1.36 mm. How much charge does it store if the voltage is 8.530E+03 V?

a) 7.359E+01 μC

b) 8.094E+01 μC

c) 8.904E+01 μC

d) 9.794E+01 μC

e) 1.077E+02 μC

5) Calculate the electric field in a 12-gauge copper wire that is 23 m long and carries a current of 64 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 2.953E-04 V/m

b) 3.248E-04 V/m

c) 3.573E-04 V/m

d) 3.930E-04 V/m

e) 4.324E-04 V/m

6)

Two sources of emf ε₁=17.3 V, and ε₂=6.46 V are oriented as shownin the circuit. The resistances are R₁=2.54 kΩ and R₂=2.79 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.1 mA and I₄=0.281 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

a) 6.488E+00 V

b) 7.137E+00 V

c) 7.850E+00 V

d) 8.635E+00 V

e) 9.499E+00 V

7) A 62 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.351 T. What current is required to maintain this balance?

a) 3.999E-01 A

b) 4.398E-01 A

c) 4.838E-01 A

d) 5.322E-01 A

e) 5.854E-01 A

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.38 kA, I₂=1.58 kA, and I₃=4.31 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 4.386E-03 T-m

b) 4.825E-03 T-m

c) 5.307E-03 T-m

d) 5.838E-03 T-m

e) 6.421E-03 T-m

9) A long solenoid has a radius of 0.857 m and 58 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 1 A and $\alpha =$ 21 s⁻¹.What is the induced electric fied at a distance 0.144 m from the axis at time t=0.0898 s ?

a) 1.256E-05 V/m

b) 1.382E-05 V/m

c) 1.520E-05 V/m

d) 1.672E-05 V/m

e) 1.839E-05 V/m

10)

A long solenoid has a length 0.777 meters, radius 3.45 cm, and 557 turns. It surrounds coil of radius 6.01 meters and 10turns. If the current in the solenoid is changing at a rate of 184 A/s, what is the emf induced in the surounding coil?

a) 1.463E-02 V

b) 1.609E-02 V

c) 1.770E-02 V

d) 1.947E-02 V

e) 2.142E-02 V

11) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 6.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

a) 2.007E-03 Watts

b) 2.208E-03 Watts

c) 2.429E-03 Watts

d) 2.672E-03 Watts

e) 2.939E-03 Watts

12) A 59 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?

a) 1.517E+02 km

b) 1.669E+02 km

c) 1.835E+02 km

d) 2.019E+02 km

e) 2.221E+02 km

T11 L1

1) A 33 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.869 T. What current is required to maintain this balance?

a) 2.259E-01 A

b) 2.485E-01 A

c) 2.734E-01 A

d) 3.007E-01 A

e) 3.308E-01 A

2)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate

f(x,y)

at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

a) 3.610E+00 V/m²

b) 3.971E+00 V/m²

c) 4.368E+00 V/m²

d) 4.804E+00 V/m²

e) 5.285E+00 V/m²

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
${\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}$

a) 2.210E+04 V·m

b) 2.431E+04 V·m

c) 2.674E+04 V·m

d) 2.941E+04 V·m

e) 3.235E+04 V·m

4)

Two sources of emf ε₁=27.9 V, and ε₂=11.1 V are oriented as shownin the circuit. The resistances are R₁=2.82 kΩ and R₂=2.25 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.1 mA and I₄=0.676 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

a) 8.334E+00 V

b) 9.167E+00 V

c) 1.008E+01 V

d) 1.109E+01 V

e) 1.220E+01 V

5) An empty parallel-plate capacitor with metal plates has an area of 2.42 m², separated by 1.33 mm. How much charge does it store if the voltage is 1.130E+03 V?

a) 1.368E+01 μC

b) 1.505E+01 μC

c) 1.655E+01 μC

d) 1.820E+01 μC

e) 2.003E+01 μC

6) Calculate the electric field in a 12-gauge copper wire that is 21 m long and carries a current of 42 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 1.602E-04 V/m

b) 1.762E-04 V/m

c) 1.938E-04 V/m

d) 2.132E-04 V/m

e) 2.345E-04 V/m

7)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.58 kA, I₂=1.11 kA, and I₃=2.47 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 4.092E-03 T-m

b) 4.501E-03 T-m

c) 4.951E-03 T-m

d) 5.446E-03 T-m

e) 5.991E-03 T-m

8) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 84 kW?

a) 9.780E+01 km

b) 1.076E+02 km

c) 1.183E+02 km

d) 1.302E+02 km

e) 1.432E+02 km

9)

A long solenoid has a length 0.794 meters, radius 4.45 cm, and 568 turns. It surrounds coil of radius 6.81 meters and 9turns. If the current in the solenoid is changing at a rate of 246 A/s, what is the emf induced in the surounding coil?

a) 3.890E-02 V

b) 4.279E-02 V

c) 4.707E-02 V

d) 5.177E-02 V

e) 5.695E-02 V

10) A long solenoid has a radius of 0.603 m and 51 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 2 A and $\alpha =$ 26 s⁻¹.What is the induced electric fied at a distance 0.105 m from the axis at time t=0.0659 s ?

a) 2.154E-05 V/m

b) 2.369E-05 V/m

c) 2.606E-05 V/m

d) 2.867E-05 V/m

e) 3.154E-05 V/m

11) The output of an ac generator connected to an RLC series combination has a frequency of 7.60E+04 Hz and an amplitude of 5 V. If R =6 Ω, L= 3.70E-03H , and C=5.80E-06 F, what is the rms power transferred to the resistor?

a) 7.239E-04 Watts

b) 7.963E-04 Watts

c) 8.759E-04 Watts

d) 9.635E-04 Watts

e) 1.060E-03 Watts

12) A 12.0 V battery can move 36,000 C of charge. How many Joules does it deliver?

a) 3.570E+05 J

b) 3.927E+05 J

c) 4.320E+05 J

d) 4.752E+05 J

e) 5.227E+05 J

T11 L2

1)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate

f(x,y)

at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

a) 6.804E+00 V/m²

b) 7.485E+00 V/m²

c) 8.233E+00 V/m²

d) 9.056E+00 V/m²

e) 9.962E+00 V/m²

2) A long solenoid has a radius of 0.861 m and 28 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 1 A and $\alpha =$ 20 s⁻¹.What is the induced electric fied at a distance 0.106 m from the axis at time t=0.055 s ?

a) 1.026E-05 V/m

b) 1.129E-05 V/m

c) 1.242E-05 V/m

d) 1.366E-05 V/m

e) 1.502E-05 V/m

3)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.42 kA, I₂=0.904 kA, and I₃=1.34 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 2.696E-03 T-m

b) 2.966E-03 T-m

c) 3.263E-03 T-m

d) 3.589E-03 T-m

e) 3.948E-03 T-m

4) An empty parallel-plate capacitor with metal plates has an area of 1.73 m², separated by 1.16 mm. How much charge does it store if the voltage is 1.130E+03 V?

a) 1.121E+01 μC

b) 1.233E+01 μC

c) 1.357E+01 μC

d) 1.492E+01 μC

e) 1.641E+01 μC

5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}$

a) 1.969E+02 V·m

b) 2.166E+02 V·m

c) 2.383E+02 V·m

d) 2.621E+02 V·m

e) 2.883E+02 V·m

6) A 62 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.351 T. What current is required to maintain this balance?

a) 3.999E-01 A

b) 4.398E-01 A

c) 4.838E-01 A

d) 5.322E-01 A

e) 5.854E-01 A

7) A 12.0 V battery can move 24,000 C of charge. How many Joules does it deliver?

a) 1.967E+05 J

b) 2.164E+05 J

c) 2.380E+05 J

d) 2.618E+05 J

e) 2.880E+05 J

8) A 41 kW radio transmitter on Earth sends it signal to a satellite 100 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?

a) 1.405E+02 km

b) 1.546E+02 km

c) 1.701E+02 km

d) 1.871E+02 km

e) 2.058E+02 km

9)

Two sources of emf ε₁=42.2 V, and ε₂=17.8 V are oriented as shownin the circuit. The resistances are R₁=4.2 kΩ and R₂=2.83 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.5 mA and I₄=0.749 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

a) 1.056E+01 V

b) 1.161E+01 V

c) 1.277E+01 V

d) 1.405E+01 V

e) 1.545E+01 V

10)

A long solenoid has a length 0.841 meters, radius 3.81 cm, and 516 turns. It surrounds coil of radius 9.2 meters and 11turns. If the current in the solenoid is changing at a rate of 190 A/s, what is the emf induced in the surounding coil?

a) 1.735E-02 V

b) 1.908E-02 V

c) 2.099E-02 V

d) 2.309E-02 V

e) 2.540E-02 V

11) The output of an ac generator connected to an RLC series combination has a frequency of 5.00E+04 Hz and an amplitude of 5 V. If R =6 Ω, L= 2.50E-03H , and C=5.20E-06 F, what is the rms power transferred to the resistor?

a) 5.097E-03 Watts

b) 5.607E-03 Watts

c) 6.167E-03 Watts

d) 6.784E-03 Watts

e) 7.463E-03 Watts

12) Calculate the electric field in a 12-gauge copper wire that is 64 m long and carries a current of 76 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 2.635E-04 V/m

b) 2.898E-04 V/m

c) 3.188E-04 V/m

d) 3.507E-04 V/m

e) 3.857E-04 V/m

T11 M0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=5e

?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.3 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=4.6 m, z=z₀=1.6 m, and z=z₁=5.8 m. The surfaces in the yz plane each have area 13.0m². Those in the xy plane have area 7.1m² ,and those in the zx plane have area 9.7m². An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 8.415E+01 N·m²/C

b) 9.256E+01 N·m²/C

c) 1.018E+02 N·m²/C

d) 1.120E+02 N·m²/C

e) 1.232E+02 N·m²/C

3) When a 5.65 V battery operates a 2.73 W bulb, how many electrons pass through it each second?

a) 3.016E+18 electrons

b) 3.317E+18 electrons

c) 3.649E+18 electrons

d) 4.014E+18 electrons

e) 4.415E+18 electrons

4)

In the figure shown C₁=18.7 μF, C₂=2.15 μF, and C₃=4.88 μF. The voltage source provides ε=11.9 V. What is the energy stored in C₂?

a) 1.270E+01 μJ

b) 1.397E+01 μJ

c) 1.537E+01 μJ

d) 1.690E+01 μJ

e) 1.859E+01 μJ

5) A DC winch moter draws 26 amps at 177 volts as it lifts a 4.820E+03 N weight at a constant speed of 0.696 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

a) 1.677E+00 Ω

b) 1.845E+00 Ω

c) 2.030E+00 Ω

d) 2.233E+00 Ω

e) 2.456E+00 Ω

6) Three resistors, R₁ = 1.52 Ω, and R₂ = R₂ = 3.38 Ω, are connected in parallel to a 5.82 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 1.842E+01 W

b) 2.026E+01 W

c) 2.228E+01 W

d) 2.451E+01 W

e) 2.696E+01 W

7) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.96 mT and 2.010E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 2.768E+05 m/s

b) 3.045E+05 m/s

c) 3.349E+05 m/s

d) 3.684E+05 m/s

e) 4.052E+05 m/s

8) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 17 turns per centimeter and the current applied to the solenoid is 331 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

1.593E+03

b)

\chi {\text{ (chi) }}=

1.753E+03

c)

\chi {\text{ (chi) }}=

1.928E+03

d)

\chi {\text{ (chi) }}=

2.121E+03

e)

\chi {\text{ (chi) }}=

2.333E+03

9)

A cylinder of height 3.82 cm and radius 5.6 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.89 cm from point O and moves at a speed of 4.25 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

a) 7.280E+01 cm³/s

b) 8.008E+01 cm³/s

c) 8.808E+01 cm³/s

d) 9.689E+01 cm³/s

e) 1.066E+02 cm³/s

10)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =0.919 s if ε = 6.65 V , R = 6.34 Ω, and L = 1.14 H?

a) 6.033E-01 V

b) 7.240E-01 V

c) 8.688E-01 V

d) 1.043E+00 V

e) 1.251E+00 V

11) An ac generator produces an emf of amplitude 8 V at a frequency of 80 Hz. What is the maximum amplitude of the current if the generator is connected to a 14 mF inductor?

a) 8.541E-01 A

b) 9.395E-01 A

c) 1.033E+00 A

d) 1.137E+00 A

e) 1.251E+00 A

12)

A parallel plate capacitor with a capicatnce C=9.10E-06 F whose plates have an area A=8.50E+03 m² and separation d=8.30E-03 m is connected via a swith to a 67 Ω resistor and a battery of voltage V₀=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.40E-03?

a) 5.946E+00 V

b) 6.541E+00 V

c) 7.195E+00 V

d) 7.914E+00 V

e) 8.706E+00 V

T11 M1

1) An ac generator produces an emf of amplitude 37 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 86 mF inductor?

a) 4.677E-01 A

b) 5.145E-01 A

c) 5.659E-01 A

d) 6.225E-01 A

e) 6.847E-01 A

2)

A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

a) 1.892E+01 cm³/s

b) 2.081E+01 cm³/s

c) 2.289E+01 cm³/s

d) 2.518E+01 cm³/s

e) 2.770E+01 cm³/s

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 18 turns per centimeter and the current applied to the solenoid is 582 mA, the net magnetic field is measured to be 1.15 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

7.211E+02

b)

\chi {\text{ (chi) }}=

7.932E+02

c)

\chi {\text{ (chi) }}=

8.726E+02

d)

\chi {\text{ (chi) }}=

9.598E+02

e)

\chi {\text{ (chi) }}=

1.056E+03

4)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=5e

?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

5)

A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m² and separation d=3.20E-03 m is connected via a swith to a 61 Ω resistor and a battery of voltage V₀=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?

a) 5.017E+01 V

b) 5.519E+01 V

c) 6.071E+01 V

d) 6.678E+01 V

e) 7.345E+01 V

6)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =13.6 s if ε = 6.56 V , R = 2.44 Ω, and L = 8.76 H?

a) 2.627E+00 V

b) 3.153E+00 V

c) 3.783E+00 V

d) 4.540E+00 V

e) 5.448E+00 V

7) When a 3.63 V battery operates a 1.34 W bulb, how many electrons pass through it each second?

a) 2.095E+18 electrons

b) 2.304E+18 electrons

c) 2.534E+18 electrons

d) 2.788E+18 electrons

e) 3.067E+18 electrons

8) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.96 mT and 2.010E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 2.768E+05 m/s

b) 3.045E+05 m/s

c) 3.349E+05 m/s

d) 3.684E+05 m/s

e) 4.052E+05 m/s

9) Three resistors, R₁ = 1.31 Ω, and R₂ = R₂ = 2.91 Ω, are connected in parallel to a 6.03 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 2.294E+01 W

b) 2.523E+01 W

c) 2.776E+01 W

d) 3.053E+01 W

e) 3.359E+01 W

10) A DC winch moter draws 29 amps at 153 volts as it lifts a 4.780E+03 N weight at a constant speed of 0.691 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

a) 1.226E+00 Ω

b) 1.348E+00 Ω

c) 1.483E+00 Ω

d) 1.632E+00 Ω

e) 1.795E+00 Ω

11)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.6 m. The other four surfaces are rectangles in y=y₀=1.3 m, y=y₁=4.4 m, z=z₀=1.4 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 13.0m². Those in the xy plane have area 5.0m² ,and those in the zx plane have area 6.6m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 2.756E+01 N·m²/C

b) 3.032E+01 N·m²/C

c) 3.335E+01 N·m²/C

d) 3.668E+01 N·m²/C

e) 4.035E+01 N·m²/C

12)

In the figure shown C₁=18.1 μF, C₂=2.13 μF, and C₃=5.48 μF. The voltage source provides ε=14.6 V. What is the energy stored in C₂?

a) 1.645E+01 μJ

b) 1.809E+01 μJ

c) 1.990E+01 μJ

d) 2.189E+01 μJ

e) 2.408E+01 μJ

T11 M2

1) A DC winch moter draws 13 amps at 159 volts as it lifts a 4.270E+03 N weight at a constant speed of 0.357 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

a) 3.211E+00 Ω

b) 3.532E+00 Ω

c) 3.885E+00 Ω

d) 4.273E+00 Ω

e) 4.701E+00 Ω

2)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =1.95 s if ε = 8.33 V , R = 6.96 Ω, and L = 2.66 H?

a) 5.736E-01 V

b) 6.884E-01 V

c) 8.260E-01 V

d) 9.912E-01 V

e) 1.189E+00 V

3) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.88 mT and 7.340E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 1.504E+06 m/s

b) 1.655E+06 m/s

c) 1.820E+06 m/s

d) 2.002E+06 m/s

e) 2.202E+06 m/s

4) An ac generator produces an emf of amplitude 70 V at a frequency of 63 Hz. What is the maximum amplitude of the current if the generator is connected to a 34 mF inductor?

a) 3.908E+00 A

b) 4.298E+00 A

c) 4.728E+00 A

d) 5.201E+00 A

e) 5.721E+00 A

5)

In the figure shown C₁=18.7 μF, C₂=2.15 μF, and C₃=4.88 μF. The voltage source provides ε=11.9 V. What is the energy stored in C₂?

a) 1.270E+01 μJ

b) 1.397E+01 μJ

c) 1.537E+01 μJ

d) 1.690E+01 μJ

e) 1.859E+01 μJ

6) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 17 turns per centimeter and the current applied to the solenoid is 331 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

1.593E+03

b)

\chi {\text{ (chi) }}=

1.753E+03

c)

\chi {\text{ (chi) }}=

1.928E+03

d)

\chi {\text{ (chi) }}=

2.121E+03

e)

\chi {\text{ (chi) }}=

2.333E+03

7)

A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

a) 1.892E+01 cm³/s

b) 2.081E+01 cm³/s

c) 2.289E+01 cm³/s

d) 2.518E+01 cm³/s

e) 2.770E+01 cm³/s

8)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.3 m, z=z₀=1.5 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 8.3m². Those in the xy plane have area 5.7m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.408E+01 N·m²/C

b) 5.949E+01 N·m²/C

c) 6.544E+01 N·m²/C

d) 7.198E+01 N·m²/C

e) 7.918E+01 N·m²/C

9) Three resistors, R₁ = 1.43 Ω, and R₂ = R₂ = 3.25 Ω, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 5.184E+01 W

b) 5.702E+01 W

c) 6.272E+01 W

d) 6.900E+01 W

e) 7.590E+01 W

10)

A parallel plate capacitor with a capicatnce C=9.10E-06 F whose plates have an area A=8.50E+03 m² and separation d=8.30E-03 m is connected via a swith to a 67 Ω resistor and a battery of voltage V₀=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.40E-03?

a) 5.946E+00 V

b) 6.541E+00 V

c) 7.195E+00 V

d) 7.914E+00 V

e) 8.706E+00 V

11)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=5e

?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

12) When a 6.97 V battery operates a 2.6 W bulb, how many electrons pass through it each second?

a) 1.749E+18 electrons

b) 1.924E+18 electrons

c) 2.117E+18 electrons

d) 2.328E+18 electrons

e) 2.561E+18 electrons

T11 N0

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.357E+01 N/C

b) 2.593E+01 N/C

c) 2.852E+01 N/C

d) 3.137E+01 N/C

e) 3.451E+01 N/C

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.3 m, y=y₁=4.2 m, z=z₀=1.9 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 10.0m². Those in the xy plane have area 8.1m² ,and those in the zx plane have area 10.0m². An electric field has the xyz components (0, 8.5, 6.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 7.081E+01 N·m²/C

b) 7.789E+01 N·m²/C

c) 8.568E+01 N·m²/C

d) 9.425E+01 N·m²/C

e) 1.037E+02 N·m²/C

3) When a 6.32 V battery operates a 1.94 W bulb, how many electrons pass through it each second?

a) 1.439E+18 electrons

b) 1.583E+18 electrons

c) 1.742E+18 electrons

d) 1.916E+18 electrons

e) 2.107E+18 electrons

4)

What is the net capacitance if C₁=2.3 μF, C₂=2.84 μF, and C₃=3.41 μF in the configuration shown?

a) 4.255E+00 μF

b) 4.681E+00 μF

c) 5.149E+00 μF

d) 5.664E+00 μF

e) 6.230E+00 μF

5) Calculate the resistance of a 12-gauge copper wire that is 45 m long and carries a current of 51 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 1.716E-01 Ω

b) 1.888E-01 Ω

c) 2.076E-01 Ω

d) 2.284E-01 Ω

e) 2.512E-01 Ω

6)

Two sources of emf ε₁=18.2 V, and ε₂=6.59 V are oriented as shownin the circuit. The resistances are R₁=5.47 kΩ and R₂=2.81 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.64 mA and I₄=0.341 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

a) 1.299E+00 mA

b) 1.429E+00 mA

c) 1.572E+00 mA

d) 1.729E+00 mA

e) 1.902E+00 mA

7) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.295 m and a magneticfield of 1.44 T. What is their maximum kinetic energy?

a) 6.534E+00 MeV

b) 7.187E+00 MeV

c) 7.906E+00 MeV

d) 8.697E+00 MeV

e) 9.566E+00 MeV

8)

Three wires sit at the corners of a square of length 0.467 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?

a) B_x= 8.371E-05 T

b) B_x= 9.208E-05 T

c) B_x= 1.013E-04 T

d) B_x= 1.114E-04 T

e) B_x= 1.226E-04 T

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to $(1.95)e^{-\alpha t}$ , where $\alpha =$ 7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

a) 7.402E-01 A

b) 8.142E-01 A

c) 8.956E-01 A

d) 9.852E-01 A

e) 1.084E+00 A

10)

A long solenoid has a length 0.841 meters, radius 3.81 cm, and 516 turns. It surrounds coil of radius 9.2 meters and 11turns. If the current in the solenoid is changing at a rate of 190 A/s, what is the emf induced in the surounding coil?

a) 1.735E-02 V

b) 1.908E-02 V

c) 2.099E-02 V

d) 2.309E-02 V

e) 2.540E-02 V

11) A step-down transformer steps 18 kV down to 170 V. The high-voltage input is provided by a 240 Ω power line that carries 5 A of currentWhat is the output current (at the 170 V side ?)

a) 5.294E+02 A

b) 5.824E+02 A

c) 6.406E+02 A

d) 7.046E+02 A

e) 7.751E+02 A

12) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?

a) 1.753E+02 km

b) 1.928E+02 km

c) 2.121E+02 km

d) 2.333E+02 km

e) 2.567E+02 km

T11 N1

1) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.157 m and a magneticfield of 1.03 T. What is their maximum kinetic energy?

a) 8.608E-01 MeV

b) 9.468E-01 MeV

c) 1.042E+00 MeV

d) 1.146E+00 MeV

e) 1.260E+00 MeV

2) A step-down transformer steps 12 kV down to 230 V. The high-voltage input is provided by a 140 Ω power line that carries 5 A of currentWhat is the output current (at the 230 V side ?)

a) 2.156E+02 A

b) 2.372E+02 A

c) 2.609E+02 A

d) 2.870E+02 A

e) 3.157E+02 A

3)

What is the net capacitance if C₁=3.97 μF, C₂=3.51 μF, and C₃=2.18 μF in the configuration shown?

a) 3.038E+00 μF

b) 3.341E+00 μF

c) 3.675E+00 μF

d) 4.043E+00 μF

e) 4.447E+00 μF

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.227 m. The magnetic field is spatially uniform but decays in time according to $(5.55)e^{-\alpha t}$ , where $\alpha =$ 3.92 s. What is the current in the coil if the impedance of the coil is 22.7 Ω?

a) 1.082E-01 A

b) 1.190E-01 A

c) 1.309E-01 A

d) 1.440E-01 A

e) 1.584E-01 A

5)

Two sources of emf ε₁=24.9 V, and ε₂=10.1 V are oriented as shownin the circuit. The resistances are R₁=2.32 kΩ and R₂=2.31 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.74 mA and I₄=0.444 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

a) 1.725E+00 mA

b) 1.898E+00 mA

c) 2.087E+00 mA

d) 2.296E+00 mA

e) 2.526E+00 mA

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 8.471E+01 N/C

b) 9.318E+01 N/C

c) 1.025E+02 N/C

d) 1.127E+02 N/C

e) 1.240E+02 N/C

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.3 m. The other four surfaces are rectangles in y=y₀=1.6 m, y=y₁=5.3 m, z=z₀=1.3 m, and z=z₁=5.6 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 4.8m² ,and those in the zx plane have area 5.6m². An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.074E+01 N·m²/C

b) 3.382E+01 N·m²/C

c) 3.720E+01 N·m²/C

d) 4.092E+01 N·m²/C

e) 4.501E+01 N·m²/C

8) Calculate the resistance of a 12-gauge copper wire that is 10 m long and carries a current of 69 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 4.614E-02 Ω

b) 5.076E-02 Ω

c) 5.583E-02 Ω

d) 6.141E-02 Ω

e) 6.756E-02 Ω

9)

A long solenoid has a length 0.864 meters, radius 3.37 cm, and 522 turns. It surrounds coil of radius 7.87 meters and 13turns. If the current in the solenoid is changing at a rate of 290 A/s, what is the emf induced in the surounding coil?

a) 2.917E-02 V

b) 3.208E-02 V

c) 3.529E-02 V

d) 3.882E-02 V

e) 4.270E-02 V

10) A 59 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 76 kW?

a) 1.008E+02 km

b) 1.109E+02 km

c) 1.219E+02 km

d) 1.341E+02 km

e) 1.475E+02 km

11) When a 7.78 V battery operates a 1.35 W bulb, how many electrons pass through it each second?

a) 7.397E+17 electrons

b) 8.137E+17 electrons

c) 8.951E+17 electrons

d) 9.846E+17 electrons

e) 1.083E+18 electrons

12)

Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?

a) B_x= 6.171E-05 T

b) B_x= 6.788E-05 T

c) B_x= 7.467E-05 T

d) B_x= 8.213E-05 T

e) B_x= 9.035E-05 T

T11 N2

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.3 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.2 m, z=z₀=1.8 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 8.5m² ,and those in the zx plane have area 6.0m². An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 4.730E+01 N·m²/C

b) 5.203E+01 N·m²/C

c) 5.723E+01 N·m²/C

d) 6.295E+01 N·m²/C

e) 6.925E+01 N·m²/C

2) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?

a) 2.094E+02 km

b) 2.304E+02 km

c) 2.534E+02 km

d) 2.788E+02 km

e) 3.066E+02 km

3)

What is the net capacitance if C₁=2.25 μF, C₂=4.16 μF, and C₃=2.49 μF in the configuration shown?

a) 2.698E+00 μF

b) 2.968E+00 μF

c) 3.265E+00 μF

d) 3.591E+00 μF

e) 3.950E+00 μF

4)

Two sources of emf ε₁=43.7 V, and ε₂=13.1 V are oriented as shownin the circuit. The resistances are R₁=5.21 kΩ and R₂=1.72 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.86 mA and I₄=0.9 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

a) 2.691E+00 mA

b) 2.960E+00 mA

c) 3.256E+00 mA

d) 3.582E+00 mA

e) 3.940E+00 mA

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to $(1.95)e^{-\alpha t}$ , where $\alpha =$ 7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

a) 7.402E-01 A

b) 8.142E-01 A

c) 8.956E-01 A

d) 9.852E-01 A

e) 1.084E+00 A

6) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.118 m and a magneticfield of 1.48 T. What is their maximum kinetic energy?

a) 1.004E+00 MeV

b) 1.104E+00 MeV

c) 1.215E+00 MeV

d) 1.336E+00 MeV

e) 1.470E+00 MeV

7)

Three wires sit at the corners of a square of length 0.774 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?

a) B_x= 7.270E-05 T

b) B_x= 7.997E-05 T

c) B_x= 8.797E-05 T

d) B_x= 9.677E-05 T

e) B_x= 1.064E-04 T

8) When a 6.97 V battery operates a 2.6 W bulb, how many electrons pass through it each second?

a) 1.749E+18 electrons

b) 1.924E+18 electrons

c) 2.117E+18 electrons

d) 2.328E+18 electrons

e) 2.561E+18 electrons

9) Calculate the resistance of a 12-gauge copper wire that is 78 m long and carries a current of 82 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

a) 2.974E-01 Ω

b) 3.272E-01 Ω

c) 3.599E-01 Ω

d) 3.959E-01 Ω

e) 4.355E-01 Ω

10)

A long solenoid has a length 0.784 meters, radius 3.57 cm, and 553 turns. It surrounds coil of radius 9.49 meters and 16turns. If the current in the solenoid is changing at a rate of 276 A/s, what is the emf induced in the surounding coil?

a) 4.476E-02 V

b) 4.924E-02 V

c) 5.416E-02 V

d) 5.958E-02 V

e) 6.553E-02 V

11) A step-down transformer steps 9 kV down to 160 V. The high-voltage input is provided by a 260 Ω power line that carries 7 A of currentWhat is the output current (at the 160 V side ?)

a) 3.938E+02 A

b) 4.331E+02 A

c) 4.764E+02 A

d) 5.241E+02 A

e) 5.765E+02 A

12) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

T11 O0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$ .

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.1 m, y=y₁=5.6 m, z=z₀=1.8 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 17.0m². Those in the xy plane have area 13.0m² ,and those in the zx plane have area 10.0m². An electric field has the xyz components (0, 7.0, 5.7) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 4.953E+01 N·m²/C

b) 5.449E+01 N·m²/C

c) 5.993E+01 N·m²/C

d) 6.593E+01 N·m²/C

e) 7.252E+01 N·m²/C

3) If a 29 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=81 V is x² + y² + z² = R², where R=

a) 3.218E+00 m

b) 3.540E+00 m

c) 3.893E+00 m

d) 4.283E+00 m

e) 4.711E+00 m

4)

In the figure shown C₁=17.7 μF, C₂=2.48 μF, and C₃=4.68 μF. The voltage source provides ε=12.7 V. What is the energy stored in C₂?

a) 2.242E+01 μJ

b) 2.467E+01 μJ

c) 2.713E+01 μJ

d) 2.985E+01 μJ

e) 3.283E+01 μJ

5) A make-believe metal has a density of 1.180E+04 kg/m³ and an atomic mass of 121.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

a) 4.010E+28 e⁻/m³

b) 4.411E+28 e⁻/m³

c) 4.852E+28 e⁻/m³

d) 5.337E+28 e⁻/m³

e) 5.871E+28 e⁻/m³

6) Three resistors, R₁ = 1.2 Ω, and R₂ = R₂ = 2.75 Ω, are connected in parallel to a 6.42 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 2.581E+01 W

b) 2.839E+01 W

c) 3.122E+01 W

d) 3.435E+01 W

e) 3.778E+01 W

7) A long rigid wire carries a 3 A current. What is the magnetic force per unit length on the wire if a 0.534 T magnetic field is directed 18° away from the wire?

a) 4.950E-01 N/m

b) 5.445E-01 N/m

c) 5.990E-01 N/m

d) 6.589E-01 N/m

e) 7.248E-01 N/m

8)

Three wires sit at the corners of a square of length 0.495 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.45 A, 1.66 A, 1.63 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 1.205E-04 T

b) B_y= 1.325E-04 T

c) B_y= 1.458E-04 T

d) B_y= 1.604E-04 T

e) B_y= 1.764E-04 T

9) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 5 A and $\alpha =$ 28 s⁻¹.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?

a) 1.616E-04 V/m

b) 1.778E-04 V/m

c) 1.955E-04 V/m

d) 2.151E-04 V/m

e) 2.366E-04 V/m

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.44% of its maximum value if ε = 5.95 V , R = 7.26 Ω, and L = 1.29 H?

a) -3.114E-01 s

b) -3.425E-01 s

c) -3.767E-01 s

d) -4.144E-01 s

e) -4.559E-01 s

11) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

a) 1.170E+00 A

b) 1.287E+00 A

c) 1.415E+00 A

d) 1.557E+00 A

e) 1.713E+00 A

12) What is the radiation pressure on an object that is 8.30E+11 m away from the sun and has cross-sectional area of 0.097 m²? The average power output of the Sun is 3.80E+26 W.

a) 2.928E-07 N/m²

b) 3.221E-07 N/m²

c) 3.543E-07 N/m²

d) 3.898E-07 N/m²

e) 4.287E-07 N/m²

T11 O1

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.1 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.2 m, z=z₀=1.1 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 8.5m². Those in the xy plane have area 2.8m² ,and those in the zx plane have area 3.7m². An electric field has the xyz components (0, 7.4, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 2.079E+01 N·m²/C

b) 2.287E+01 N·m²/C

c) 2.516E+01 N·m²/C

d) 2.768E+01 N·m²/C

e) 3.044E+01 N·m²/C

2)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 2.16% of its maximum value if ε = 4.79 V , R = 4.37 Ω, and L = 5.29 H?

a) -2.110E+00 s

b) -2.321E+00 s

c) -2.553E+00 s

d) -2.809E+00 s

e) -3.090E+00 s

3) If a 14 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=26 V is x² + y² + z² = R², where R=

a) 3.636E+00 m

b) 4.000E+00 m

c) 4.399E+00 m

d) 4.839E+00 m

e) 5.323E+00 m

4)

In the figure shown C₁=16.5 μF, C₂=2.7 μF, and C₃=4.82 μF. The voltage source provides ε=15.7 V. What is the energy stored in C₂?

a) 2.188E+01 μJ

b) 2.407E+01 μJ

c) 2.647E+01 μJ

d) 2.912E+01 μJ

e) 3.203E+01 μJ

5) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.052 m²? The average power output of the Sun is 3.80E+26 W.

a) 2.392E-06 N/m²

b) 2.631E-06 N/m²

c) 2.894E-06 N/m²

d) 3.184E-06 N/m²

e) 3.502E-06 N/m²

6) An ac generator produces an emf of amplitude 53 V at a frequency of 190 Hz. What is the maximum amplitude of the current if the generator is connected to a 85 mF capacitor?

a) 4.445E+00 A

b) 4.889E+00 A

c) 5.378E+00 A

d) 5.916E+00 A

e) 6.507E+00 A

7) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3{\text{ m}}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$ .

a) 6.877E+00 V/m²

b) 7.565E+00 V/m²

c) 8.321E+00 V/m²

d) 9.153E+00 V/m²

e) 1.007E+01 V/m²

8) A make-believe metal has a density of 2.670E+03 kg/m³ and an atomic mass of 40.9 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

a) 3.930E+28 e⁻/m³

b) 4.323E+28 e⁻/m³

c) 4.755E+28 e⁻/m³

d) 5.231E+28 e⁻/m³

e) 5.754E+28 e⁻/m³

9) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.265 T magnetic field is directed 26° away from the wire?

a) 3.840E-01 N/m

b) 4.224E-01 N/m

c) 4.647E-01 N/m

d) 5.111E-01 N/m

e) 5.623E-01 N/m

10) Three resistors, R₁ = 0.855 Ω, and R₂ = R₂ = 1.91 Ω, are connected in parallel to a 6.97 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 5.682E+01 W

b) 6.250E+01 W

c) 6.875E+01 W

d) 7.563E+01 W

e) 8.319E+01 W

11)

Three wires sit at the corners of a square of length 0.702 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 7.576E-05 T

b) B_y= 8.333E-05 T

c) B_y= 9.167E-05 T

d) B_y= 1.008E-04 T

e) B_y= 1.109E-04 T

12) A long solenoid has a radius of 0.434 m and 41 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 9 A and $\alpha =$ 28 s⁻¹.What is the induced electric fied at a distance 2.28 m from the axis at time t=0.0392 s ?

a) 1.479E-04 V/m

b) 1.627E-04 V/m

c) 1.789E-04 V/m

d) 1.968E-04 V/m

e) 2.165E-04 V/m

T11 O2

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.0 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.7 m, z=z₀=1.2 m, and z=z₁=4.1 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 6.6m² ,and those in the zx plane have area 5.8m². An electric field has the xyz components (0, 8.4, 5.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.328E+01 N·m²/C

b) 3.660E+01 N·m²/C

c) 4.026E+01 N·m²/C

d) 4.429E+01 N·m²/C

e) 4.872E+01 N·m²/C

2) A long solenoid has a radius of 0.578 m and 34 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 27 s⁻¹.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0462 s ?

a) 1.473E-04 V/m

b) 1.621E-04 V/m

c) 1.783E-04 V/m

d) 1.961E-04 V/m

e) 2.157E-04 V/m

3)

Three wires sit at the corners of a square of length 0.793 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.32 A, 1.4 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 3.480E-05 T

b) B_y= 3.828E-05 T

c) B_y= 4.210E-05 T

d) B_y= 4.631E-05 T

e) B_y= 5.095E-05 T

4) Three resistors, R₁ = 1.43 Ω, and R₂ = R₂ = 3.25 Ω, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 5.184E+01 W

b) 5.702E+01 W

c) 6.272E+01 W

d) 6.900E+01 W

e) 7.590E+01 W

5) An ac generator produces an emf of amplitude 53 V at a frequency of 190 Hz. What is the maximum amplitude of the current if the generator is connected to a 85 mF capacitor?

a) 4.445E+00 A

b) 4.889E+00 A

c) 5.378E+00 A

d) 5.916E+00 A

e) 6.507E+00 A

6) If a 19 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=73 V is x² + y² + z² = R², where R=

a) 1.598E+00 m

b) 1.757E+00 m

c) 1.933E+00 m

d) 2.127E+00 m

e) 2.339E+00 m

7) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.016 m²? The average power output of the Sun is 3.80E+26 W.

a) 6.669E-07 N/m²

b) 7.336E-07 N/m²

c) 8.069E-07 N/m²

d) 8.876E-07 N/m²

e) 9.764E-07 N/m²

8) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.578 T magnetic field is directed 38° away from the wire?

a) 2.847E+00 N/m

b) 3.132E+00 N/m

c) 3.445E+00 N/m

d) 3.789E+00 N/m

e) 4.168E+00 N/m

9) A make-believe metal has a density of 1.810E+04 kg/m³ and an atomic mass of 14.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

a) 5.847E+29 e⁻/m³

b) 6.432E+29 e⁻/m³

c) 7.075E+29 e⁻/m³

d) 7.783E+29 e⁻/m³

e) 8.561E+29 e⁻/m³

10) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=4.3{\text{ m}}$ .

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

11)

In the figure shown C₁=18.1 μF, C₂=2.89 μF, and C₃=4.2 μF. The voltage source provides ε=9.19 V. What is the energy stored in C₂?

a) 1.303E+01 μJ

b) 1.434E+01 μJ

c) 1.577E+01 μJ

d) 1.735E+01 μJ

e) 1.908E+01 μJ

12)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?

a) -1.700E+00 s

b) -1.870E+00 s

c) -2.057E+00 s

d) -2.262E+00 s

e) -2.489E+00 s

T11 P0

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.571E+01 N/C

b) 2.828E+01 N/C

c) 3.111E+01 N/C

d) 3.422E+01 N/C

e) 3.765E+01 N/C

2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.7 (r≤R) where a=3 nC·m^-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 1.390E+03 N/C

b) 1.530E+03 N/C

c) 1.682E+03 N/C

d) 1.851E+03 N/C

e) 2.036E+03 N/C

3)

A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.

a) 8.672E+02 V

b) 9.539E+02 V

c) 1.049E+03 V

d) 1.154E+03 V

e) 1.270E+03 V

4)

What is the net capacitance if C₁=2.25 μF, C₂=4.16 μF, and C₃=2.49 μF in the configuration shown?

a) 2.698E+00 μF

b) 2.968E+00 μF

c) 3.265E+00 μF

d) 3.591E+00 μF

e) 3.950E+00 μF

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =38 C and $\tau =$ 0.0167 s. What is the current at $t=$ 0.0183 s?

a) 5.715E+02 A

b) 6.286E+02 A

c) 6.915E+02 A

d) 7.606E+02 A

e) 8.367E+02 A

6)

Two sources of emf ε₁=38.9 V, and ε₂=16.9 V are oriented as shownin the circuit. The resistances are R₁=3.3 kΩ and R₂=2.51 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.34 mA and I₄=0.955 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 7.031E+00 V

b) 7.734E+00 V

c) 8.507E+00 V

d) 9.358E+00 V

e) 1.029E+01 V

7) A charged particle in a magnetic field of 4.480E-04 T is moving perpendicular to the magnetic field with a speed of 7.700E+05 m/s. What is the period of orbit if orbital radius is 0.368 m?

a) 2.730E-06 s

b) 3.003E-06 s

c) 3.303E-06 s

d) 3.633E-06 s

e) 3.997E-06 s

8) Two parallel wires each carry a 7.68 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.36 cm, 1.58 cm), while the other is located at (5.29 cm, 5.18 cm). What is the force per unit length between the wires?

a) 1.973E-10 N/m

b) 2.170E-10 N/m

c) 2.387E-10 N/m

d) 2.625E-10 N/m

e) 2.888E-10 N/m

9) A square coil has sides that are L= 0.738 m long and is tightly wound with N=717 turns of wire. The resistance of the coil is R=5.25 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0655 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.660E+00 A

b) 4.027E+00 A

c) 4.429E+00 A

d) 4.872E+00 A

e) 5.359E+00 A

10) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?

a) 6.166E-04 s

b) 6.783E-04 s

c) 7.461E-04 s

d) 8.207E-04 s

e) 9.028E-04 s

11) The output of an ac generator connected to an RLC series combination has a frequency of 3.50E+04 Hz and an amplitude of 8 V. If R =7 Ω, L= 9.40E-03H , and C=8.50E-06 F, what is the rms power transferred to the resistor?

a) 2.111E-03 Watts

b) 2.323E-03 Watts

c) 2.555E-03 Watts

d) 2.810E-03 Watts

e) 3.091E-03 Watts

12)

A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=4.00E+03 m² and separation d=4.70E-03 m is connected via a swith to a 38 Ω resistor and a battery of voltage V₀=28 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=8.10E-04?

a) 3.351E-02 A

b) 3.686E-02 A

c) 4.054E-02 A

d) 4.460E-02 A

e) 4.906E-02 A

T11 P1

1)

A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m² and separation d=4.60E-03 m is connected via a swith to a 96 Ω resistor and a battery of voltage V₀=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?

a) 7.315E-02 A

b) 8.047E-02 A

c) 8.851E-02 A

d) 9.737E-02 A

e) 1.071E-01 A

2)

What is the net capacitance if C₁=2.55 μF, C₂=4.13 μF, and C₃=2.5 μF in the configuration shown?

a) 4.077E+00 μF

b) 4.484E+00 μF

c) 4.933E+00 μF

d) 5.426E+00 μF

e) 5.969E+00 μF

3)

Two sources of emf ε₁=52.7 V, and ε₂=17.5 V are oriented as shownin the circuit. The resistances are R₁=5.86 kΩ and R₂=2.08 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.48 mA and I₄=0.988 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 2.064E+01 V

b) 2.270E+01 V

c) 2.497E+01 V

d) 2.747E+01 V

e) 3.021E+01 V

4) Two parallel wires each carry a 6.53 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.82 cm, 1.17 cm), while the other is located at (4.07 cm, 5.5 cm). What is the force per unit length between the wires?

a) 1.788E-10 N/m

b) 1.966E-10 N/m

c) 2.163E-10 N/m

d) 2.379E-10 N/m

e) 2.617E-10 N/m

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =16 C and $\tau =$ 0.0214 s. What is the current at $t=$ 0.0207 s?

a) 2.135E+02 A

b) 2.349E+02 A

c) 2.584E+02 A

d) 2.842E+02 A

e) 3.126E+02 A

6) A charged particle in a magnetic field of 3.600E-04 T is moving perpendicular to the magnetic field with a speed of 5.960E+05 m/s. What is the period of orbit if orbital radius is 0.397 m?

a) 3.805E-06 s

b) 4.185E-06 s

c) 4.604E-06 s

d) 5.064E-06 s

e) 5.571E-06 s

7)

A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.48 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.8 cm, y=2.24 cm)? Note that following the textbook's example, the y-value of the field point at 2.24 cm matches the disance of the positive charge above the x-axis.

a) 5.134E+02 V

b) 5.648E+02 V

c) 6.212E+02 V

d) 6.834E+02 V

e) 7.517E+02 V

8) In an LC circuit, the self-inductance is 0.0126 H and the capacitance is 3.350E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.420E-05 C. How long does it take for the capacitor to become completely discharged?

a) 2.204E-04 s

b) 2.425E-04 s

c) 2.667E-04 s

d) 2.934E-04 s

e) 3.227E-04 s

9) A square coil has sides that are L= 0.547 m long and is tightly wound with N=198 turns of wire. The resistance of the coil is R=4.62 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0768 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 8.953E-01 A

b) 9.848E-01 A

c) 1.083E+00 A

d) 1.192E+00 A

e) 1.311E+00 A

10) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.571E+01 N/C

b) 2.828E+01 N/C

c) 3.111E+01 N/C

d) 3.422E+01 N/C

e) 3.765E+01 N/C

11) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 6.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

a) 2.007E-03 Watts

b) 2.208E-03 Watts

c) 2.429E-03 Watts

d) 2.672E-03 Watts

e) 2.939E-03 Watts

12) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.5 (r≤R) where a=2 nC·m^-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?

a) 2.285E+01 N/C

b) 2.514E+01 N/C

c) 2.765E+01 N/C

d) 3.042E+01 N/C

e) 3.346E+01 N/C

T11 P2

1)

A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=6.10E+03 m² and separation d=7.40E-03 m is connected via a swith to a 18 Ω resistor and a battery of voltage V₀=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.20E-04?

a) 6.259E-02 A

b) 6.885E-02 A

c) 7.573E-02 A

d) 8.331E-02 A

e) 9.164E-02 A

2) The output of an ac generator connected to an RLC series combination has a frequency of 4.30E+04 Hz and an amplitude of 6 V. If R =6 Ω, L= 5.20E-03H , and C=8.60E-06 F, what is the rms power transferred to the resistor?

a) 1.511E-03 Watts

b) 1.662E-03 Watts

c) 1.828E-03 Watts

d) 2.011E-03 Watts

e) 2.212E-03 Watts

3)

A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.3 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.86 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.

a) 6.325E+02 V

b) 6.957E+02 V

c) 7.653E+02 V

d) 8.418E+02 V

e) 9.260E+02 V

4) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =52 C and $\tau =$ 0.018 s. What is the current at $t=$ 0.0207 s?

a) 6.872E+02 A

b) 7.560E+02 A

c) 8.316E+02 A

d) 9.147E+02 A

e) 1.006E+03 A

5) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 9.546E+01 N/C

b) 1.050E+02 N/C

c) 1.155E+02 N/C

d) 1.271E+02 N/C

e) 1.398E+02 N/C

6)

What is the net capacitance if C₁=2.55 μF, C₂=4.13 μF, and C₃=2.5 μF in the configuration shown?

a) 4.077E+00 μF

b) 4.484E+00 μF

c) 4.933E+00 μF

d) 5.426E+00 μF

e) 5.969E+00 μF

7)

Two sources of emf ε₁=38.9 V, and ε₂=16.9 V are oriented as shownin the circuit. The resistances are R₁=3.3 kΩ and R₂=2.51 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.34 mA and I₄=0.955 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 7.031E+00 V

b) 7.734E+00 V

c) 8.507E+00 V

d) 9.358E+00 V

e) 1.029E+01 V

8) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?

a) 2.977E-11 N/m

b) 3.274E-11 N/m

c) 3.602E-11 N/m

d) 3.962E-11 N/m

e) 4.358E-11 N/m

9) A square coil has sides that are L= 0.219 m long and is tightly wound with N=508 turns of wire. The resistance of the coil is R=8.42 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0619 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.791E-01 A

b) 1.970E-01 A

c) 2.167E-01 A

d) 2.384E-01 A

e) 2.622E-01 A

10) A charged particle in a magnetic field of 4.090E-04 T is moving perpendicular to the magnetic field with a speed of 5.980E+05 m/s. What is the period of orbit if orbital radius is 0.633 m?

a) 4.543E-06 s

b) 4.997E-06 s

c) 5.497E-06 s

d) 6.046E-06 s

e) 6.651E-06 s

11) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.5 (r≤R) where a=2 nC·m^-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?

a) 2.285E+01 N/C

b) 2.514E+01 N/C

c) 2.765E+01 N/C

d) 3.042E+01 N/C

e) 3.346E+01 N/C

12) In an LC circuit, the self-inductance is 0.0237 H and the capacitance is 6.140E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.260E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.093E-04 s

b) 4.502E-04 s

c) 4.952E-04 s

d) 5.447E-04 s

e) 5.992E-04 s

T11 Q0

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

a) 2.964E+00 N/C

b) 3.260E+00 N/C

c) 3.586E+00 N/C

d) 3.944E+00 N/C

e) 4.339E+00 N/C

3) A 12.0 V battery can move 49,000 C of charge. How many Joules does it deliver?

a) 5.880E+05 J

b) 6.468E+05 J

c) 7.115E+05 J

d) 7.826E+05 J

e) 8.609E+05 J

4) An empty parallel-plate capacitor with metal plates has an area of 1.81 m², separated by 1.26 mm. How much charge does it store if the voltage is 4.610E+03 V?

a) 4.005E+01 μC

b) 4.405E+01 μC

c) 4.846E+01 μC

d) 5.330E+01 μC

e) 5.864E+01 μC

5) A make-believe metal has a density of 1.430E+04 kg/m³ and an atomic mass of 37.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

a) 1.882E+29 e⁻/m³

b) 2.070E+29 e⁻/m³

c) 2.277E+29 e⁻/m³

d) 2.505E+29 e⁻/m³

e) 2.756E+29 e⁻/m³

6)

The resistances in the figure shown are R₁= 1.1 Ω, R₂= 1.55 Ω, and R₂= 2.11 Ω. V₁ and V₃ are text 0.545 V and 3.22 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.744 V. What is the absolute value of the current through R₁?

a) 1.886E-01 A

b) 2.075E-01 A

c) 2.282E-01 A

d) 2.510E-01 A

e) 2.761E-01 A

7) A 11 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.809 T. What current is required to maintain this balance?

a) 1.432E+00 A

b) 1.575E+00 A

c) 1.732E+00 A

d) 1.905E+00 A

e) 2.096E+00 A

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.38 kA, I₂=0.839 kA, and I₃=2.27 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 4.354E-03 T-m

b) 4.789E-03 T-m

c) 5.268E-03 T-m

d) 5.795E-03 T-m

e) 6.374E-03 T-m

9) A long solenoid has a radius of 0.644 m and 20 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 27 s⁻¹.What is the induced electric fied at a distance 2.84 m from the axis at time t=0.083 s ?

a) 3.353E-05 V/m

b) 3.689E-05 V/m

c) 4.058E-05 V/m

d) 4.463E-05 V/m

e) 4.910E-05 V/m

10) In an LC circuit, the self-inductance is 0.0262 H and the capacitance is 4.540E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 4.700E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.070E-04 s

b) 4.477E-04 s

c) 4.925E-04 s

d) 5.417E-04 s

e) 5.959E-04 s

11) A step-down transformer steps 14 kV down to 210 V. The high-voltage input is provided by a 240 Ω power line that carries 3 A of currentWhat is the output current (at the 210 V side ?)

a) 2.000E+02 A

b) 2.200E+02 A

c) 2.420E+02 A

d) 2.662E+02 A

e) 2.928E+02 A

12) What is the radiation force on an object that is 3.80E+11 m away from the sun and has cross-sectional area of 0.094 m²? The average power output of the Sun is 3.80E+26 W.

a) 8.969E-08 N

b) 9.866E-08 N

c) 1.085E-07 N

d) 1.194E-07 N

e) 1.313E-07 N

T11 Q1

1) A make-believe metal has a density of 7.000E+03 kg/m³ and an atomic mass of 89.4 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

a) 3.219E+28 e⁻/m³

b) 3.541E+28 e⁻/m³

c) 3.896E+28 e⁻/m³

d) 4.285E+28 e⁻/m³

e) 4.714E+28 e⁻/m³

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 9.546E+01 N/C

b) 1.050E+02 N/C

c) 1.155E+02 N/C

d) 1.271E+02 N/C

e) 1.398E+02 N/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.3 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.5 m from the center of the shells?

a) 1.994E+01 N/C

b) 2.194E+01 N/C

c) 2.413E+01 N/C

d) 2.655E+01 N/C

e) 2.920E+01 N/C

4) What is the radiation force on an object that is 5.40E+11 m away from the sun and has cross-sectional area of 0.021 m²? The average power output of the Sun is 3.80E+26 W.

a) 9.923E-09 N

b) 1.092E-08 N

c) 1.201E-08 N

d) 1.321E-08 N

e) 1.453E-08 N

5) In an LC circuit, the self-inductance is 0.0273 H and the capacitance is 6.440E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.620E-05 C. How long does it take for the capacitor to become completely discharged?

a) 5.443E-04 s

b) 5.988E-04 s

c) 6.586E-04 s

d) 7.245E-04 s

e) 7.969E-04 s

6)

The resistances in the figure shown are R₁= 2.73 Ω, R₂= 1.4 Ω, and R₂= 2.35 Ω. V₁ and V₃ are text 0.549 V and 1.27 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.584 V. What is the absolute value of the current through R₁?

a) 1.213E-01 A

b) 1.334E-01 A

c) 1.468E-01 A

d) 1.614E-01 A

e) 1.776E-01 A

7) A long solenoid has a radius of 0.644 m and 20 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 27 s⁻¹.What is the induced electric fied at a distance 2.84 m from the axis at time t=0.083 s ?

a) 3.353E-05 V/m

b) 3.689E-05 V/m

c) 4.058E-05 V/m

d) 4.463E-05 V/m

e) 4.910E-05 V/m

8) A step-down transformer steps 15 kV down to 250 V. The high-voltage input is provided by a 130 Ω power line that carries 4 A of currentWhat is the output current (at the 250 V side ?)

a) 1.983E+02 A

b) 2.182E+02 A

c) 2.400E+02 A

d) 2.640E+02 A

e) 2.904E+02 A

9) A 97 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 7 g, and the magnitude of the magnetic field is 0.753 T. What current is required to maintain this balance?

a) 7.056E-02 A

b) 7.762E-02 A

c) 8.538E-02 A

d) 9.392E-02 A

e) 1.033E-01 A

10) An empty parallel-plate capacitor with metal plates has an area of 2.84 m², separated by 1.42 mm. How much charge does it store if the voltage is 1.510E+03 V?

a) 1.826E+01 μC

b) 2.009E+01 μC

c) 2.210E+01 μC

d) 2.431E+01 μC

e) 2.674E+01 μC

11)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.84 kA, I₂=3.3 kA, and I₃=5.85 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 5.598E-03 T-m

b) 6.158E-03 T-m

c) 6.773E-03 T-m

d) 7.451E-03 T-m

e) 8.196E-03 T-m

12) A 12.0 V battery can move 44,000 C of charge. How many Joules does it deliver?

a) 4.800E+05 J

b) 5.280E+05 J

c) 5.808E+05 J

d) 6.389E+05 J

e) 7.028E+05 J

T11 Q2

1) A make-believe metal has a density of 1.510E+04 kg/m³ and an atomic mass of 33.6 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

a) 2.236E+29 e⁻/m³

b) 2.459E+29 e⁻/m³

c) 2.705E+29 e⁻/m³

d) 2.976E+29 e⁻/m³

e) 3.274E+29 e⁻/m³

2) A step-down transformer steps 8 kV down to 220 V. The high-voltage input is provided by a 110 Ω power line that carries 8 A of currentWhat is the output current (at the 220 V side ?)

a) 2.404E+02 A

b) 2.645E+02 A

c) 2.909E+02 A

d) 3.200E+02 A

e) 3.520E+02 A

3)

The resistances in the figure shown are R₁= 1.57 Ω, R₂= 1.25 Ω, and R₂= 3.38 Ω. V₁ and V₃ are text 0.585 V and 2.91 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.55 V. What is the absolute value of the current through R₁?

a) 1.427E-01 A

b) 1.569E-01 A

c) 1.726E-01 A

d) 1.899E-01 A

e) 2.089E-01 A

4) A 62 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.351 T. What current is required to maintain this balance?

a) 3.999E-01 A

b) 4.398E-01 A

c) 4.838E-01 A

d) 5.322E-01 A

e) 5.854E-01 A

5)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.38 kA, I₂=1.58 kA, and I₃=4.31 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 4.386E-03 T-m

b) 4.825E-03 T-m

c) 5.307E-03 T-m

d) 5.838E-03 T-m

e) 6.421E-03 T-m

6) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

a) 1.491E+01 N/C

b) 1.640E+01 N/C

c) 1.804E+01 N/C

d) 1.984E+01 N/C

e) 2.182E+01 N/C

7) What is the radiation force on an object that is 9.90E+11 m away from the sun and has cross-sectional area of 0.083 m²? The average power output of the Sun is 3.80E+26 W.

a) 1.167E-08 N

b) 1.284E-08 N

c) 1.412E-08 N

d) 1.553E-08 N

e) 1.708E-08 N

8) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 1.694E+02 N/C

b) 1.864E+02 N/C

c) 2.050E+02 N/C

d) 2.255E+02 N/C

e) 2.480E+02 N/C

9) A long solenoid has a radius of 0.887 m and 43 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 28 s⁻¹.What is the induced electric fied at a distance 2.66 m from the axis at time t=0.0332 s ?

a) 6.182E-04 V/m

b) 6.801E-04 V/m

c) 7.481E-04 V/m

d) 8.229E-04 V/m

e) 9.052E-04 V/m

10) An empty parallel-plate capacitor with metal plates has an area of 1.94 m², separated by 1.27 mm. How much charge does it store if the voltage is 8.780E+03 V?

a) 1.080E+02 μC

b) 1.188E+02 μC

c) 1.306E+02 μC

d) 1.437E+02 μC

e) 1.581E+02 μC

11) In an LC circuit, the self-inductance is 0.0795 H and the capacitance is 7.930E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 2.420E-05 C. How long does it take for the capacitor to become completely discharged?

a) 9.370E-04 s

b) 1.031E-03 s

c) 1.134E-03 s

d) 1.247E-03 s

e) 1.372E-03 s

12) A 12.0 V battery can move 32,000 C of charge. How many Joules does it deliver?

a) 2.885E+05 J

b) 3.174E+05 J

c) 3.491E+05 J

d) 3.840E+05 J

e) 4.224E+05 J

T11 R0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=1e

,

q_{2}=-9e

, and

q_{3}=4e

?

a) 5.014E-14 N

b) 5.515E-14 N

c) 6.067E-14 N

d) 6.674E-14 N

e) 7.341E-14 N

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.9 m, y=y₁=5.3 m, z=z₀=1.4 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 14.0m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 9.8m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.270E+01 N·m²/C

b) 6.897E+01 N·m²/C

c) 7.586E+01 N·m²/C

d) 8.345E+01 N·m²/C

e) 9.179E+01 N·m²/C

3) A 7 C charge is separated from a 15 C charge by distance of 14 cm. What is the work done by increasing this separation to 20 cm?

a) 1.519E-06 J

b) 1.671E-06 J

c) 1.838E-06 J

d) 2.022E-06 J

e) 2.224E-06 J

4)

In the figure shown C₁=15.0 μF, C₂=2.65 μF, and C₃=5.67 μF. The voltage source provides ε=7.44 V. What is the charge on C₁?

a) 3.982E+01 μC

b) 4.380E+01 μC

c) 4.818E+01 μC

d) 5.300E+01 μC

e) 5.829E+01 μC

5) What is the average current involved when a truck battery sets in motion 738 C of charge in 3.87 s while starting an engine?

a) 1.907E+02 A

b) 2.098E+02 A

c) 2.307E+02 A

d) 2.538E+02 A

e) 2.792E+02 A

6)

Two sources of emf ε₁=39.2 V, and ε₂=12.6 V are oriented as shownin the circuit. The resistances are R₁=3.86 kΩ and R₂=1.89 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=4.05 mA and I₄=0.701 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 8.687E+00 V

b) 9.555E+00 V

c) 1.051E+01 V

d) 1.156E+01 V

e) 1.272E+01 V

7) A circular current loop of radius 2.84 cm carries a current of 3.01 mA. What is the magnitude of the torque if the dipole is oriented at 63 ° to a uniform magnetic fied of 0.174 T?

a) 1.075E-06 N m

b) 1.182E-06 N m

c) 1.301E-06 N m

d) 1.431E-06 N m

e) 1.574E-06 N m

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.61 kA, I₂=2.2 kA, and I₃=5.1 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 3.644E-03 T-m

b) 4.009E-03 T-m

c) 4.410E-03 T-m

d) 4.850E-03 T-m

e) 5.336E-03 T-m

9) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 3.31 T and $\omega =$ 8.360E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.547 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

a) 7.145E+04 V

b) 7.860E+04 V

c) 8.646E+04 V

d) 9.510E+04 V

e) 1.046E+05 V

10) An induced emf of 7.87V is measured across a coil of 66 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.05A in 0.781s. What is the self-inductance of the coil?

a) 7.926E-01 H

b) 8.718E-01 H

c) 9.590E-01 H

d) 1.055E+00 H

e) 1.160E+00 H

11) An ac generator produces an emf of amplitude 7 V at a frequency of 95 Hz. What is the maximum amplitude of the current if the generator is connected to a 50 mF capacitor?

a) 1.427E-01 A

b) 1.570E-01 A

c) 1.727E-01 A

d) 1.899E-01 A

e) 2.089E-01 A

12) What is the radiation force on an object that is 1.20E+11 m away from the sun and has cross-sectional area of 0.055 m²? The average power output of the Sun is 3.80E+26 W.

a) 5.263E-07 N

b) 5.789E-07 N

c) 6.368E-07 N

d) 7.005E-07 N

e) 7.705E-07 N

T11 R1

1) An ac generator produces an emf of amplitude 90 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 16 mF capacitor?

a) 4.351E-01 A

b) 4.786E-01 A

c) 5.264E-01 A

d) 5.791E-01 A

e) 6.370E-01 A

2)

In the figure shown C₁=17.7 μF, C₂=2.5 μF, and C₃=5.0 μF. The voltage source provides ε=12.8 V. What is the charge on C₁?

a) 5.066E+01 μC

b) 5.573E+01 μC

c) 6.130E+01 μC

d) 6.743E+01 μC

e) 7.417E+01 μC

3)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=3e

?

a) 1.473E-14 N

b) 1.620E-14 N

c) 1.782E-14 N

d) 1.960E-14 N

e) 2.156E-14 N

4) A circular current loop of radius 2.99 cm carries a current of 4.54 mA. What is the magnitude of the torque if the dipole is oriented at 34 ° to a uniform magnetic fied of 0.107 T?

a) 7.629E-07 N m

b) 8.392E-07 N m

c) 9.232E-07 N m

d) 1.015E-06 N m

e) 1.117E-06 N m

5) A 2 C charge is separated from a 10 C charge by distance of 10 cm. What is the work done by increasing this separation to 16 cm?

a) 6.128E-07 J

b) 6.741E-07 J

c) 7.415E-07 J

d) 8.156E-07 J

e) 8.972E-07 J

6) An induced emf of 5.08V is measured across a coil of 78 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.07A in 0.681s. What is the self-inductance of the coil?

a) 4.660E-01 H

b) 5.127E-01 H

c) 5.639E-01 H

d) 6.203E-01 H

e) 6.823E-01 H

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.5 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.9 m, z=z₀=1.1 m, and z=z₁=5.3 m. The surfaces in the yz plane each have area 15.0m². Those in the xy plane have area 8.8m² ,and those in the zx plane have area 10.0m². An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.439E+01 N·m²/C

b) 5.983E+01 N·m²/C

c) 6.581E+01 N·m²/C

d) 7.239E+01 N·m²/C

e) 7.963E+01 N·m²/C

8) What is the average current involved when a truck battery sets in motion 669 C of charge in 4.3 s while starting an engine?

a) 1.063E+02 A

b) 1.169E+02 A

c) 1.286E+02 A

d) 1.414E+02 A

e) 1.556E+02 A

9) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 3.71 T and $\omega =$ 6.600E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.31 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

a) 4.769E+04 V

b) 5.246E+04 V

c) 5.771E+04 V

d) 6.348E+04 V

e) 6.983E+04 V

10)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.82 kA, I₂=0.964 kA, and I₃=2.21 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 1.069E-03 T-m

b) 1.176E-03 T-m

c) 1.294E-03 T-m

d) 1.423E-03 T-m

e) 1.566E-03 T-m

11)

Two sources of emf ε₁=26.8 V, and ε₂=10.1 V are oriented as shownin the circuit. The resistances are R₁=2.2 kΩ and R₂=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.29 mA and I₄=0.464 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 3.436E+00 V

b) 3.779E+00 V

c) 4.157E+00 V

d) 4.573E+00 V

e) 5.030E+00 V

12) What is the radiation force on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.044 m²? The average power output of the Sun is 3.80E+26 W.

a) 7.088E-09 N

b) 7.796E-09 N

c) 8.576E-09 N

d) 9.434E-09 N

e) 1.038E-08 N

T11 R2

1) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?

a) 2.549E-01 H

b) 2.804E-01 H

c) 3.084E-01 H

d) 3.392E-01 H

e) 3.732E-01 H

2)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=2e

,

q_{2}=-8e

, and

q_{3}=3e

?

a) 2.036E-14 N

b) 2.240E-14 N

c) 2.464E-14 N

d) 2.710E-14 N

e) 2.981E-14 N

3)

Two sources of emf ε₁=30.6 V, and ε₂=12.0 V are oriented as shownin the circuit. The resistances are R₁=3.46 kΩ and R₂=2.77 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.97 mA and I₄=0.643 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 4.986E+00 V

b) 5.484E+00 V

c) 6.033E+00 V

d) 6.636E+00 V

e) 7.299E+00 V

4) A 7 C charge is separated from a 15 C charge by distance of 14 cm. What is the work done by increasing this separation to 20 cm?

a) 1.519E-06 J

b) 1.671E-06 J

c) 1.838E-06 J

d) 2.022E-06 J

e) 2.224E-06 J

5) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

a) 1.170E+00 A

b) 1.287E+00 A

c) 1.415E+00 A

d) 1.557E+00 A

e) 1.713E+00 A

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 2.18 T and $\omega =$ 4.840E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.387 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

a) 1.928E+04 V

b) 2.120E+04 V

c) 2.332E+04 V

d) 2.566E+04 V

e) 2.822E+04 V

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.9 m, y=y₁=5.3 m, z=z₀=1.4 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 14.0m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 9.8m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.270E+01 N·m²/C

b) 6.897E+01 N·m²/C

c) 7.586E+01 N·m²/C

d) 8.345E+01 N·m²/C

e) 9.179E+01 N·m²/C

8) What is the radiation force on an object that is 5.40E+11 m away from the sun and has cross-sectional area of 0.021 m²? The average power output of the Sun is 3.80E+26 W.

a) 9.923E-09 N

b) 1.092E-08 N

c) 1.201E-08 N

d) 1.321E-08 N

e) 1.453E-08 N

9) A circular current loop of radius 1.56 cm carries a current of 2.57 mA. What is the magnitude of the torque if the dipole is oriented at 38 ° to a uniform magnetic fied of 0.79 T?

a) 7.898E-07 N m

b) 8.688E-07 N m

c) 9.557E-07 N m

d) 1.051E-06 N m

e) 1.156E-06 N m

10) What is the average current involved when a truck battery sets in motion 572 C of charge in 3.33 s while starting an engine?

a) 1.173E+02 A

b) 1.291E+02 A

c) 1.420E+02 A

d) 1.562E+02 A

e) 1.718E+02 A

11)

In the figure shown C₁=17.9 μF, C₂=2.71 μF, and C₃=4.14 μF. The voltage source provides ε=7.12 V. What is the charge on C₁?

a) 3.527E+01 μC

b) 3.880E+01 μC

c) 4.268E+01 μC

d) 4.695E+01 μC

e) 5.164E+01 μC

12)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.51 kA, I₂=1.32 kA, and I₃=2.73 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 1.331E-03 T-m

b) 1.464E-03 T-m

c) 1.611E-03 T-m

d) 1.772E-03 T-m

e) 1.949E-03 T-m

T11 S0

1) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 4.492E+01 N/C

b) 4.941E+01 N/C

c) 5.435E+01 N/C

d) 5.979E+01 N/C

e) 6.577E+01 N/C

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.8 m, z=z₀=1.1 m, and z=z₁=5.2 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 12.0m² ,and those in the zx plane have area 11.0m². An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.606E+01 N·m²/C

b) 6.167E+01 N·m²/C

c) 6.784E+01 N·m²/C

d) 7.462E+01 N·m²/C

e) 8.208E+01 N·m²/C

3)

An electron gun has parallel plates separated by 4.2 cm and gives electrons 51 keV of energy. What force would the field between the plates exert on a 0.84 μC charge that gets between the plates?

a) 8.430E-01 N

b) 9.273E-01 N

c) 1.020E+00 N

d) 1.122E+00 N

e) 1.234E+00 N

4) An empty parallel-plate capacitor with metal plates has an area of 1.94 m², separated by 1.27 mm. How much charge does it store if the voltage is 8.780E+03 V?

a) 1.080E+02 μC

b) 1.188E+02 μC

c) 1.306E+02 μC

d) 1.437E+02 μC

e) 1.581E+02 μC

5) Calculate the drift speed of electrons in a copper wire with a diameter of 2.17 mm carrying a 19.4 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

a) 3.569E-04 m/s

b) 3.926E-04 m/s

c) 4.319E-04 m/s

d) 4.750E-04 m/s

e) 5.226E-04 m/s

6)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 554 V. If the combined external and internal resistance is 228 &Omega and the capacitance is 93 mF, how long will it take for the capacitor's voltage to reach 450.0 V?

a) 3.224E+01 s

b) 3.547E+01 s

c) 3.902E+01 s

d) 4.292E+01 s

e) 4.721E+01 s

7) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 3.43 mT and 4.670E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 1.362E+06 m/s

b) 1.498E+06 m/s

c) 1.647E+06 m/s

d) 1.812E+06 m/s

e) 1.993E+06 m/s

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.32 kA, I₂=2.0 kA, and I₃=3.66 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 1.724E-03 T-m

b) 1.896E-03 T-m

c) 2.086E-03 T-m

d) 2.295E-03 T-m

e) 2.524E-03 T-m

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to $(5.62)e^{-\alpha t}$ , where $\alpha =$ 9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

a) 7.890E-01 A

b) 8.679E-01 A

c) 9.547E-01 A

d) 1.050E+00 A

e) 1.155E+00 A

10) A washer has an inner diameter of 2.21 cm and an outer diamter of 4.5 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.29mm$ , and $n=2.62$ . What is the volume of the washer?

a) 1.325E+00 cm³

b) 1.457E+00 cm³

c) 1.603E+00 cm³

d) 1.763E+00 cm³

e) 1.939E+00 cm³

11) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.8 V. The resistance, inductance, and capacitance are R =7 Ω, L= 4.90E-03H , and C=8.50E-04 F, respectively. What is the amplitude of the current?

a) 1.039E-01 A

b) 1.143E-01 A

c) 1.257E-01 A

d) 1.383E-01 A

e) 1.521E-01 A

12)

A parallel plate capacitor with a capicatnce C=6.60E-06 F whose plates have an area A=4.90E+03 m² and separation d=6.60E-03 m is connected via a swith to a 20 Ω resistor and a battery of voltage V₀=59 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.70E-04?

a) 8.138E-01 A

b) 8.952E-01 A

c) 9.847E-01 A

d) 1.083E+00 A

e) 1.191E+00 A

T11 S1

1) A washer has an inner diameter of 2.46 cm and an outer diamter of 4.24 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.32mm$ , and $n=2.63$ . What is the volume of the washer?

a) 7.499E-01 cm³

b) 8.249E-01 cm³

c) 9.074E-01 cm³

d) 9.982E-01 cm³

e) 1.098E+00 cm³

2)

An electron gun has parallel plates separated by 3.39 cm and gives electrons 57 keV of energy. What force would the field between the plates exert on a 0.218 μC charge that gets between the plates?

a) 3.029E-01 N

b) 3.332E-01 N

c) 3.665E-01 N

d) 4.032E-01 N

e) 4.435E-01 N

3)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 130 V. If the combined external and internal resistance is 109 &Omega and the capacitance is 59 mF, how long will it take for the capacitor's voltage to reach 69.9 V?

a) 3.728E+00 s

b) 4.101E+00 s

c) 4.511E+00 s

d) 4.962E+00 s

e) 5.458E+00 s

4) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.82 V. The resistance, inductance, and capacitance are R =3 Ω, L= 6.20E-03H , and C=6.70E-04 F, respectively. What is the amplitude of the current?

a) 2.259E-01 A

b) 2.485E-01 A

c) 2.733E-01 A

d) 3.007E-01 A

e) 3.307E-01 A

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.274 m. The magnetic field is spatially uniform but decays in time according to $(1.84)e^{-\alpha t}$ , where $\alpha =$ 9.59 s. What is the current in the coil if the impedance of the coil is 33.0 Ω?

a) 7.007E-02 A

b) 7.708E-02 A

c) 8.479E-02 A

d) 9.327E-02 A

e) 1.026E-01 A

6) An empty parallel-plate capacitor with metal plates has an area of 2.1 m², separated by 1.13 mm. How much charge does it store if the voltage is 1.680E+03 V?

a) 2.764E+01 μC

b) 3.041E+01 μC

c) 3.345E+01 μC

d) 3.679E+01 μC

e) 4.047E+01 μC

7)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=1.00E+04 m² and separation d=9.00E-03 m is connected via a swith to a 15 Ω resistor and a battery of voltage V₀=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?

a) 6.394E-02 A

b) 7.033E-02 A

c) 7.736E-02 A

d) 8.510E-02 A

e) 9.361E-02 A

8) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

9) Calculate the drift speed of electrons in a copper wire with a diameter of 3.3 mm carrying a 18.5 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

a) 1.472E-04 m/s

b) 1.619E-04 m/s

c) 1.781E-04 m/s

d) 1.959E-04 m/s

e) 2.155E-04 m/s

10) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 2.62 mT and 2.120E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 8.092E+05 m/s

b) 8.901E+05 m/s

c) 9.791E+05 m/s

d) 1.077E+06 m/s

e) 1.185E+06 m/s

11)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.44 kA, I₂=1.1 kA, and I₃=1.99 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 1.017E-03 T-m

b) 1.118E-03 T-m

c) 1.230E-03 T-m

d) 1.353E-03 T-m

e) 1.489E-03 T-m

12)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.7 m. The other four surfaces are rectangles in y=y₀=1.9 m, y=y₁=4.3 m, z=z₀=1.7 m, and z=z₁=5.7 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 4.1m² ,and those in the zx plane have area 6.8m². An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 7.876E+01 N·m²/C

b) 8.664E+01 N·m²/C

c) 9.531E+01 N·m²/C

d) 1.048E+02 N·m²/C

e) 1.153E+02 N·m²/C

T11 S2

1)

An electron gun has parallel plates separated by 4.24 cm and gives electrons 48 keV of energy. What force would the field between the plates exert on a 0.48 μC charge that gets between the plates?

a) 5.434E-01 N

b) 5.977E-01 N

c) 6.575E-01 N

d) 7.233E-01 N

e) 7.956E-01 N

2)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.66 kA, I₂=1.25 kA, and I₃=2.74 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

a) 1.547E-03 T-m

b) 1.702E-03 T-m

c) 1.872E-03 T-m

d) 2.060E-03 T-m

e) 2.266E-03 T-m

3) Calculate the drift speed of electrons in a copper wire with a diameter of 3.3 mm carrying a 18.5 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

a) 1.472E-04 m/s

b) 1.619E-04 m/s

c) 1.781E-04 m/s

d) 1.959E-04 m/s

e) 2.155E-04 m/s

4)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 467 V. If the combined external and internal resistance is 172 &Omega and the capacitance is 74 mF, how long will it take for the capacitor's voltage to reach 258.0 V?

a) 7.688E+00 s

b) 8.457E+00 s

c) 9.303E+00 s

d) 1.023E+01 s

e) 1.126E+01 s

5) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

6) A washer has an inner diameter of 2.37 cm and an outer diamter of 4.84 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.67mm$ , and $n=2.56$ . What is the volume of the washer?

a) 1.570E+00 cm³

b) 1.727E+00 cm³

c) 1.900E+00 cm³

d) 2.090E+00 cm³

e) 2.299E+00 cm³

7) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.44 V. The resistance, inductance, and capacitance are R =7 Ω, L= 5.40E-03H , and C=5.70E-04 F, respectively. What is the amplitude of the current?

a) 4.723E-02 A

b) 5.195E-02 A

c) 5.714E-02 A

d) 6.286E-02 A

e) 6.914E-02 A

8)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.2 m, y=y₁=4.2 m, z=z₀=1.2 m, and z=z₁=4.1 m. The surfaces in the yz plane each have area 8.7m². Those in the xy plane have area 7.2m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 4.024E+01 N·m²/C

b) 4.426E+01 N·m²/C

c) 4.868E+01 N·m²/C

d) 5.355E+01 N·m²/C

e) 5.891E+01 N·m²/C

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to $(5.62)e^{-\alpha t}$ , where $\alpha =$ 9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

a) 7.890E-01 A

b) 8.679E-01 A

c) 9.547E-01 A

d) 1.050E+00 A

e) 1.155E+00 A

10)

A parallel plate capacitor with a capicatnce C=4.40E-06 F whose plates have an area A=1.80E+03 m² and separation d=3.60E-03 m is connected via a swith to a 87 Ω resistor and a battery of voltage V₀=61 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.70E-04?

a) 8.320E-02 A

b) 9.152E-02 A

c) 1.007E-01 A

d) 1.107E-01 A

e) 1.218E-01 A

11) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 7.67 mT and 4.260E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 5.554E+05 m/s

b) 6.110E+05 m/s

c) 6.720E+05 m/s

d) 7.393E+05 m/s

e) 8.132E+05 m/s

12) An empty parallel-plate capacitor with metal plates has an area of 2.78 m², separated by 1.16 mm. How much charge does it store if the voltage is 8.980E+03 V?

a) 1.432E+02 μC

b) 1.575E+02 μC

c) 1.732E+02 μC

d) 1.906E+02 μC

e) 2.096E+02 μC

T11 T0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=4.2{\text{ m}}$ .

a) 5.134E-01 V/m²

b) 5.648E-01 V/m²

c) 6.212E-01 V/m²

d) 6.834E-01 V/m²

e) 7.517E-01 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.6 m. The other four surfaces are rectangles in y=y₀=1.2 m, y=y₁=5.6 m, z=z₀=1.2 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 14.0m². Those in the xy plane have area 11.0m² ,and those in the zx plane have area 8.3m². An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 4.809E+01 N·m²/C

b) 5.290E+01 N·m²/C

c) 5.819E+01 N·m²/C

d) 6.401E+01 N·m²/C

e) 7.041E+01 N·m²/C

3)

A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.57 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.59 cm, y=1.78 cm)? Note that following the textbook's example, the y-value of the field point at 1.78 cm matches the disance of the positive charge above the x-axis.

a) 2.727E+02 V

b) 2.999E+02 V

c) 3.299E+02 V

d) 3.629E+02 V

e) 3.992E+02 V

4)

In the figure shown C₁=18.1 μF, C₂=2.13 μF, and C₃=5.48 μF. The voltage source provides ε=14.6 V. What is the energy stored in C₂?

a) 1.645E+01 μJ

b) 1.809E+01 μJ

c) 1.990E+01 μJ

d) 2.189E+01 μJ

e) 2.408E+01 μJ

5) What is consumer cost to operate one 89−W incandescent bulb for 10 hours per day for 1 year (365 days) if the cost of electricity is $0.141 per kilowatt-hour?

a) $3.785E+01

b) $4.164E+01

c) $4.580E+01

d) $5.038E+01

e) $5.542E+01

6)

Two sources of emf ε₁=44.4 V, and ε₂=16.8 V are oriented as shownin the circuit. The resistances are R₁=4.58 kΩ and R₂=1.2 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=8.43 mA and I₄=1.46 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

a) 6.970E+00 mA

b) 7.667E+00 mA

c) 8.434E+00 mA

d) 9.277E+00 mA

e) 1.020E+01 mA

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 9.82 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(7.64 i + 4.85 j + 6.02 k) x 10⁴ m/s?

a) 1.386E-13 N

b) 1.524E-13 N

c) 1.676E-13 N

d) 1.844E-13 N

e) 2.029E-13 N

8) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 533 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

7.512E+02

b)

\chi {\text{ (chi) }}=

8.264E+02

c)

\chi {\text{ (chi) }}=

9.090E+02

d)

\chi {\text{ (chi) }}=

9.999E+02

e)

\chi {\text{ (chi) }}=

1.100E+03

9) The current through the windings of a solenoid with n= 2.060E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 68 cm long and has a cross-sectional diameter of 2.96 cm. A small coil consisting of N=29turns wraped in a circle of diameter 1.74 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.463E-04 V

b) 1.609E-04 V

c) 1.770E-04 V

d) 1.947E-04 V

e) 2.142E-04 V

10) An induced emf of 6.78V is measured across a coil of 58 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.98A in 0.726s. What is the self-inductance of the coil?

a) 1.022E+00 H

b) 1.124E+00 H

c) 1.237E+00 H

d) 1.360E+00 H

e) 1.496E+00 H

11) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

a) 5.042E+00 A

b) 5.546E+00 A

c) 6.100E+00 A

d) 6.710E+00 A

e) 7.381E+00 A

12)

A parallel plate capacitor with a capicatnce C=2.90E-06 F whose plates have an area A=1.60E+03 m² and separation d=5.00E-03 m is connected via a swith to a 41 Ω resistor and a battery of voltage V₀=92 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=4.50E-04?

a) 6.755E+01 V

b) 7.431E+01 V

c) 8.174E+01 V

d) 8.991E+01 V

e) 9.890E+01 V

T11 T1

1) An ac generator produces an emf of amplitude 7 V at a frequency of 95 Hz. What is the maximum amplitude of the current if the generator is connected to a 50 mF capacitor?

a) 1.427E-01 A

b) 1.570E-01 A

c) 1.727E-01 A

d) 1.899E-01 A

e) 2.089E-01 A

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 533 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

7.512E+02

b)

\chi {\text{ (chi) }}=

8.264E+02

c)

\chi {\text{ (chi) }}=

9.090E+02

d)

\chi {\text{ (chi) }}=

9.999E+02

e)

\chi {\text{ (chi) }}=

1.100E+03

3)

In the figure shown C₁=18.2 μF, C₂=2.44 μF, and C₃=5.0 μF. The voltage source provides ε=7.78 V. What is the energy stored in C₂?

a) 1.225E+01 μJ

b) 1.347E+01 μJ

c) 1.482E+01 μJ

d) 1.630E+01 μJ

e) 1.793E+01 μJ

4)

Two sources of emf ε₁=40.6 V, and ε₂=13.5 V are oriented as shownin the circuit. The resistances are R₁=4.35 kΩ and R₂=2.44 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.73 mA and I₄=0.78 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

a) 1.332E+00 mA

b) 1.465E+00 mA

c) 1.612E+00 mA

d) 1.773E+00 mA

e) 1.950E+00 mA

5)

A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.17 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.

a) 5.261E+02 V

b) 5.787E+02 V

c) 6.365E+02 V

d) 7.002E+02 V

e) 7.702E+02 V

6)

A parallel plate capacitor with a capicatnce C=7.40E-06 F whose plates have an area A=5.30E+03 m² and separation d=6.30E-03 m is connected via a swith to a 5 Ω resistor and a battery of voltage V₀=58 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.10E-04?

a) 4.548E+01 V

b) 5.003E+01 V

c) 5.503E+01 V

d) 6.054E+01 V

e) 6.659E+01 V

7) The current through the windings of a solenoid with n= 2.590E+03 turns per meter is changing at a rate dI/dt=11 A/s. The solenoid is 95 cm long and has a cross-sectional diameter of 2.29 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.15 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 6.985E-05 V

b) 7.683E-05 V

c) 8.452E-05 V

d) 9.297E-05 V

e) 1.023E-04 V

8) What is consumer cost to operate one 73−W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.113 per kilowatt-hour?

a) $3.312E+01

b) $3.643E+01

c) $4.007E+01

d) $4.408E+01

e) $4.849E+01

9) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7{\text{ m}}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=5.8{\text{ m}}$ .

a) 3.722E-01 V/m²

b) 4.094E-01 V/m²

c) 4.504E-01 V/m²

d) 4.954E-01 V/m²

e) 5.450E-01 V/m²

10)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.8 m. The other four surfaces are rectangles in y=y₀=1.1 m, y=y₁=4.9 m, z=z₀=1.3 m, and z=z₁=5.6 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 6.8m² ,and those in the zx plane have area 7.7m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.898E+01 N·m²/C

b) 7.588E+01 N·m²/C

c) 8.347E+01 N·m²/C

d) 9.181E+01 N·m²/C

e) 1.010E+02 N·m²/C

11) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 7.83 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(6.16 i + 2.1 j + 1.74 k) x 10⁴ m/s?

a) 4.783E-14 N

b) 5.262E-14 N

c) 5.788E-14 N

d) 6.367E-14 N

e) 7.003E-14 N

12) An induced emf of 4.02V is measured across a coil of 85 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.53A in 0.438s. What is the self-inductance of the coil?

a) 4.535E-01 H

b) 4.988E-01 H

c) 5.487E-01 H

d) 6.035E-01 H

e) 6.639E-01 H

T11 T2

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.8 m, z=z₀=1.3 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 13.0m². Those in the xy plane have area 9.8m² ,and those in the zx plane have area 7.4m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 8.457E+01 N·m²/C

b) 9.303E+01 N·m²/C

c) 1.023E+02 N·m²/C

d) 1.126E+02 N·m²/C

e) 1.238E+02 N·m²/C

2) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 4.6 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(1.92 i + 1.55 j + 6.22 k) x 10⁴ m/s?

a) 2.074E-14 N

b) 2.282E-14 N

c) 2.510E-14 N

d) 2.761E-14 N

e) 3.037E-14 N

3) What is consumer cost to operate one 65−W incandescent bulb for 12 hours per day for 1 year (365 days) if the cost of electricity is $0.134 per kilowatt-hour?

a) $2.866E+01

b) $3.153E+01

c) $3.468E+01

d) $3.815E+01

e) $4.196E+01

4)

A parallel plate capacitor with a capicatnce C=6.20E-06 F whose plates have an area A=5.30E+03 m² and separation d=7.50E-03 m is connected via a swith to a 95 Ω resistor and a battery of voltage V₀=15 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=9.20E-04?

a) 8.097E+00 V

b) 8.906E+00 V

c) 9.797E+00 V

d) 1.078E+01 V

e) 1.185E+01 V

5) The current through the windings of a solenoid with n= 2.040E+03 turns per meter is changing at a rate dI/dt=19 A/s. The solenoid is 76 cm long and has a cross-sectional diameter of 3.23 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.67 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 2.204E-04 V

b) 2.425E-04 V

c) 2.667E-04 V

d) 2.934E-04 V

e) 3.227E-04 V

6) An ac generator produces an emf of amplitude 87 V at a frequency of 44 Hz. What is the maximum amplitude of the current if the generator is connected to a 9 mF capacitor?

a) 1.626E-01 A

b) 1.789E-01 A

c) 1.968E-01 A

d) 2.165E-01 A

e) 2.381E-01 A

7)

Two sources of emf ε₁=44.4 V, and ε₂=16.8 V are oriented as shownin the circuit. The resistances are R₁=4.58 kΩ and R₂=1.2 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=8.43 mA and I₄=1.46 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

a) 6.970E+00 mA

b) 7.667E+00 mA

c) 8.434E+00 mA

d) 9.277E+00 mA

e) 1.020E+01 mA

8) An induced emf of 5.33V is measured across a coil of 77 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.57A in 0.648s. What is the self-inductance of the coil?

a) 4.779E-01 H

b) 5.257E-01 H

c) 5.783E-01 H

d) 6.361E-01 H

e) 6.997E-01 H

9)

A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.39 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.56 cm, y=2.19 cm)? Note that following the textbook's example, the y-value of the field point at 2.19 cm matches the disance of the positive charge above the x-axis.

a) 3.852E+02 V

b) 4.238E+02 V

c) 4.661E+02 V

d) 5.127E+02 V

e) 5.640E+02 V

10)

In the figure shown C₁=17.6 μF, C₂=2.12 μF, and C₃=4.72 μF. The voltage source provides ε=5.35 V. What is the energy stored in C₂?

a) 6.750E+00 μJ

b) 7.425E+00 μJ

c) 8.168E+00 μJ

d) 8.984E+00 μJ

e) 9.883E+00 μJ

11) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 533 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

7.512E+02

b)

\chi {\text{ (chi) }}=

8.264E+02

c)

\chi {\text{ (chi) }}=

9.090E+02

d)

\chi {\text{ (chi) }}=

9.999E+02

e)

\chi {\text{ (chi) }}=

1.100E+03

12) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$ .

a) 2.567E+01 V/m²

b) 2.824E+01 V/m²

c) 3.106E+01 V/m²

d) 3.417E+01 V/m²

e) 3.759E+01 V/m²

T11 U0

1)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.8 (r≤R) where a=2 nC·m^-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.079E+02 N/C

b) 2.287E+02 N/C

c) 2.516E+02 N/C

d) 2.767E+02 N/C

e) 3.044E+02 N/C

3) A 5 C charge is separated from a 9 C charge by distance of 14 cm. What is the work done by increasing this separation to 18 cm?

a) 4.385E-07 J

b) 4.823E-07 J

c) 5.306E-07 J

d) 5.836E-07 J

e) 6.420E-07 J

4)

In the figure shown C₁=19.0 μF, C₂=2.35 μF, and C₃=5.22 μF. The voltage source provides ε=6.01 V. What is the charge on C₁?

a) 2.444E+01 μC

b) 2.689E+01 μC

c) 2.958E+01 μC

d) 3.253E+01 μC

e) 3.579E+01 μC

5) What is consumer cost to operate one 57−W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.146 per kilowatt-hour?

a) $2.282E+01

b) $2.510E+01

c) $2.761E+01

d) $3.038E+01

e) $3.341E+01

6) A battery with a terminal voltage of 10.6 V is connected to a circuit consisting of 2 21.1 Ω resistors and one 12.8 Ω resistor. What is the voltage drop across the 12.8 Ω resistor?

a) 2.467E+00 V

b) 2.714E+00 V

c) 2.985E+00 V

d) 3.283E+00 V

e) 3.612E+00 V

7) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.96 mT and 2.010E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 2.768E+05 m/s

b) 3.045E+05 m/s

c) 3.349E+05 m/s

d) 3.684E+05 m/s

e) 4.052E+05 m/s

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.253 m and $B_{max}=\,$ 0.489 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.112 m that is centered on the axis with its plane perpendicular to the axis?

a) 1.289E+05 A

b) 1.418E+05 A

c) 1.560E+05 A

d) 1.716E+05 A

e) 1.888E+05 A

9) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 2.34 T and $\omega =$ 2.670E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.646 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

a) 1.905E+04 V

b) 2.096E+04 V

c) 2.305E+04 V

d) 2.536E+04 V

e) 2.790E+04 V

10)

A long solenoid has a length 0.605 meters, radius 4.26 cm, and 597 turns. It surrounds coil of radius 9.08 meters and 12turns. If the current in the solenoid is changing at a rate of 250 A/s, what is the emf induced in the surounding coil?

a) 4.551E-02 V

b) 5.006E-02 V

c) 5.507E-02 V

d) 6.057E-02 V

e) 6.663E-02 V

11) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.12 V. The resistance, inductance, and capacitance are R =3 Ω, L= 8.80E-03H , and C=6.40E-04 F, respectively. What is the amplitude of the current?

a) 2.732E-02 A

b) 3.005E-02 A

c) 3.306E-02 A

d) 3.636E-02 A

e) 4.000E-02 A

12)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 23 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?

a) 2.877E+00 V

b) 3.165E+00 V

c) 3.481E+00 V

d) 3.829E+00 V

e) 4.212E+00 V

T11 U1

1)

A parallel plate capacitor with a capicatnce C=1.80E-06 F whose plates have an area A=670.0 m² and separation d=3.30E-03 m is connected via a swith to a 40 Ω resistor and a battery of voltage V₀=97 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.40E-04?

a) 7.731E+01 V

b) 8.504E+01 V

c) 9.354E+01 V

d) 1.029E+02 V

e) 1.132E+02 V

2) What is consumer cost to operate one 74−W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.119 per kilowatt-hour?

a) $1.976E+01

b) $2.173E+01

c) $2.391E+01

d) $2.630E+01

e) $2.893E+01

3)

In the figure shown C₁=16.0 μF, C₂=2.27 μF, and C₃=4.4 μF. The voltage source provides ε=7.11 V. What is the charge on C₁?

a) 2.515E+01 μC

b) 2.766E+01 μC

c) 3.043E+01 μC

d) 3.347E+01 μC

e) 3.682E+01 μC

4) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 3.58 T and $\omega =$ 4.310E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.879 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

a) 7.043E+04 V

b) 7.747E+04 V

c) 8.522E+04 V

d) 9.374E+04 V

e) 1.031E+05 V

5) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.645 m and $B_{max}=\,$ 0.469 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.26 m that is centered on the axis with its plane perpendicular to the axis?

a) 2.949E+05 A

b) 3.244E+05 A

c) 3.568E+05 A

d) 3.925E+05 A

e) 4.317E+05 A

6) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 8.971E+05 m/s

b) 9.868E+05 m/s

c) 1.085E+06 m/s

d) 1.194E+06 m/s

e) 1.313E+06 m/s

7)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

8) A battery with a terminal voltage of 12.4 V is connected to a circuit consisting of 3 21.6 Ω resistors and one 12.1 Ω resistor. What is the voltage drop across the 12.1 Ω resistor?

a) 1.333E+00 V

b) 1.466E+00 V

c) 1.612E+00 V

d) 1.774E+00 V

e) 1.951E+00 V

9) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C

b) 2.501E+02 N/C

c) 2.751E+02 N/C

d) 3.026E+02 N/C

e) 3.329E+02 N/C

10)

A long solenoid has a length 0.923 meters, radius 4.08 cm, and 579 turns. It surrounds coil of radius 6.86 meters and 14turns. If the current in the solenoid is changing at a rate of 139 A/s, what is the emf induced in the surounding coil?

a) 1.894E-02 V

b) 2.083E-02 V

c) 2.291E-02 V

d) 2.520E-02 V

e) 2.772E-02 V

11) A 4 C charge is separated from a 9 C charge by distance of 9 cm. What is the work done by increasing this separation to 14 cm?

a) 8.769E-07 J

b) 9.646E-07 J

c) 1.061E-06 J

d) 1.167E-06 J

e) 1.284E-06 J

12) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.16 V. The resistance, inductance, and capacitance are R =8 Ω, L= 5.40E-03H , and C=5.40E-04 F, respectively. What is the amplitude of the current?

a) 2.000E-02 A

b) 2.200E-02 A

c) 2.420E-02 A

d) 2.662E-02 A

e) 2.928E-02 A

T11 U2

1) A battery with a terminal voltage of 8.41 V is connected to a circuit consisting of 3 16.1 Ω resistors and one 10.9 Ω resistor. What is the voltage drop across the 10.9 Ω resistor?

a) 1.058E+00 V

b) 1.163E+00 V

c) 1.280E+00 V

d) 1.408E+00 V

e) 1.548E+00 V

2)

In the figure shown C₁=15.4 μF, C₂=2.22 μF, and C₃=4.77 μF. The voltage source provides ε=6.8 V. What is the charge on C₁?

a) 2.702E+01 μC

b) 2.972E+01 μC

c) 3.269E+01 μC

d) 3.596E+01 μC

e) 3.956E+01 μC

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

4) A 7 C charge is separated from a 12 C charge by distance of 9 cm. What is the work done by increasing this separation to 15 cm?

a) 2.292E-06 J

b) 2.521E-06 J

c) 2.773E-06 J

d) 3.050E-06 J

e) 3.355E-06 J

5) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.7 (r≤R) where a=3 nC·m^-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 1.390E+03 N/C

b) 1.530E+03 N/C

c) 1.682E+03 N/C

d) 1.851E+03 N/C

e) 2.036E+03 N/C

6)

A parallel plate capacitor with a capicatnce C=7.10E-06 F whose plates have an area A=5.10E+03 m² and separation d=6.40E-03 m is connected via a swith to a 54 Ω resistor and a battery of voltage V₀=83 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-03?

a) 6.111E+01 V

b) 6.722E+01 V

c) 7.395E+01 V

d) 8.134E+01 V

e) 8.947E+01 V

7) What is consumer cost to operate one 89−W incandescent bulb for 10 hours per day for 1 year (365 days) if the cost of electricity is $0.141 per kilowatt-hour?

a) $3.785E+01

b) $4.164E+01

c) $4.580E+01

d) $5.038E+01

e) $5.542E+01

8) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.77 V. The resistance, inductance, and capacitance are R =3 Ω, L= 6.70E-03H , and C=7.10E-04 F, respectively. What is the amplitude of the current?

a) 2.333E-01 A

b) 2.567E-01 A

c) 2.823E-01 A

d) 3.106E-01 A

e) 3.416E-01 A

9)

A long solenoid has a length 0.923 meters, radius 4.08 cm, and 579 turns. It surrounds coil of radius 6.86 meters and 14turns. If the current in the solenoid is changing at a rate of 139 A/s, what is the emf induced in the surounding coil?

a) 1.894E-02 V

b) 2.083E-02 V

c) 2.291E-02 V

d) 2.520E-02 V

e) 2.772E-02 V

10) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.96 mT and 2.010E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 2.768E+05 m/s

b) 3.045E+05 m/s

c) 3.349E+05 m/s

d) 3.684E+05 m/s

e) 4.052E+05 m/s

11) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 1.97 T and $\omega =$ 5.410E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.244 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

a) 1.485E+04 V

b) 1.634E+04 V

c) 1.797E+04 V

d) 1.977E+04 V

e) 2.175E+04 V

12) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.736 m and $B_{max}=\,$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.532 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.764E+05 A

b) 4.140E+05 A

c) 4.554E+05 A

d) 5.010E+05 A

e) 5.510E+05 A

T11 V0

1)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.1 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.6 m, z=z₀=1.8 m, and z=z₁=4.2 m. The surfaces in the yz plane each have area 9.4m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 5.0m². An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 2.186E+01 N·m²/C

b) 2.404E+01 N·m²/C

c) 2.645E+01 N·m²/C

d) 2.909E+01 N·m²/C

e) 3.200E+01 N·m²/C

3) When a 6.97 V battery operates a 2.6 W bulb, how many electrons pass through it each second?

a) 1.749E+18 electrons

b) 1.924E+18 electrons

c) 2.117E+18 electrons

d) 2.328E+18 electrons

e) 2.561E+18 electrons

4)

In the figure shown C₁=20.6 μF, C₂=2.38 μF, and C₃=5.66 μF. The voltage source provides ε=12.6 V. What is the charge on C₁?

a) 5.474E+01 μC

b) 6.022E+01 μC

c) 6.624E+01 μC

d) 7.287E+01 μC

e) 8.015E+01 μC

5) What is the average current involved when a truck battery sets in motion 669 C of charge in 4.3 s while starting an engine?

a) 1.063E+02 A

b) 1.169E+02 A

c) 1.286E+02 A

d) 1.414E+02 A

e) 1.556E+02 A

6)

Two sources of emf ε₁=16.8 V, and ε₂=7.15 V are oriented as shownin the circuit. The resistances are R₁=3.12 kΩ and R₂=1.51 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.95 mA and I₄=0.603 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 4.108E+00 V

b) 4.519E+00 V

c) 4.970E+00 V

d) 5.468E+00 V

e) 6.014E+00 V

7) A charged particle in a magnetic field of 3.350E-04 T is moving perpendicular to the magnetic field with a speed of 4.350E+05 m/s. What is the period of orbit if orbital radius is 0.841 m?

a) 1.004E-05 s

b) 1.104E-05 s

c) 1.215E-05 s

d) 1.336E-05 s

e) 1.470E-05 s

8)

Three wires sit at the corners of a square of length 0.495 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.45 A, 1.66 A, 1.63 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 1.205E-04 T

b) B_y= 1.325E-04 T

c) B_y= 1.458E-04 T

d) B_y= 1.604E-04 T

e) B_y= 1.764E-04 T

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.477 m. The magnetic field is spatially uniform but decays in time according to $(4.67)e^{-\alpha t}$ , where $\alpha =$ 8.01 s. What is the current in the coil if the impedance of the coil is 75.6 Ω?

a) 2.215E-01 A

b) 2.437E-01 A

c) 2.681E-01 A

d) 2.949E-01 A

e) 3.244E-01 A

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?

a) -1.700E+00 s

b) -1.870E+00 s

c) -2.057E+00 s

d) -2.262E+00 s

e) -2.489E+00 s

11) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, X_L, X_C). Since Q is calculatedat resonance, X_L, X_C and only twoimpedances are involved, Q=≡ω₀L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V₀sin(ωt), where V₀=2 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 5.40E-03H , and C=3.20E-06 F, respectively.

a) Q = 9.395E+01

b) Q = 1.080E+02

c) Q = 1.242E+02

d) Q = 1.429E+02

e) Q = 1.643E+02

12) What is the radiation force on an object that is 5.40E+11 m away from the sun and has cross-sectional area of 0.021 m²? The average power output of the Sun is 3.80E+26 W.

a) 9.923E-09 N

b) 1.092E-08 N

c) 1.201E-08 N

d) 1.321E-08 N

e) 1.453E-08 N

T11 V1

1)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

a) 5.352E+09 N/C²

b) 5.887E+09 N/C²

c) 6.476E+09 N/C²

d) 7.124E+09 N/C²

e) 7.836E+09 N/C²

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to $(5.62)e^{-\alpha t}$ , where $\alpha =$ 9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

a) 7.890E-01 A

b) 8.679E-01 A

c) 9.547E-01 A

d) 1.050E+00 A

e) 1.155E+00 A

3)

Two sources of emf ε₁=26.8 V, and ε₂=10.1 V are oriented as shownin the circuit. The resistances are R₁=2.2 kΩ and R₂=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.29 mA and I₄=0.464 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 3.436E+00 V

b) 3.779E+00 V

c) 4.157E+00 V

d) 4.573E+00 V

e) 5.030E+00 V

4)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?

a) -1.700E+00 s

b) -1.870E+00 s

c) -2.057E+00 s

d) -2.262E+00 s

e) -2.489E+00 s

5) When a 7.1 V battery operates a 1.8 W bulb, how many electrons pass through it each second?

a) 1.439E+18 electrons

b) 1.582E+18 electrons

c) 1.741E+18 electrons

d) 1.915E+18 electrons

e) 2.106E+18 electrons

6)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.8 m, z=z₀=1.1 m, and z=z₁=5.2 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 12.0m² ,and those in the zx plane have area 11.0m². An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.606E+01 N·m²/C

b) 6.167E+01 N·m²/C

c) 6.784E+01 N·m²/C

d) 7.462E+01 N·m²/C

e) 8.208E+01 N·m²/C

7) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m²? The average power output of the Sun is 3.80E+26 W.

a) 5.275E-07 N

b) 5.803E-07 N

c) 6.383E-07 N

d) 7.021E-07 N

e) 7.723E-07 N

8)

In the figure shown C₁=18.0 μF, C₂=2.88 μF, and C₃=5.34 μF. The voltage source provides ε=11.9 V. What is the charge on C₁?

a) 5.045E+01 μC

b) 5.550E+01 μC

c) 6.105E+01 μC

d) 6.715E+01 μC

e) 7.387E+01 μC

9) A charged particle in a magnetic field of 4.480E-04 T is moving perpendicular to the magnetic field with a speed of 7.700E+05 m/s. What is the period of orbit if orbital radius is 0.368 m?

a) 2.730E-06 s

b) 3.003E-06 s

c) 3.303E-06 s

d) 3.633E-06 s

e) 3.997E-06 s

10) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, X_L, X_C). Since Q is calculatedat resonance, X_L, X_C and only twoimpedances are involved, Q=≡ω₀L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V₀sin(ωt), where V₀=3 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 4.70E-03H , and C=3.30E-06 F, respectively.

a) Q = 1.313E+02

b) Q = 1.510E+02

c) Q = 1.736E+02

d) Q = 1.996E+02

e) Q = 2.296E+02

11)

Three wires sit at the corners of a square of length 0.699 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.87 A, 2.18 A, 1.34 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 6.999E-05 T

b) B_y= 7.699E-05 T

c) B_y= 8.469E-05 T

d) B_y= 9.316E-05 T

e) B_y= 1.025E-04 T

12) What is the average current involved when a truck battery sets in motion 760 C of charge in 5.35 s while starting an engine?

a) 1.291E+02 A

b) 1.421E+02 A

c) 1.563E+02 A

d) 1.719E+02 A

e) 1.891E+02 A

T11 V2

1)

Two sources of emf ε₁=49.8 V, and ε₂=18.1 V are oriented as shownin the circuit. The resistances are R₁=2.78 kΩ and R₂=2.63 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.51 mA and I₄=0.969 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

a) 7.886E+00 V

b) 8.675E+00 V

c) 9.542E+00 V

d) 1.050E+01 V

e) 1.155E+01 V

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.1 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.6 m, z=z₀=1.8 m, and z=z₁=4.2 m. The surfaces in the yz plane each have area 9.4m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 5.0m². An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 2.186E+01 N·m²/C

b) 2.404E+01 N·m²/C

c) 2.645E+01 N·m²/C

d) 2.909E+01 N·m²/C

e) 3.200E+01 N·m²/C

3)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.594 m. The magnetic field is spatially uniform but decays in time according to $(2.89)e^{-\alpha t}$ , where $\alpha =$ 9.6 s. What is the current in the coil if the impedance of the coil is 6.65 Ω?

a) 2.088E+00 A

b) 2.297E+00 A

c) 2.527E+00 A

d) 2.779E+00 A

e) 3.057E+00 A

5)

Three wires sit at the corners of a square of length 0.834 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.26 A, 1.75 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 7.518E-05 T

b) B_y= 8.270E-05 T

c) B_y= 9.097E-05 T

d) B_y= 1.001E-04 T

e) B_y= 1.101E-04 T

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, X_L, X_C). Since Q is calculatedat resonance, X_L, X_C and only twoimpedances are involved, Q=≡ω₀L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V₀sin(ωt), where V₀=5 V. The resistance, inductance, and capacitance are R =0.21 Ω, L= 5.40E-03H , and C=3.20E-06 F, respectively.

a) Q = 1.286E+02

b) Q = 1.479E+02

c) Q = 1.701E+02

d) Q = 1.956E+02

e) Q = 2.250E+02

7) When a 4.89 V battery operates a 1.44 W bulb, how many electrons pass through it each second?

a) 1.838E+18 electrons

b) 2.022E+18 electrons

c) 2.224E+18 electrons

d) 2.446E+18 electrons

e) 2.691E+18 electrons

8) A charged particle in a magnetic field of 5.500E-04 T is moving perpendicular to the magnetic field with a speed of 2.930E+05 m/s. What is the period of orbit if orbital radius is 0.787 m?

a) 1.688E-05 s

b) 1.856E-05 s

c) 2.042E-05 s

d) 2.246E-05 s

e) 2.471E-05 s

9) What is the average current involved when a truck battery sets in motion 701 C of charge in 4.98 s while starting an engine?

a) 1.280E+02 A

b) 1.408E+02 A

c) 1.548E+02 A

d) 1.703E+02 A

e) 1.874E+02 A

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 2.59% of its maximum value if ε = 1.14 V , R = 6.17 Ω, and L = 5.45 H?

a) -1.614E+00 s

b) -1.775E+00 s

c) -1.952E+00 s

d) -2.148E+00 s

e) -2.362E+00 s

11)

In the figure shown C₁=17.5 μF, C₂=2.63 μF, and C₃=5.76 μF. The voltage source provides ε=15.9 V. What is the charge on C₁?

a) 8.197E+01 μC

b) 9.017E+01 μC

c) 9.919E+01 μC

d) 1.091E+02 μC

e) 1.200E+02 μC

12) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m²? The average power output of the Sun is 3.80E+26 W.

a) 2.673E-07 N

b) 2.940E-07 N

c) 3.234E-07 N

d) 3.558E-07 N

e) 3.913E-07 N

T11 W0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=3e

?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

2) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C

b) 2.501E+02 N/C

c) 2.751E+02 N/C

d) 3.026E+02 N/C

e) 3.329E+02 N/C

3)

An electron gun has parallel plates separated by 2.68 cm and gives electrons 29 keV of energy. What force would the field between the plates exert on a 0.496 μC charge that gets between the plates?

a) 5.367E-01 N

b) 5.904E-01 N

c) 6.494E-01 N

d) 7.144E-01 N

e) 7.858E-01 N

4)

In the figure shown C₁=17.5 μF, C₂=2.63 μF, and C₃=5.76 μF. The voltage source provides ε=15.9 V. What is the charge on C₁?

a) 8.197E+01 μC

b) 9.017E+01 μC

c) 9.919E+01 μC

d) 1.091E+02 μC

e) 1.200E+02 μC

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =97 C and $\tau =$ 0.0132 s. What is the current at $t=$ 0.0225 s?

a) 1.336E+03 A

b) 1.470E+03 A

c) 1.617E+03 A

d) 1.779E+03 A

e) 1.957E+03 A

6)

In the circuit shown V=17.8 V, R₁=2.27 Ω, R₂=6.79 Ω, and R₃=15.1 Ω. What is the power dissipated by R₂?

a) 1.446E+01 W

b) 1.591E+01 W

c) 1.750E+01 W

d) 1.925E+01 W

e) 2.117E+01 W

7) A 14 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 11 g, and the magnitude of the magnetic field is 0.448 T. What current is required to maintain this balance?

a) 1.174E+00 A

b) 1.291E+00 A

c) 1.420E+00 A

d) 1.562E+00 A

e) 1.719E+00 A

8) Two loops of wire carry the same current of 29 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.76 m while the other has a radius of 1.12 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.544 m from the first (smaller) loopif the disance between the loops is 1.56 m?

a) 1.950E-02 T

b) 2.145E-02 T

c) 2.360E-02 T

d) 2.596E-02 T

e) 2.855E-02 T

9) Calculate the motional emf induced along a 37.9 km conductor moving at an orbital speed of 7.84 km/s perpendicular to Earth's 5.410E-05 Tesla magnetic field.

a) 1.208E+04 V

b) 1.329E+04 V

c) 1.461E+04 V

d) 1.608E+04 V

e) 1.768E+04 V

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.65% of its maximum value if ε = 3.62 V , R = 4.07 Ω, and L = 7.19 H?

a) -2.476E+00 s

b) -2.724E+00 s

c) -2.996E+00 s

d) -3.296E+00 s

e) -3.625E+00 s

11) An ac generator produces an emf of amplitude 75 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 22 mF inductor?

a) 2.466E+00 A

b) 2.713E+00 A

c) 2.984E+00 A

d) 3.283E+00 A

e) 3.611E+00 A

12)

A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=6.10E+03 m² and separation d=7.40E-03 m is connected via a swith to a 18 Ω resistor and a battery of voltage V₀=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.20E-04?

a) 6.259E-02 A

b) 6.885E-02 A

c) 7.573E-02 A

d) 8.331E-02 A

e) 9.164E-02 A

T11 W1

1)

A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=6.80E+03 m² and separation d=8.30E-03 m is connected via a swith to a 84 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.60E-03?

a) 4.678E-04 A

b) 5.145E-04 A

c) 5.660E-04 A

d) 6.226E-04 A

e) 6.848E-04 A

2) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.5 (r≤R) where a=3 nC·m^-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.579E+02 N/C

b) 2.837E+02 N/C

c) 3.121E+02 N/C

d) 3.433E+02 N/C

e) 3.776E+02 N/C

3)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=1e

,

q_{2}=-8e

, and

q_{3}=4e

?

a) 3.719E+01 degrees

b) 4.091E+01 degrees

c) 4.500E+01 degrees

d) 4.950E+01 degrees

e) 5.445E+01 degrees

4) Calculate the motional emf induced along a 42.1 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 4.730E-05 Tesla magnetic field.

a) 1.279E+04 V

b) 1.407E+04 V

c) 1.547E+04 V

d) 1.702E+04 V

e) 1.872E+04 V

5) An ac generator produces an emf of amplitude 73 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF inductor?

a) 1.134E+00 A

b) 1.247E+00 A

c) 1.372E+00 A

d) 1.509E+00 A

e) 1.660E+00 A

6) Two loops of wire carry the same current of 39 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.49 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.552 m from the first (smaller) loopif the disance between the loops is 1.62 m?

a) 1.564E-02 T

b) 1.720E-02 T

c) 1.892E-02 T

d) 2.081E-02 T

e) 2.289E-02 T

7) A 14 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 11 g, and the magnitude of the magnetic field is 0.448 T. What current is required to maintain this balance?

a) 1.174E+00 A

b) 1.291E+00 A

c) 1.420E+00 A

d) 1.562E+00 A

e) 1.719E+00 A

8)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 2.28% of its maximum value if ε = 7.39 V , R = 7.05 Ω, and L = 3.51 H?

a) -6.429E-01 s

b) -7.072E-01 s

c) -7.779E-01 s

d) -8.557E-01 s

e) -9.412E-01 s

9)

An electron gun has parallel plates separated by 4.2 cm and gives electrons 51 keV of energy. What force would the field between the plates exert on a 0.84 μC charge that gets between the plates?

a) 8.430E-01 N

b) 9.273E-01 N

c) 1.020E+00 N

d) 1.122E+00 N

e) 1.234E+00 N

10)

In the figure shown C₁=17.9 μF, C₂=2.71 μF, and C₃=4.14 μF. The voltage source provides ε=7.12 V. What is the charge on C₁?

a) 3.527E+01 μC

b) 3.880E+01 μC

c) 4.268E+01 μC

d) 4.695E+01 μC

e) 5.164E+01 μC

11)

In the circuit shown V=15.4 V, R₁=2.55 Ω, R₂=5.12 Ω, and R₃=12.7 Ω. What is the power dissipated by R₂?

a) 1.096E+01 W

b) 1.206E+01 W

c) 1.326E+01 W

d) 1.459E+01 W

e) 1.605E+01 W

12) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =30 C and $\tau =$ 0.0178 s. What is the current at $t=$ 0.0161 s?

a) 5.125E+02 A

b) 5.638E+02 A

c) 6.201E+02 A

d) 6.822E+02 A

e) 7.504E+02 A

T11 W2

1) A 27 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.85 T. What current is required to maintain this balance?

a) 3.106E-01 A

b) 3.416E-01 A

c) 3.758E-01 A

d) 4.134E-01 A

e) 4.547E-01 A

2) Two loops of wire carry the same current of 39 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.49 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.552 m from the first (smaller) loopif the disance between the loops is 1.62 m?

a) 1.564E-02 T

b) 1.720E-02 T

c) 1.892E-02 T

d) 2.081E-02 T

e) 2.289E-02 T

3)

A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m² and separation d=4.60E-03 m is connected via a swith to a 96 Ω resistor and a battery of voltage V₀=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?

a) 7.315E-02 A

b) 8.047E-02 A

c) 8.851E-02 A

d) 9.737E-02 A

e) 1.071E-01 A

4) An ac generator produces an emf of amplitude 46 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 63 mF inductor?

a) 4.961E-01 A

b) 5.457E-01 A

c) 6.002E-01 A

d) 6.603E-01 A

e) 7.263E-01 A

5) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=3 nC·m^-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?

a) 4.874E+01 N/C

b) 5.362E+01 N/C

c) 5.898E+01 N/C

d) 6.488E+01 N/C

e) 7.137E+01 N/C

6) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =23 C and $\tau =$ 0.0204 s. What is the current at $t=$ 0.0106 s?

a) 6.096E+02 A

b) 6.706E+02 A

c) 7.376E+02 A

d) 8.114E+02 A

e) 8.925E+02 A

7)

An electron gun has parallel plates separated by 2.98 cm and gives electrons 11 keV of energy. What force would the field between the plates exert on a 0.685 μC charge that gets between the plates?

a) 1.900E-01 N

b) 2.090E-01 N

c) 2.299E-01 N

d) 2.529E-01 N

e) 2.781E-01 N

8)

In the circuit shown V=17.5 V, R₁=2.34 Ω, R₂=7.1 Ω, and R₃=15.3 Ω. What is the power dissipated by R₂?

a) 1.784E+01 W

b) 1.963E+01 W

c) 2.159E+01 W

d) 2.375E+01 W

e) 2.612E+01 W

9) Calculate the motional emf induced along a 49.5 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.310E-05 Tesla magnetic field.

a) 1.395E+04 V

b) 1.534E+04 V

c) 1.688E+04 V

d) 1.857E+04 V

e) 2.042E+04 V

10)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-9e

, and

q_{3}=5e

?

a) 6.125E+01 degrees

b) 6.738E+01 degrees

c) 7.412E+01 degrees

d) 8.153E+01 degrees

e) 8.968E+01 degrees

11)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?

a) -1.700E+00 s

b) -1.870E+00 s

c) -2.057E+00 s

d) -2.262E+00 s

e) -2.489E+00 s

12)

In the figure shown C₁=15.4 μF, C₂=2.22 μF, and C₃=4.77 μF. The voltage source provides ε=6.8 V. What is the charge on C₁?

a) 2.702E+01 μC

b) 2.972E+01 μC

c) 3.269E+01 μC

d) 3.596E+01 μC

e) 3.956E+01 μC

T11 X0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-7e

, and

q_{3}=4e

?

a) 5.377E+01 degrees

b) 5.914E+01 degrees

c) 6.506E+01 degrees

d) 7.157E+01 degrees

e) 7.872E+01 degrees

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\vec {E}}=2y^{2.0}{\hat {i}}+2x^{2.1}{\hat {j}}+3y^{2.5}{\hat {k}}$

a) 9.027E+03 V·m

b) 9.930E+03 V·m

c) 1.092E+04 V·m

d) 1.202E+04 V·m

e) 1.322E+04 V·m

3) Calculate the final speed of a free electron accelerated from rest through a potential difference of 19 V.

a) 1.942E+06 m/s

b) 2.137E+06 m/s

c) 2.350E+06 m/s

d) 2.585E+06 m/s

e) 2.844E+06 m/s

4)

In the figure shown C₁=16.9 μF, C₂=2.86 μF, and C₃=5.1 μF. The voltage source provides ε=9.98 V. What is the energy stored in C₂?

a) 1.764E+01 μJ

b) 1.940E+01 μJ

c) 2.134E+01 μJ

d) 2.348E+01 μJ

e) 2.583E+01 μJ

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =23 C and $\tau =$ 0.0204 s. What is the current at $t=$ 0.0106 s?

a) 6.096E+02 A

b) 6.706E+02 A

c) 7.376E+02 A

d) 8.114E+02 A

e) 8.925E+02 A

6) Three resistors, R₁ = 1.41 Ω, and R₂ = R₂ = 3.17 Ω, are connected in parallel to a 5.89 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 1.681E+01 W

b) 1.849E+01 W

c) 2.033E+01 W

d) 2.237E+01 W

e) 2.460E+01 W

7)

The silver ribbon shown are a=3.89 cm, b=3.43 cm, and c= 1.21 cm. The current carries a current of 77 A and it lies in a uniform magnetic field of 2.16 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

a) 1.322E-06 V

b) 1.454E-06 V

c) 1.600E-06 V

d) 1.759E-06 V

e) 1.935E-06 V

8) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 424 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

1.092E+03

b)

\chi {\text{ (chi) }}=

1.201E+03

c)

\chi {\text{ (chi) }}=

1.321E+03

d)

\chi {\text{ (chi) }}=

1.454E+03

e)

\chi {\text{ (chi) }}=

1.599E+03

9) Calculate the motional emf induced along a 30.3 km conductor moving at an orbital speed of 7.76 km/s perpendicular to Earth's 5.100E-05 Tesla magnetic field.

a) 1.090E+04 V

b) 1.199E+04 V

c) 1.319E+04 V

d) 1.451E+04 V

e) 1.596E+04 V

10) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.62 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.66mm$ , and $n=2.61$ . What is the volume of the washer?

a) 6.960E-01 cm³

b) 7.656E-01 cm³

c) 8.421E-01 cm³

d) 9.264E-01 cm³

e) 1.019E+00 cm³

11) An ac generator produces an emf of amplitude 93 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF capacitor?

a) 4.917E+00 A

b) 5.409E+00 A

c) 5.950E+00 A

d) 6.545E+00 A

e) 7.199E+00 A

12)

A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=5.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 98 Ω resistor and a battery of voltage V₀=67 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.80E-03?

a) 5.050E+03 V/m

b) 5.555E+03 V/m

c) 6.111E+03 V/m

d) 6.722E+03 V/m

e) 7.394E+03 V/m

T11 X1

1) Three resistors, R₁ = 1.43 Ω, and R₂ = R₂ = 3.25 Ω, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 5.184E+01 W

b) 5.702E+01 W

c) 6.272E+01 W

d) 6.900E+01 W

e) 7.590E+01 W

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}$

a) 2.067E+03 V·m

b) 2.274E+03 V·m

c) 2.501E+03 V·m

d) 2.752E+03 V·m

e) 3.027E+03 V·m

3) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.

a) 5.102E+06 m/s

b) 5.612E+06 m/s

c) 6.173E+06 m/s

d) 6.791E+06 m/s

e) 7.470E+06 m/s

4)

A parallel plate capacitor with a capicatnce C=1.60E-06 F whose plates have an area A=890.0 m² and separation d=4.90E-03 m is connected via a swith to a 80 Ω resistor and a battery of voltage V₀=44 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.90E-04?

a) 6.651E+03 V/m

b) 7.316E+03 V/m

c) 8.048E+03 V/m

d) 8.853E+03 V/m

e) 9.738E+03 V/m

5) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.62 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.66mm$ , and $n=2.61$ . What is the volume of the washer?

a) 6.960E-01 cm³

b) 7.656E-01 cm³

c) 8.421E-01 cm³

d) 9.264E-01 cm³

e) 1.019E+00 cm³

6)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-9e

, and

q_{3}=5e

?

a) 6.125E+01 degrees

b) 6.738E+01 degrees

c) 7.412E+01 degrees

d) 8.153E+01 degrees

e) 8.968E+01 degrees

7) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =38 C and $\tau =$ 0.0167 s. What is the current at $t=$ 0.0183 s?

a) 5.715E+02 A

b) 6.286E+02 A

c) 6.915E+02 A

d) 7.606E+02 A

e) 8.367E+02 A

8)

The silver ribbon shown are a=3.89 cm, b=2.94 cm, and c= 0.58 cm. The current carries a current of 242 A and it lies in a uniform magnetic field of 2.47 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

a) 9.911E-06 V

b) 1.090E-05 V

c) 1.199E-05 V

d) 1.319E-05 V

e) 1.451E-05 V

9) Calculate the motional emf induced along a 30.3 km conductor moving at an orbital speed of 7.76 km/s perpendicular to Earth's 5.100E-05 Tesla magnetic field.

a) 1.090E+04 V

b) 1.199E+04 V

c) 1.319E+04 V

d) 1.451E+04 V

e) 1.596E+04 V

10) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

a) 5.042E+00 A

b) 5.546E+00 A

c) 6.100E+00 A

d) 6.710E+00 A

e) 7.381E+00 A

11) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 24 turns per centimeter and the current applied to the solenoid is 595 mA, the net magnetic field is measured to be 1.46 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

6.716E+02

b)

\chi {\text{ (chi) }}=

7.387E+02

c)

\chi {\text{ (chi) }}=

8.126E+02

d)

\chi {\text{ (chi) }}=

8.939E+02

e)

\chi {\text{ (chi) }}=

9.833E+02

12)

In the figure shown C₁=19.2 μF, C₂=2.24 μF, and C₃=4.93 μF. The voltage source provides ε=11.7 V. What is the energy stored in C₂?

a) 1.303E+01 μJ

b) 1.434E+01 μJ

c) 1.577E+01 μJ

d) 1.735E+01 μJ

e) 1.908E+01 μJ

T11 X2

1) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.14mm$ , and $n=2.86$ . What is the volume of the washer?

a) 1.071E+00 cm³

b) 1.178E+00 cm³

c) 1.296E+00 cm³

d) 1.425E+00 cm³

e) 1.568E+00 cm³

2)

In the figure shown C₁=15.4 μF, C₂=2.6 μF, and C₃=5.17 μF. The voltage source provides ε=9.6 V. What is the energy stored in C₂?

a) 1.508E+01 μJ

b) 1.659E+01 μJ

c) 1.825E+01 μJ

d) 2.007E+01 μJ

e) 2.208E+01 μJ

3) Three resistors, R₁ = 0.855 Ω, and R₂ = R₂ = 1.91 Ω, are connected in parallel to a 6.97 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

a) 5.682E+01 W

b) 6.250E+01 W

c) 6.875E+01 W

d) 7.563E+01 W

e) 8.319E+01 W

4) Calculate the motional emf induced along a 32.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 5.280E-05 Tesla magnetic field.

a) 1.093E+04 V

b) 1.202E+04 V

c) 1.322E+04 V

d) 1.454E+04 V

e) 1.600E+04 V

5) Calculate the final speed of a free electron accelerated from rest through a potential difference of 12 V.

a) 1.698E+06 m/s

b) 1.868E+06 m/s

c) 2.055E+06 m/s

d) 2.260E+06 m/s

e) 2.486E+06 m/s

6) An ac generator produces an emf of amplitude 58 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 66 mF capacitor?

a) 3.976E+00 A

b) 4.373E+00 A

c) 4.810E+00 A

d) 5.291E+00 A

e) 5.821E+00 A

7) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 17 turns per centimeter and the current applied to the solenoid is 455 mA, the net magnetic field is measured to be 1.14 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

8.804E+02

b)

\chi {\text{ (chi) }}=

9.685E+02

c)

\chi {\text{ (chi) }}=

1.065E+03

d)

\chi {\text{ (chi) }}=

1.172E+03

e)

\chi {\text{ (chi) }}=

1.289E+03

8)

The silver ribbon shown are a=3.96 cm, b=3.35 cm, and c= 1.07 cm. The current carries a current of 295 A and it lies in a uniform magnetic field of 3.4 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

a) 9.015E-06 V

b) 9.916E-06 V

c) 1.091E-05 V

d) 1.200E-05 V

e) 1.320E-05 V

9) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =84 C and $\tau =$ 0.0199 s. What is the current at $t=$ 0.0104 s?

a) 2.275E+03 A

b) 2.503E+03 A

c) 2.753E+03 A

d) 3.029E+03 A

e) 3.331E+03 A

10)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-7e

, and

q_{3}=4e

?

a) 5.914E+01 degrees

b) 6.506E+01 degrees

c) 7.157E+01 degrees

d) 7.872E+01 degrees

e) 8.659E+01 degrees

11)

A parallel plate capacitor with a capicatnce C=7.90E-06 F whose plates have an area A=6.10E+03 m² and separation d=6.80E-03 m is connected via a swith to a 22 Ω resistor and a battery of voltage V₀=6 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=5.20E-04?

a) 7.619E+02 V/m

b) 8.381E+02 V/m

c) 9.219E+02 V/m

d) 1.014E+03 V/m

e) 1.115E+03 V/m

12) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
${\vec {E}}=1y^{2.4}{\hat {i}}+4x^{1.7}{\hat {j}}+4y^{2.1}{\hat {k}}$

a) 1.206E+03 V·m

b) 1.326E+03 V·m

c) 1.459E+03 V·m

d) 1.605E+03 V·m

e) 1.765E+03 V·m

T11 Y0

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

a) 6.925E+09 N/C²

b) 7.617E+09 N/C²

c) 8.379E+09 N/C²

d) 9.217E+09 N/C²

e) 1.014E+10 N/C²

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?

a) 6.641E+00 N/C

b) 7.305E+00 N/C

c) 8.036E+00 N/C

d) 8.839E+00 N/C

e) 9.723E+00 N/C

3)

A Van de Graff generator has a 116 cm diameter metal sphere that produces 246 kV near its surface. What is the excess charge on the sphere?

a) 1.193E+01 μC

b) 1.312E+01 μC

c) 1.443E+01 μC

d) 1.588E+01 μC

e) 1.746E+01 μC

4)

In the figure shown C₁=17.7 μF, C₂=2.48 μF, and C₃=4.68 μF. The voltage source provides ε=12.7 V. What is the energy stored in C₂?

a) 2.242E+01 μJ

b) 2.467E+01 μJ

c) 2.713E+01 μJ

d) 2.985E+01 μJ

e) 3.283E+01 μJ

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =63 C and $\tau =$ 0.0149 s. What is the current at $t=$ 0.0172 s?

a) 1.212E+03 A

b) 1.333E+03 A

c) 1.466E+03 A

d) 1.613E+03 A

e) 1.774E+03 A

6) A given battery has a 11 V emf and an internal resistance of 0.0998 Ω. If it is connected to a 0.417 Ω resistor what is the power dissipated by that load?

a) 1.419E+02 W

b) 1.561E+02 W

c) 1.717E+02 W

d) 1.889E+02 W

e) 2.078E+02 W

7) A 72 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 14 g, and the magnitude of the magnetic field is 0.54 T. What current is required to maintain this balance?

a) 2.651E-01 A

b) 2.916E-01 A

c) 3.208E-01 A

d) 3.529E-01 A

e) 3.882E-01 A

8)

Three wires sit at the corners of a square of length 0.823 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 6.718E-05 T

b) B_y= 7.390E-05 T

c) B_y= 8.129E-05 T

d) B_y= 8.942E-05 T

e) B_y= 9.836E-05 T

9) A long solenoid has a radius of 0.442 m and 41 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 4 A and $\alpha =$ 20 s⁻¹.What is the induced electric fied at a distance 0.2 m from the axis at time t=0.0833 s ?

a) 6.438E-05 V/m

b) 7.082E-05 V/m

c) 7.790E-05 V/m

d) 8.569E-05 V/m

e) 9.426E-05 V/m

10) An induced emf of 7.48V is measured across a coil of 95 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.33A in 0.304s. What is the self-inductance of the coil?

a) 2.914E-01 H

b) 3.205E-01 H

c) 3.526E-01 H

d) 3.878E-01 H

e) 4.266E-01 H

11) The output of an ac generator connected to an RLC series combination has a frequency of 1.00E+03 Hz and an amplitude of 0.6 V;. If R =3 Ω, L= 1.70E-03H , and C=5.40E-04 F, what is the impedance?

a) 8.123E+00 Ω

b) 8.935E+00 Ω

c) 9.828E+00 Ω

d) 1.081E+01 Ω

e) 1.189E+01 Ω

12) What is the radiation force on an object that is 7.40E+11 m away from the sun and has cross-sectional area of 0.082 m²? The average power output of the Sun is 3.80E+26 W.

a) 2.063E-08 N

b) 2.270E-08 N

c) 2.497E-08 N

d) 2.746E-08 N

e) 3.021E-08 N

T11 Y1

1)

Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 4.028E-05 T

b) B_y= 4.431E-05 T

c) B_y= 4.874E-05 T

d) B_y= 5.361E-05 T

e) B_y= 5.897E-05 T

2) A long solenoid has a radius of 0.447 m and 85 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 23 s⁻¹.What is the induced electric fied at a distance 0.212 m from the axis at time t=0.0819 s ?

a) 1.893E-04 V/m

b) 2.082E-04 V/m

c) 2.290E-04 V/m

d) 2.519E-04 V/m

e) 2.771E-04 V/m

3) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m²? The average power output of the Sun is 3.80E+26 W.

a) 2.673E-07 N

b) 2.940E-07 N

c) 3.234E-07 N

d) 3.558E-07 N

e) 3.913E-07 N

4) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =16 C and $\tau =$ 0.0214 s. What is the current at $t=$ 0.0207 s?

a) 2.135E+02 A

b) 2.349E+02 A

c) 2.584E+02 A

d) 2.842E+02 A

e) 3.126E+02 A

5) A given battery has a 12 V emf and an internal resistance of 0.107 Ω. If it is connected to a 0.814 Ω resistor what is the power dissipated by that load?

a) 1.382E+02 W

b) 1.520E+02 W

c) 1.672E+02 W

d) 1.839E+02 W

e) 2.023E+02 W

6) The output of an ac generator connected to an RLC series combination has a frequency of 680 Hz and an amplitude of 0.79 V;. If R =5 Ω, L= 2.40E-03H , and C=9.10E-04 F, what is the impedance?

a) 8.398E+00 Ω

b) 9.238E+00 Ω

c) 1.016E+01 Ω

d) 1.118E+01 Ω

e) 1.230E+01 Ω

7)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

8) A 34 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.348 T. What current is required to maintain this balance?

a) 6.626E-01 A

b) 7.289E-01 A

c) 8.018E-01 A

d) 8.819E-01 A

e) 9.701E-01 A

9)

In the figure shown C₁=16.3 μF, C₂=2.17 μF, and C₃=4.67 μF. The voltage source provides ε=8.35 V. What is the energy stored in C₂?

a) 8.718E+00 μJ

b) 9.589E+00 μJ

c) 1.055E+01 μJ

d) 1.160E+01 μJ

e) 1.276E+01 μJ

10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.3 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.5 m from the center of the shells?

a) 1.994E+01 N/C

b) 2.194E+01 N/C

c) 2.413E+01 N/C

d) 2.655E+01 N/C

e) 2.920E+01 N/C

11) An induced emf of 6.78V is measured across a coil of 58 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.98A in 0.726s. What is the self-inductance of the coil?

a) 1.022E+00 H

b) 1.124E+00 H

c) 1.237E+00 H

d) 1.360E+00 H

e) 1.496E+00 H

12)

A Van de Graff generator has a 141 cm diameter metal sphere that produces 280 kV near its surface. What is the excess charge on the sphere?

a) 1.500E+01 μC

b) 1.650E+01 μC

c) 1.815E+01 μC

d) 1.997E+01 μC

e) 2.196E+01 μC

T11 Y2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

a) 2.988E+00 N/C

b) 3.287E+00 N/C

c) 3.616E+00 N/C

d) 3.977E+00 N/C

e) 4.375E+00 N/C

2) The output of an ac generator connected to an RLC series combination has a frequency of 290 Hz and an amplitude of 0.75 V;. If R =2 Ω, L= 8.00E-03H , and C=9.90E-04 F, what is the impedance?

a) 9.675E+00 Ω

b) 1.064E+01 Ω

c) 1.171E+01 Ω

d) 1.288E+01 Ω

e) 1.416E+01 Ω

3)

In the figure shown C₁=20.7 μF, C₂=2.79 μF, and C₃=5.18 μF. The voltage source provides ε=15.0 V. What is the energy stored in C₂?

a) 2.064E+01 μJ

b) 2.270E+01 μJ

c) 2.497E+01 μJ

d) 2.747E+01 μJ

e) 3.022E+01 μJ

4) What is the radiation force on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.044 m²? The average power output of the Sun is 3.80E+26 W.

a) 7.088E-09 N

b) 7.796E-09 N

c) 8.576E-09 N

d) 9.434E-09 N

e) 1.038E-08 N

5) A long solenoid has a radius of 0.732 m and 55 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 9 A and $\alpha =$ 25 s⁻¹.What is the induced electric fied at a distance 0.203 m from the axis at time t=0.0448 s ?

a) 5.150E-04 V/m

b) 5.665E-04 V/m

c) 6.232E-04 V/m

d) 6.855E-04 V/m

e) 7.540E-04 V/m

6)

Three wires sit at the corners of a square of length 0.702 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

a) B_y= 7.576E-05 T

b) B_y= 8.333E-05 T

c) B_y= 9.167E-05 T

d) B_y= 1.008E-04 T

e) B_y= 1.109E-04 T

7) An induced emf of 7.48V is measured across a coil of 95 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.33A in 0.304s. What is the self-inductance of the coil?

a) 2.914E-01 H

b) 3.205E-01 H

c) 3.526E-01 H

d) 3.878E-01 H

e) 4.266E-01 H

8) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =38 C and $\tau =$ 0.0167 s. What is the current at $t=$ 0.0183 s?

a) 5.715E+02 A

b) 6.286E+02 A

c) 6.915E+02 A

d) 7.606E+02 A

e) 8.367E+02 A

9)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

10) A 96 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.325 T. What current is required to maintain this balance?

a) 2.596E-01 A

b) 2.855E-01 A

c) 3.141E-01 A

d) 3.455E-01 A

e) 3.801E-01 A

11) A given battery has a 14 V emf and an internal resistance of 0.198 Ω. If it is connected to a 0.534 Ω resistor what is the power dissipated by that load?

a) 1.776E+02 W

b) 1.953E+02 W

c) 2.149E+02 W

d) 2.364E+02 W

e) 2.600E+02 W

12)

A Van de Graff generator has a 95 cm diameter metal sphere that produces 190 kV near its surface. What is the excess charge on the sphere?

a) 9.129E+00 μC

b) 1.004E+01 μC

c) 1.105E+01 μC

d) 1.215E+01 μC

e) 1.337E+01 μC

T11 Z0

1)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

a) 7.415E+09 N/C²

b) 8.156E+09 N/C²

c) 8.972E+09 N/C²

d) 9.869E+09 N/C²

e) 1.086E+10 N/C²

2) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C

b) 2.501E+02 N/C

c) 2.751E+02 N/C

d) 3.026E+02 N/C

e) 3.329E+02 N/C

3)

Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.) The charges are q₁=3 μC, q₂=6 μC, q₃=9 μC, and q₄=12 μC. How much work was required to assemble these four charges from infinity?

a) 7.789E+01 J

b) 8.568E+01 J

c) 9.425E+01 J

d) 1.037E+02 J

e) 1.140E+02 J

4)

What is the net capacitance if C₁=3.54 μF, C₂=3.53 μF, and C₃=3.65 μF in the configuration shown?

a) 3.700E+00 μF

b) 4.070E+00 μF

c) 4.477E+00 μF

d) 4.925E+00 μF

e) 5.417E+00 μF

5) What is consumer cost to operate one 102−W incandescent bulb for 6 hours per day for 1 year (365 days) if the cost of electricity is $0.127 per kilowatt-hour?

a) $2.131E+01

b) $2.345E+01

c) $2.579E+01

d) $2.837E+01

e) $3.121E+01

6)

Two sources of emf ε₁=18.6 V, and ε₂=5.63 V are oriented as shownin the circuit. The resistances are R₁=3.9 kΩ and R₂=1.1 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.41 mA and I₄=0.614 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

a) 4.342E+00 V

b) 4.776E+00 V

c) 5.254E+00 V

d) 5.779E+00 V

e) 6.357E+00 V

7)

The silver ribbon shown are a=4.23 cm, b=3.7 cm, and c= 0.721 cm. The current carries a current of 144 A and it lies in a uniform magnetic field of 1.21 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

a) 1.746E-06 V

b) 1.921E-06 V

c) 2.113E-06 V

d) 2.324E-06 V

e) 2.557E-06 V

8) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 344 mA, the net magnetic field is measured to be 1.12 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

7.922E+02

b)

\chi {\text{ (chi) }}=

8.714E+02

c)

\chi {\text{ (chi) }}=

9.586E+02

d)

\chi {\text{ (chi) }}=

1.054E+03

e)

\chi {\text{ (chi) }}=

1.160E+03

9)

A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

a) 7.479E+00 cm³/s

b) 8.227E+00 cm³/s

c) 9.049E+00 cm³/s

d) 9.954E+00 cm³/s

e) 1.095E+01 cm³/s

10) A washer has an inner diameter of 2.46 cm and an outer diamter of 4.24 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.32mm$ , and $n=2.63$ . What is the volume of the washer?

a) 7.499E-01 cm³

b) 8.249E-01 cm³

c) 9.074E-01 cm³

d) 9.982E-01 cm³

e) 1.098E+00 cm³

11) The output of an ac generator connected to an RLC series combination has a frequency of 5.70E+04 Hz and an amplitude of 5 V. If R =9 Ω, L= 6.10E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

a) 9.443E-04 Watts

b) 1.039E-03 Watts

c) 1.143E-03 Watts

d) 1.257E-03 Watts

e) 1.383E-03 Watts

12) A 57 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?

a) 1.020E+02 km

b) 1.122E+02 km

c) 1.235E+02 km

d) 1.358E+02 km

e) 1.494E+02 km

T11 Z1

1) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 23 turns per centimeter and the current applied to the solenoid is 534 mA, the net magnetic field is measured to be 1.48 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

7.917E+02

b)

\chi {\text{ (chi) }}=

8.708E+02

c)

\chi {\text{ (chi) }}=

9.579E+02

d)

\chi {\text{ (chi) }}=

1.054E+03

e)

\chi {\text{ (chi) }}=

1.159E+03

2)

Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.) The charges are q₁=4 μC, q₂=7 μC, q₃=8 μC, and q₄=10 μC. How much work was required to assemble these four charges from infinity?

a) 1.241E+02 J

b) 1.365E+02 J

c) 1.501E+02 J

d) 1.652E+02 J

e) 1.817E+02 J

3)

The silver ribbon shown are a=4.12 cm, b=3.32 cm, and c= 1.46 cm. The current carries a current of 120 A and it lies in a uniform magnetic field of 1.39 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

a) 1.209E-06 V

b) 1.329E-06 V

c) 1.462E-06 V

d) 1.609E-06 V

e) 1.770E-06 V

4) The output of an ac generator connected to an RLC series combination has a frequency of 5.40E+04 Hz and an amplitude of 6 V. If R =2 Ω, L= 6.80E-03H , and C=9.90E-06 F, what is the rms power transferred to the resistor?

a) 2.452E-04 Watts

b) 2.697E-04 Watts

c) 2.967E-04 Watts

d) 3.264E-04 Watts

e) 3.590E-04 Watts

5)

Two sources of emf ε₁=36.7 V, and ε₂=13.6 V are oriented as shownin the circuit. The resistances are R₁=2.86 kΩ and R₂=2.2 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.02 mA and I₄=0.854 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

a) 1.380E+01 V

b) 1.518E+01 V

c) 1.670E+01 V

d) 1.837E+01 V

e) 2.020E+01 V

6)

A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

a) 3.093E+01 cm³/s

b) 3.403E+01 cm³/s

c) 3.743E+01 cm³/s

d) 4.117E+01 cm³/s

e) 4.529E+01 cm³/s

7) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.28mm$ , and $n=2.4$ . What is the volume of the washer?

a) 1.097E+00 cm³

b) 1.207E+00 cm³

c) 1.328E+00 cm³

d) 1.460E+00 cm³

e) 1.606E+00 cm³

8) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?

a) 1.003E+02 km

b) 1.103E+02 km

c) 1.213E+02 km

d) 1.335E+02 km

e) 1.468E+02 km

9)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

10) What is consumer cost to operate one 104−W incandescent bulb for 6 hours per day for 1 year (365 days) if the cost of electricity is $0.136 per kilowatt-hour?

a) $2.116E+01

b) $2.327E+01

c) $2.560E+01

d) $2.816E+01

e) $3.098E+01

11)

What is the net capacitance if C₁=2.96 μF, C₂=3.95 μF, and C₃=3.74 μF in the configuration shown?

a) 4.489E+00 μF

b) 4.938E+00 μF

c) 5.432E+00 μF

d) 5.975E+00 μF

e) 6.573E+00 μF

12) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=2 nC·m^-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

a) 3.821E+02 N/C

b) 4.203E+02 N/C

c) 4.624E+02 N/C

d) 5.086E+02 N/C

e) 5.594E+02 N/C

T11 Z2

1)

A cylinder of height 2.91 cm and radius 8.33 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.7 cm from point O and moves at a speed of 9.14 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

a) 2.061E+02 cm³/s

b) 2.267E+02 cm³/s

c) 2.494E+02 cm³/s

d) 2.743E+02 cm³/s

e) 3.018E+02 cm³/s

2)

The silver ribbon shown are a=3.89 cm, b=2.94 cm, and c= 0.58 cm. The current carries a current of 242 A and it lies in a uniform magnetic field of 2.47 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

a) 9.911E-06 V

b) 1.090E-05 V

c) 1.199E-05 V

d) 1.319E-05 V

e) 1.451E-05 V

3)

Two sources of emf ε₁=36.7 V, and ε₂=12.1 V are oriented as shownin the circuit. The resistances are R₁=2.52 kΩ and R₂=1.22 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=4.14 mA and I₄=1.19 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

a) 7.805E+00 V

b) 8.586E+00 V

c) 9.444E+00 V

d) 1.039E+01 V

e) 1.143E+01 V

4) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C

b) 2.501E+02 N/C

c) 2.751E+02 N/C

d) 3.026E+02 N/C

e) 3.329E+02 N/C

5) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 344 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

a)

\chi {\text{ (chi) }}=

1.185E+03

b)

\chi {\text{ (chi) }}=

1.303E+03

c)

\chi {\text{ (chi) }}=

1.433E+03

d)

\chi {\text{ (chi) }}=

1.577E+03

e)

\chi {\text{ (chi) }}=

1.734E+03

6) The output of an ac generator connected to an RLC series combination has a frequency of 4.30E+04 Hz and an amplitude of 6 V. If R =6 Ω, L= 5.20E-03H , and C=8.60E-06 F, what is the rms power transferred to the resistor?

a) 1.511E-03 Watts

b) 1.662E-03 Watts

c) 1.828E-03 Watts

d) 2.011E-03 Watts

e) 2.212E-03 Watts

7) A washer has an inner diameter of 2.6 cm and an outer diamter of 4.17 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.38mm$ , and $n=2.62$ . What is the volume of the washer?

a) 7.196E-01 cm³

b) 7.916E-01 cm³

c) 8.707E-01 cm³

d) 9.578E-01 cm³

e) 1.054E+00 cm³

8) A 58 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 88 kW?

a) 1.111E+02 km

b) 1.222E+02 km

c) 1.344E+02 km

d) 1.478E+02 km

e) 1.626E+02 km

9)

What is the net capacitance if C₁=2.96 μF, C₂=3.95 μF, and C₃=3.74 μF in the configuration shown?

a) 4.489E+00 μF

b) 4.938E+00 μF

c) 5.432E+00 μF

d) 5.975E+00 μF

e) 6.573E+00 μF

10) What is consumer cost to operate one 76−W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.144 per kilowatt-hour?

a) $3.595E+01

b) $3.955E+01

c) $4.350E+01

d) $4.785E+01

e) $5.264E+01

11)

Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.) The charges are q₁=3 μC, q₂=5 μC, q₃=6 μC, and q₄=9 μC. How much work was required to assemble these four charges from infinity?

a) 2.617E+01 J

b) 2.879E+01 J

c) 3.167E+01 J

d) 3.484E+01 J

e) 3.832E+01 J

12)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

a) 7.119E+09 N/C²

b) 7.831E+09 N/C²

c) 8.614E+09 N/C²

d) 9.476E+09 N/C²

e) 1.042E+10 N/C²

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of 10 blank lines to separate exams from keys
of 10 blank lines to separate exams from keys
of 10 blank lines to separate exams from keys
of 10 blank lines to separate exams from keys
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of 10 blank lines to separate exams from keys
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Key: A0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$ .

+a) 1.606E+00 V/m²

-b) 1.767E+00 V/m²

-c) 1.943E+00 V/m²

-d) 2.138E+00 V/m²

-e) 2.351E+00 V/m²

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}$

-a) 2.067E+03 V·m

-b) 2.274E+03 V·m

+c) 2.501E+03 V·m

-d) 2.752E+03 V·m

-e) 3.027E+03 V·m

3)

A diploe has a charge magnitude of q=4 nC and a separation distance of d=3.79 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.2 cm, y=1.9 cm)? Note that following the textbook's example, the y-value of the field point at 1.9 cm matches the disance of the positive charge above the x-axis.

-a) 2.731E+02 V

-b) 3.004E+02 V

-c) 3.304E+02 V

-d) 3.634E+02 V

+e) 3.998E+02 V

4)

In the figure shown C₁=16.0 μF, C₂=2.27 μF, and C₃=4.4 μF. The voltage source provides ε=7.11 V. What is the charge on C₁?

-a) 2.515E+01 μC

-b) 2.766E+01 μC

-c) 3.043E+01 μC

+d) 3.347E+01 μC

-e) 3.682E+01 μC

5) What is the average current involved when a truck battery sets in motion 537 C of charge in 5.08 s while starting an engine?

-a) 8.736E+01 A

-b) 9.610E+01 A

+c) 1.057E+02 A

-d) 1.163E+02 A

-e) 1.279E+02 A

6)

The resistances in the figure shown are R₁= 1.6 Ω, R₂= 1.3 Ω, and R₂= 2.22 Ω. V₁ and V₃ are text 0.55 V and 3.18 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.743 V. What is the absolute value of the current through R₁?

+a) 1.721E-01 A

-b) 1.893E-01 A

-c) 2.082E-01 A

-d) 2.291E-01 A

-e) 2.520E-01 A

7) A circular current loop of radius 1.67 cm carries a current of 3.81 mA. What is the magnitude of the torque if the dipole is oriented at 40 ° to a uniform magnetic fied of 0.884 T?

-a) 1.568E-06 N m

-b) 1.724E-06 N m

+c) 1.897E-06 N m

-d) 2.087E-06 N m

-e) 2.295E-06 N m

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.51 m and $B_{max}=\,$ 0.649 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.376 m that is centered on the axis with its plane perpendicular to the axis?

-a) 9.388E+05 A

-b) 1.033E+06 A

+c) 1.136E+06 A

-d) 1.249E+06 A

-e) 1.374E+06 A

9) A square coil has sides that are L= 0.727 m long and is tightly wound with N=376 turns of wire. The resistance of the coil is R=5.59 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0485 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 1.567E+00 A

+b) 1.724E+00 A

-c) 1.897E+00 A

-d) 2.086E+00 A

-e) 2.295E+00 A

10) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?

-a) 3.856E-04 s

-b) 4.242E-04 s

+c) 4.666E-04 s

-d) 5.133E-04 s

-e) 5.646E-04 s

11) The output of an ac generator connected to an RLC series combination has a frequency of 280 Hz and an amplitude of 0.35 V;. If R =5 Ω, L= 9.50E-03H , and C=6.90E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

-a) 8.646E-01 &rad;

-b) 9.511E-01 &rad;

-c) 1.046E+00 &rad;

-d) 1.151E+00 &rad;

+e) 1.266E+00 &rad;

12) What is the radiation force on an object that is 4.70E+11 m away from the sun and has cross-sectional area of 0.098 m²? The average power output of the Sun is 3.80E+26 W.

-a) 7.396E-08 N

-b) 8.136E-08 N

+c) 8.950E-08 N

-d) 9.845E-08 N

-e) 1.083E-07 N

Key: A1

1)

The resistances in the figure shown are R₁= 1.81 Ω, R₂= 1.18 Ω, and R₂= 2.62 Ω. V₁ and V₃ are text 0.628 V and 2.54 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.748 V. What is the absolute value of the current through R₁?

-a) 1.552E-01 A

-b) 1.707E-01 A

-c) 1.878E-01 A

-d) 2.065E-01 A

+e) 2.272E-01 A

2) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m²? The average power output of the Sun is 3.80E+26 W.

-a) 5.275E-07 N

-b) 5.803E-07 N

+c) 6.383E-07 N

-d) 7.021E-07 N

-e) 7.723E-07 N

3) What is the average current involved when a truck battery sets in motion 631 C of charge in 3.8 s while starting an engine?

+a) 1.661E+02 A

-b) 1.827E+02 A

-c) 2.009E+02 A

-d) 2.210E+02 A

-e) 2.431E+02 A

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.407 m and $B_{max}=\,$ 0.605 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.196 m that is centered on the axis with its plane perpendicular to the axis?

-a) 3.583E+05 A

-b) 3.941E+05 A

+c) 4.335E+05 A

-d) 4.769E+05 A

-e) 5.246E+05 A

5) A square coil has sides that are L= 0.738 m long and is tightly wound with N=717 turns of wire. The resistance of the coil is R=5.25 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0655 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 3.660E+00 A

-b) 4.027E+00 A

-c) 4.429E+00 A

+d) 4.872E+00 A

-e) 5.359E+00 A

6)

In the figure shown C₁=19.2 μF, C₂=2.86 μF, and C₃=5.03 μF. The voltage source provides ε=9.46 V. What is the charge on C₁?

-a) 4.809E+01 μC

+b) 5.290E+01 μC

-c) 5.819E+01 μC

-d) 6.401E+01 μC

-e) 7.041E+01 μC

7) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?

-a) 6.230E-04 s

-b) 6.853E-04 s

-c) 7.538E-04 s

-d) 8.292E-04 s

+e) 9.121E-04 s

8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}$

-a) 1.997E+03 V·m

+b) 2.197E+03 V·m

-c) 2.417E+03 V·m

-d) 2.659E+03 V·m

-e) 2.924E+03 V·m

9) The output of an ac generator connected to an RLC series combination has a frequency of 320 Hz and an amplitude of 0.69 V;. If R =6 Ω, L= 6.80E-03H , and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

+a) 1.143E+00 &rad;

-b) 1.257E+00 &rad;

-c) 1.382E+00 &rad;

-d) 1.521E+00 &rad;

-e) 1.673E+00 &rad;

10) A circular current loop of radius 1.63 cm carries a current of 2.38 mA. What is the magnitude of the torque if the dipole is oriented at 54 ° to a uniform magnetic fied of 0.125 T?

+a) 2.009E-07 N m

-b) 2.210E-07 N m

-c) 2.431E-07 N m

-d) 2.674E-07 N m

-e) 2.941E-07 N m

11) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=4.2{\text{ m}}$ .

-a) 5.134E-01 V/m²

+b) 5.648E-01 V/m²

-c) 6.212E-01 V/m²

-d) 6.834E-01 V/m²

-e) 7.517E-01 V/m²

12)

A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.17 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.

-a) 5.261E+02 V

-b) 5.787E+02 V

+c) 6.365E+02 V

-d) 7.002E+02 V

-e) 7.702E+02 V

Key: A2

1) A circular current loop of radius 1.11 cm carries a current of 4.0 mA. What is the magnitude of the torque if the dipole is oriented at 68 ° to a uniform magnetic fied of 0.173 T?

-a) 1.866E-07 N m

-b) 2.052E-07 N m

-c) 2.258E-07 N m

+d) 2.484E-07 N m

-e) 2.732E-07 N m

2) What is the average current involved when a truck battery sets in motion 572 C of charge in 3.33 s while starting an engine?

-a) 1.173E+02 A

-b) 1.291E+02 A

-c) 1.420E+02 A

-d) 1.562E+02 A

+e) 1.718E+02 A

3)

The resistances in the figure shown are R₁= 2.38 Ω, R₂= 1.87 Ω, and R₂= 2.32 Ω. V₁ and V₃ are text 0.605 V and 3.8 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.67 V. What is the absolute value of the current through R₁?

-a) 8.147E-02 A

-b) 8.962E-02 A

-c) 9.858E-02 A

+d) 1.084E-01 A

-e) 1.193E-01 A

4)

In the figure shown C₁=17.1 μF, C₂=2.87 μF, and C₃=4.74 μF. The voltage source provides ε=6.63 V. What is the charge on C₁?

-a) 2.385E+01 μC

-b) 2.623E+01 μC

-c) 2.886E+01 μC

-d) 3.174E+01 μC

+e) 3.492E+01 μC

5) What is the radiation force on an object that is 3.60E+11 m away from the sun and has cross-sectional area of 0.069 m²? The average power output of the Sun is 3.80E+26 W.

-a) 7.336E-08 N

-b) 8.069E-08 N

-c) 8.876E-08 N

-d) 9.764E-08 N

+e) 1.074E-07 N

6) In an LC circuit, the self-inductance is 0.0815 H and the capacitance is 6.520E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.410E-05 C. How long does it take for the capacitor to become completely discharged?

-a) 7.821E-04 s

-b) 8.603E-04 s

-c) 9.463E-04 s

-d) 1.041E-03 s

+e) 1.145E-03 s

7) The output of an ac generator connected to an RLC series combination has a frequency of 510 Hz and an amplitude of 0.24 V;. If R =7 Ω, L= 2.90E-03H , and C=9.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

-a) 7.495E-01 &rad;

-b) 8.244E-01 &rad;

+c) 9.068E-01 &rad;

-d) 9.975E-01 &rad;

-e) 1.097E+00 &rad;

8) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$ .

-a) 8.253E-01 V/m²

-b) 9.079E-01 V/m²

+c) 9.987E-01 V/m²

-d) 1.099E+00 V/m²

-e) 1.208E+00 V/m²

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}$

-a) 8.545E+01 V·m

-b) 9.400E+01 V·m

-c) 1.034E+02 V·m

-d) 1.137E+02 V·m

+e) 1.251E+02 V·m

10) A square coil has sides that are L= 0.219 m long and is tightly wound with N=508 turns of wire. The resistance of the coil is R=8.42 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0619 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

+a) 1.791E-01 A

-b) 1.970E-01 A

-c) 2.167E-01 A

-d) 2.384E-01 A

-e) 2.622E-01 A

11) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.736 m and $B_{max}=\,$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.532 m that is centered on the axis with its plane perpendicular to the axis?

-a) 3.764E+05 A

-b) 4.140E+05 A

-c) 4.554E+05 A

+d) 5.010E+05 A

-e) 5.510E+05 A

12)

A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.29 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.33 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.

-a) 4.324E+02 V

-b) 4.757E+02 V

+c) 5.232E+02 V

-d) 5.755E+02 V

-e) 6.331E+02 V

Key: B0

1)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate

f(x,y)

at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 6.311E+00 V/m²

-b) 6.943E+00 V/m²

+c) 7.637E+00 V/m²

-d) 8.401E+00 V/m²

-e) 9.241E+00 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.6 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.4 m, z=z₀=1.4 m, and z=z₁=5.6 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 9.6m² ,and those in the zx plane have area 11.0m². An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

+a) 8.921E+01 N·m²/C

-b) 9.813E+01 N·m²/C

-c) 1.079E+02 N·m²/C

-d) 1.187E+02 N·m²/C

-e) 1.306E+02 N·m²/C

3) If a 28 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=77 V is x² + y² + z² = R², where R=

-a) 2.701E+00 m

-b) 2.971E+00 m

+c) 3.268E+00 m

-d) 3.595E+00 m

-e) 3.955E+00 m

4)

What is the net capacitance if C₁=3.56 μF, C₂=4.23 μF, and C₃=2.61 μF in the configuration shown?

-a) 3.755E+00 μF

-b) 4.130E+00 μF

+c) 4.543E+00 μF

-d) 4.997E+00 μF

-e) 5.497E+00 μF

5) Calculate the drift speed of electrons in a copper wire with a diameter of 2.17 mm carrying a 19.4 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

-a) 3.569E-04 m/s

+b) 3.926E-04 m/s

-c) 4.319E-04 m/s

-d) 4.750E-04 m/s

-e) 5.226E-04 m/s

6) Three resistors, R₁ = 0.855 Ω, and R₂ = R₂ = 1.91 Ω, are connected in parallel to a 6.97 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

+a) 5.682E+01 W

-b) 6.250E+01 W

-c) 6.875E+01 W

-d) 7.563E+01 W

-e) 8.319E+01 W

7) A charged particle in a magnetic field of 5.500E-04 T is moving perpendicular to the magnetic field with a speed of 2.930E+05 m/s. What is the period of orbit if orbital radius is 0.787 m?

+a) 1.688E-05 s

-b) 1.856E-05 s

-c) 2.042E-05 s

-d) 2.246E-05 s

-e) 2.471E-05 s

8) Two loops of wire carry the same current of 44 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.678 m while the other has a radius of 1.14 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.508 m from the first (smaller) loopif the disance between the loops is 1.16 m?

-a) 3.342E-02 T

+b) 3.676E-02 T

-c) 4.044E-02 T

-d) 4.448E-02 T

-e) 4.893E-02 T

9) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 2.609E+00 A

-b) 2.870E+00 A

+c) 3.157E+00 A

-d) 3.473E+00 A

-e) 3.820E+00 A

10) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?

-a) 2.549E-01 H

-b) 2.804E-01 H

-c) 3.084E-01 H

+d) 3.392E-01 H

-e) 3.732E-01 H

11) An ac generator produces an emf of amplitude 66 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a 97 mF inductor?

-a) 4.972E-01 A

-b) 5.469E-01 A

+c) 6.016E-01 A

-d) 6.618E-01 A

-e) 7.280E-01 A

12) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.016 m²? The average power output of the Sun is 3.80E+26 W.

+a) 6.669E-07 N/m²

-b) 7.336E-07 N/m²

-c) 8.069E-07 N/m²

-d) 8.876E-07 N/m²

-e) 9.764E-07 N/m²

Key: B1

1) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.052 m²? The average power output of the Sun is 3.80E+26 W.

-a) 2.392E-06 N/m²

-b) 2.631E-06 N/m²

-c) 2.894E-06 N/m²

-d) 3.184E-06 N/m²

+e) 3.502E-06 N/m²

2) Three resistors, R₁ = 1.82 Ω, and R₂ = R₂ = 4.14 Ω, are connected in parallel to a 5.65 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

+a) 1.754E+01 W

-b) 1.929E+01 W

-c) 2.122E+01 W

-d) 2.335E+01 W

-e) 2.568E+01 W

3)

What is the net capacitance if C₁=2.96 μF, C₂=3.95 μF, and C₃=3.74 μF in the configuration shown?

-a) 4.489E+00 μF

-b) 4.938E+00 μF

+c) 5.432E+00 μF

-d) 5.975E+00 μF

-e) 6.573E+00 μF

4)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate

f(x,y)

at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 8.690E+00 V/m²

-b) 9.559E+00 V/m²

+c) 1.051E+01 V/m²

-d) 1.157E+01 V/m²

-e) 1.272E+01 V/m²

5) An induced emf of 6.29V is measured across a coil of 85 closely wound turns while the current throuth it increases uniformly from 0.0 to 2.15A in 0.913s. What is the self-inductance of the coil?

-a) 2.428E+00 H

+b) 2.671E+00 H

-c) 2.938E+00 H

-d) 3.232E+00 H

-e) 3.555E+00 H

6) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=43 V is x² + y² + z² = R², where R=

+a) 2.299E+00 m

-b) 2.529E+00 m

-c) 2.782E+00 m

-d) 3.060E+00 m

-e) 3.366E+00 m

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.9 m, y=y₁=5.3 m, z=z₀=1.4 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 14.0m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 9.8m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 6.270E+01 N·m²/C

-b) 6.897E+01 N·m²/C

-c) 7.586E+01 N·m²/C

-d) 8.345E+01 N·m²/C

+e) 9.179E+01 N·m²/C

8) Calculate the drift speed of electrons in a copper wire with a diameter of 3.17 mm carrying a 12.0 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

+a) 1.138E-04 m/s

-b) 1.252E-04 m/s

-c) 1.377E-04 m/s

-d) 1.515E-04 m/s

-e) 1.666E-04 m/s

9) Two loops of wire carry the same current of 85 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.854 m while the other has a radius of 1.18 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.5 m from the first (smaller) loopif the disance between the loops is 1.66 m?

-a) 4.253E-02 T

-b) 4.678E-02 T

-c) 5.146E-02 T

+d) 5.661E-02 T

-e) 6.227E-02 T

10) An ac generator produces an emf of amplitude 58 V at a frequency of 99 Hz. What is the maximum amplitude of the current if the generator is connected to a 35 mF inductor?

-a) 2.422E+00 A

+b) 2.664E+00 A

-c) 2.930E+00 A

-d) 3.224E+00 A

-e) 3.546E+00 A

11) A square coil has sides that are L= 0.308 m long and is tightly wound with N=969 turns of wire. The resistance of the coil is R=8.64 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0498 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 4.817E-01 A

+b) 5.298E-01 A

-c) 5.828E-01 A

-d) 6.411E-01 A

-e) 7.052E-01 A

12) A charged particle in a magnetic field of 3.330E-04 T is moving perpendicular to the magnetic field with a speed of 4.800E+05 m/s. What is the period of orbit if orbital radius is 0.402 m?

-a) 4.784E-06 s

+b) 5.262E-06 s

-c) 5.788E-06 s

-d) 6.367E-06 s

-e) 7.004E-06 s

Key: B2

1) An ac generator produces an emf of amplitude 97 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 55 mF inductor?

+a) 4.386E+00 A

-b) 4.824E+00 A

-c) 5.307E+00 A

-d) 5.838E+00 A

-e) 6.421E+00 A

2) What is the radiation pressure on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.098 m²? The average power output of the Sun is 3.80E+26 W.

+a) 2.144E-07 N/m²

-b) 2.358E-07 N/m²

-c) 2.594E-07 N/m²

-d) 2.854E-07 N/m²

-e) 3.139E-07 N/m²

3) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=43 V is x² + y² + z² = R², where R=

+a) 2.299E+00 m

-b) 2.529E+00 m

-c) 2.782E+00 m

-d) 3.060E+00 m

-e) 3.366E+00 m

4) A square coil has sides that are L= 0.727 m long and is tightly wound with N=376 turns of wire. The resistance of the coil is R=5.59 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0485 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 1.567E+00 A

+b) 1.724E+00 A

-c) 1.897E+00 A

-d) 2.086E+00 A

-e) 2.295E+00 A

5)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate

f(x,y)

at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

-a) 3.610E+00 V/m²

+b) 3.971E+00 V/m²

-c) 4.368E+00 V/m²

-d) 4.804E+00 V/m²

-e) 5.285E+00 V/m²

6) A charged particle in a magnetic field of 3.350E-04 T is moving perpendicular to the magnetic field with a speed of 4.350E+05 m/s. What is the period of orbit if orbital radius is 0.841 m?

-a) 1.004E-05 s

-b) 1.104E-05 s

+c) 1.215E-05 s

-d) 1.336E-05 s

-e) 1.470E-05 s

7) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.838 m while the other has a radius of 1.17 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?

-a) 3.863E-02 T

+b) 4.249E-02 T

-c) 4.674E-02 T

-d) 5.141E-02 T

-e) 5.655E-02 T

8) Three resistors, R₁ = 1.52 Ω, and R₂ = R₂ = 3.38 Ω, are connected in parallel to a 5.82 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

-a) 1.842E+01 W

-b) 2.026E+01 W

+c) 2.228E+01 W

-d) 2.451E+01 W

-e) 2.696E+01 W

9) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?

-a) 2.549E-01 H

-b) 2.804E-01 H

-c) 3.084E-01 H

+d) 3.392E-01 H

-e) 3.732E-01 H

10)

What is the net capacitance if C₁=2.55 μF, C₂=4.13 μF, and C₃=2.5 μF in the configuration shown?

+a) 4.077E+00 μF

-b) 4.484E+00 μF

-c) 4.933E+00 μF

-d) 5.426E+00 μF

-e) 5.969E+00 μF

11)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.6 m, z=z₀=1.4 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 9.0m². Those in the xy plane have area 6.4m² ,and those in the zx plane have area 6.8m². An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 3.959E+01 N·m²/C

-b) 4.354E+01 N·m²/C

-c) 4.790E+01 N·m²/C

+d) 5.269E+01 N·m²/C

-e) 5.796E+01 N·m²/C

12) Calculate the drift speed of electrons in a copper wire with a diameter of 3.3 mm carrying a 18.5 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

-a) 1.472E-04 m/s

+b) 1.619E-04 m/s

-c) 1.781E-04 m/s

-d) 1.959E-04 m/s

-e) 2.155E-04 m/s

Key: C0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.3{\text{ m}}$ and the surface charge density is $\sigma =5{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=5.3{\text{ m}}$ .

+a) 1.022E+00 V/m²

-b) 1.125E+00 V/m²

-c) 1.237E+00 V/m²

-d) 1.361E+00 V/m²

-e) 1.497E+00 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.3 m, z=z₀=1.5 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 8.3m². Those in the xy plane have area 5.7m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 5.408E+01 N·m²/C

+b) 5.949E+01 N·m²/C

-c) 6.544E+01 N·m²/C

-d) 7.198E+01 N·m²/C

-e) 7.918E+01 N·m²/C

3)

An electron gun has parallel plates separated by 5.38 cm and gives electrons 54 keV of energy. What force would the field between the plates exert on a 0.427 μC charge that gets between the plates?

-a) 3.542E-01 N

-b) 3.896E-01 N

+c) 4.286E-01 N

-d) 4.714E-01 N

-e) 5.186E-01 N

4)

In the figure shown C₁=16.5 μF, C₂=2.7 μF, and C₃=4.82 μF. The voltage source provides ε=15.7 V. What is the energy stored in C₂?

-a) 2.188E+01 μJ

-b) 2.407E+01 μJ

-c) 2.647E+01 μJ

+d) 2.912E+01 μJ

-e) 3.203E+01 μJ

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =78 C and $\tau =$ 0.0244 s. What is the current at $t=$ 0.0225 s?

+a) 1.271E+03 A

-b) 1.398E+03 A

-c) 1.538E+03 A

-d) 1.692E+03 A

-e) 1.861E+03 A

6) A given battery has a 12 V emf and an internal resistance of 0.0984 Ω. If it is connected to a 0.485 Ω resistor what is the power dissipated by that load?

+a) 2.052E+02 W

-b) 2.257E+02 W

-c) 2.483E+02 W

-d) 2.731E+02 W

-e) 3.004E+02 W

7) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.44 m and a magneticfield of 1.31 T. What is their maximum kinetic energy?

-a) 1.323E+01 MeV

-b) 1.456E+01 MeV

+c) 1.601E+01 MeV

-d) 1.761E+01 MeV

-e) 1.937E+01 MeV

8) Two parallel wires each carry a 9.08 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.17 cm, 1.32 cm), while the other is located at (5.72 cm, 4.47 cm). What is the force per unit length between the wires?

-a) 3.882E-10 N/m

-b) 4.270E-10 N/m

+c) 4.697E-10 N/m

-d) 5.167E-10 N/m

-e) 5.683E-10 N/m

9) A recangular coil with an area of 0.449 m² and 20 turns is placed in a uniform magnetic field of 3.58 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.990E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 66 s?

-a) 7.734E+04 V

+b) 8.507E+04 V

-c) 9.358E+04 V

-d) 1.029E+05 V

-e) 1.132E+05 V

10) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.28mm$ , and $n=2.4$ . What is the volume of the washer?

+a) 1.097E+00 cm³

-b) 1.207E+00 cm³

-c) 1.328E+00 cm³

-d) 1.460E+00 cm³

-e) 1.606E+00 cm³

11) A step-down transformer steps 6 kV down to 190 V. The high-voltage input is provided by a 130 Ω power line that carries 6 A of currentWhat is the output current (at the 190 V side ?)

-a) 1.424E+02 A

-b) 1.566E+02 A

-c) 1.722E+02 A

+d) 1.895E+02 A

-e) 2.084E+02 A

12) What is the radiation force on an object that is 2.50E+11 m away from the sun and has cross-sectional area of 0.045 m²? The average power output of the Sun is 3.80E+26 W.

-a) 1.200E-07 N

-b) 1.320E-07 N

+c) 1.452E-07 N

-d) 1.598E-07 N

-e) 1.757E-07 N

Key: C1

1) Two parallel wires each carry a 8.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.66 cm, 1.4 cm), while the other is located at (5.64 cm, 5.66 cm). What is the force per unit length between the wires?

-a) 2.449E-10 N/m

-b) 2.694E-10 N/m

-c) 2.963E-10 N/m

+d) 3.260E-10 N/m

-e) 3.586E-10 N/m

2) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.14mm$ , and $n=2.86$ . What is the volume of the washer?

+a) 1.071E+00 cm³

-b) 1.178E+00 cm³

-c) 1.296E+00 cm³

-d) 1.425E+00 cm³

-e) 1.568E+00 cm³

3)

In the figure shown C₁=20.7 μF, C₂=2.79 μF, and C₃=5.18 μF. The voltage source provides ε=15.0 V. What is the energy stored in C₂?

-a) 2.064E+01 μJ

-b) 2.270E+01 μJ

-c) 2.497E+01 μJ

-d) 2.747E+01 μJ

+e) 3.022E+01 μJ

4) A given battery has a 13 V emf and an internal resistance of 0.159 Ω. If it is connected to a 0.617 Ω resistor what is the power dissipated by that load?

-a) 1.301E+02 W

-b) 1.431E+02 W

-c) 1.574E+02 W

+d) 1.732E+02 W

-e) 1.905E+02 W

5) What is the radiation force on an object that is 1.70E+11 m away from the sun and has cross-sectional area of 0.033 m²? The average power output of the Sun is 3.80E+26 W.

-a) 1.904E-07 N

-b) 2.094E-07 N

+c) 2.303E-07 N

-d) 2.534E-07 N

-e) 2.787E-07 N

6) A recangular coil with an area of 0.137 m² and 18 turns is placed in a uniform magnetic field of 1.18 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.120E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 47 s?

-a) 1.086E+04 V

+b) 1.195E+04 V

-c) 1.314E+04 V

-d) 1.446E+04 V

-e) 1.590E+04 V

7) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =91 C and $\tau =$ 0.0156 s. What is the current at $t=$ 0.0131 s?

-a) 2.082E+03 A

-b) 2.290E+03 A

+c) 2.519E+03 A

-d) 2.771E+03 A

-e) 3.048E+03 A

8)

An electron gun has parallel plates separated by 2.98 cm and gives electrons 11 keV of energy. What force would the field between the plates exert on a 0.685 μC charge that gets between the plates?

-a) 1.900E-01 N

-b) 2.090E-01 N

-c) 2.299E-01 N

+d) 2.529E-01 N

-e) 2.781E-01 N

9) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$ .

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

10) A step-down transformer steps 15 kV down to 250 V. The high-voltage input is provided by a 130 Ω power line that carries 4 A of currentWhat is the output current (at the 250 V side ?)

-a) 1.983E+02 A

-b) 2.182E+02 A

+c) 2.400E+02 A

-d) 2.640E+02 A

-e) 2.904E+02 A

11)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.6 m, z=z₀=1.4 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 9.0m². Those in the xy plane have area 6.4m² ,and those in the zx plane have area 6.8m². An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 3.959E+01 N·m²/C

-b) 4.354E+01 N·m²/C

-c) 4.790E+01 N·m²/C

+d) 5.269E+01 N·m²/C

-e) 5.796E+01 N·m²/C

12) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.413 m and a magneticfield of 0.988 T. What is their maximum kinetic energy?

-a) 6.029E+00 MeV

-b) 6.631E+00 MeV

-c) 7.295E+00 MeV

+d) 8.024E+00 MeV

-e) 8.827E+00 MeV

Key: C2

1) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.28mm$ , and $n=2.4$ . What is the volume of the washer?

+a) 1.097E+00 cm³

-b) 1.207E+00 cm³

-c) 1.328E+00 cm³

-d) 1.460E+00 cm³

-e) 1.606E+00 cm³

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.8 m. The other four surfaces are rectangles in y=y₀=1.2 m, y=y₁=5.9 m, z=z₀=1.3 m, and z=z₁=5.2 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 8.5m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 4.777E+01 N·m²/C

-b) 5.254E+01 N·m²/C

-c) 5.780E+01 N·m²/C

+d) 6.358E+01 N·m²/C

-e) 6.993E+01 N·m²/C

3) A recangular coil with an area of 0.39 m² and 16 turns is placed in a uniform magnetic field of 3.07 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.320E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 44 s?

-a) 3.792E+04 V

-b) 4.172E+04 V

-c) 4.589E+04 V

+d) 5.048E+04 V

-e) 5.552E+04 V

4) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=1.2{\text{ m}}$ .

-a) 8.933E+00 V/m²

-b) 9.826E+00 V/m²

+c) 1.081E+01 V/m²

-d) 1.189E+01 V/m²

-e) 1.308E+01 V/m²

5)

In the figure shown C₁=15.7 μF, C₂=2.87 μF, and C₃=5.46 μF. The voltage source provides ε=5.38 V. What is the energy stored in C₂?

-a) 6.890E+00 μJ

-b) 7.579E+00 μJ

-c) 8.337E+00 μJ

-d) 9.171E+00 μJ

+e) 1.009E+01 μJ

6) A given battery has a 9 V emf and an internal resistance of 0.16 Ω. If it is connected to a 0.45 Ω resistor what is the power dissipated by that load?

-a) 6.691E+01 W

-b) 7.360E+01 W

-c) 8.096E+01 W

-d) 8.905E+01 W

+e) 9.796E+01 W

7) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =18 C and $\tau =$ 0.0169 s. What is the current at $t=$ 0.0137 s?

-a) 3.913E+02 A

-b) 4.305E+02 A

+c) 4.735E+02 A

-d) 5.209E+02 A

-e) 5.729E+02 A

8) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.145 m and a magneticfield of 1.03 T. What is their maximum kinetic energy?

-a) 7.342E-01 MeV

-b) 8.076E-01 MeV

-c) 8.884E-01 MeV

-d) 9.772E-01 MeV

+e) 1.075E+00 MeV

9)

An electron gun has parallel plates separated by 3.68 cm and gives electrons 54 keV of energy. What force would the field between the plates exert on a 0.181 μC charge that gets between the plates?

+a) 2.656E-01 N

-b) 2.922E-01 N

-c) 3.214E-01 N

-d) 3.535E-01 N

-e) 3.889E-01 N

10) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?

-a) 1.283E-10 N/m

-b) 1.411E-10 N/m

-c) 1.552E-10 N/m

-d) 1.708E-10 N/m

+e) 1.878E-10 N/m

11) A step-down transformer steps 8 kV down to 220 V. The high-voltage input is provided by a 110 Ω power line that carries 8 A of currentWhat is the output current (at the 220 V side ?)

-a) 2.404E+02 A

-b) 2.645E+02 A

+c) 2.909E+02 A

-d) 3.200E+02 A

-e) 3.520E+02 A

12) What is the radiation force on an object that is 9.90E+11 m away from the sun and has cross-sectional area of 0.083 m²? The average power output of the Sun is 3.80E+26 W.

-a) 1.167E-08 N

-b) 1.284E-08 N

-c) 1.412E-08 N

-d) 1.553E-08 N

+e) 1.708E-08 N

Key: D0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$ .

+a) 1.606E+00 V/m²

-b) 1.767E+00 V/m²

-c) 1.943E+00 V/m²

-d) 2.138E+00 V/m²

-e) 2.351E+00 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.8 m, y=y₁=5.3 m, z=z₀=1.2 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 15.0m². Those in the xy plane have area 7.7m² ,and those in the zx plane have area 9.5m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 5.989E+01 N·m²/C

-b) 6.588E+01 N·m²/C

-c) 7.247E+01 N·m²/C

+d) 7.971E+01 N·m²/C

-e) 8.769E+01 N·m²/C

3) When a 6.03 V battery operates a 1.56 W bulb, how many electrons pass through it each second?

+a) 1.615E+18 electrons

-b) 1.776E+18 electrons

-c) 1.954E+18 electrons

-d) 2.149E+18 electrons

-e) 2.364E+18 electrons

4) An empty parallel-plate capacitor with metal plates has an area of 2.02 m², separated by 1.44 mm. How much charge does it store if the voltage is 2.170E+03 V?

-a) 2.450E+01 μC

+b) 2.695E+01 μC

-c) 2.965E+01 μC

-d) 3.261E+01 μC

-e) 3.587E+01 μC

5) Calculate the electric field in a 12-gauge copper wire that is 84 m long and carries a current of 48 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 1.664E-04 V/m

-b) 1.830E-04 V/m

-c) 2.013E-04 V/m

-d) 2.215E-04 V/m

+e) 2.436E-04 V/m

6)

Two sources of emf ε₁=26.2 V, and ε₂=8.29 V are oriented as shownin the circuit. The resistances are R₁=3.43 kΩ and R₂=1.16 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=4.09 mA and I₄=1.06 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 6.720E+00 V

-b) 7.392E+00 V

-c) 8.131E+00 V

-d) 8.944E+00 V

+e) 9.838E+00 V

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 5.75 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(1.81 i + 2.05 j + 4.49 k) x 10⁴ m/s?

-a) 2.576E-14 N

-b) 2.834E-14 N

-c) 3.117E-14 N

-d) 3.429E-14 N

+e) 3.772E-14 N

8)

Three wires sit at the corners of a square of length 0.716 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.94 A, 2.04 A, 2.41 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 6.833E-05 T

-b) B_y= 7.517E-05 T

+c) B_y= 8.268E-05 T

-d) B_y= 9.095E-05 T

-e) B_y= 1.000E-04 T

9) Calculate the motional emf induced along a 48.8 km conductor moving at an orbital speed of 7.88 km/s perpendicular to Earth's 4.660E-05 Tesla magnetic field.

-a) 1.224E+04 V

-b) 1.346E+04 V

-c) 1.481E+04 V

-d) 1.629E+04 V

+e) 1.792E+04 V

10) An induced emf of 7.94V is measured across a coil of 94 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.65A in 0.478s. What is the self-inductance of the coil?

-a) 5.047E-01 H

-b) 5.552E-01 H

-c) 6.107E-01 H

+d) 6.717E-01 H

-e) 7.389E-01 H

11) An ac generator produces an emf of amplitude 71 V at a frequency of 68 Hz. What is the maximum amplitude of the current if the generator is connected to a 35 mF capacitor?

-a) 7.252E-01 A

-b) 7.977E-01 A

-c) 8.775E-01 A

-d) 9.652E-01 A

+e) 1.062E+00 A

12) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?

-a) 1.753E+02 km

-b) 1.928E+02 km

+c) 2.121E+02 km

-d) 2.333E+02 km

-e) 2.567E+02 km

Key: D1

1) Calculate the electric field in a 12-gauge copper wire that is 48 m long and carries a current of 63 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

+a) 3.198E-04 V/m

-b) 3.517E-04 V/m

-c) 3.869E-04 V/m

-d) 4.256E-04 V/m

-e) 4.682E-04 V/m

2) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.13 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(5.64 i + 1.93 j + 8.71 k) x 10⁴ m/s?

-a) 1.757E-14 N

+b) 1.933E-14 N

-c) 2.126E-14 N

-d) 2.339E-14 N

-e) 2.573E-14 N

3) An empty parallel-plate capacitor with metal plates has an area of 2.1 m², separated by 1.13 mm. How much charge does it store if the voltage is 1.680E+03 V?

+a) 2.764E+01 μC

-b) 3.041E+01 μC

-c) 3.345E+01 μC

-d) 3.679E+01 μC

-e) 4.047E+01 μC

4) An ac generator produces an emf of amplitude 54 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 7 mF capacitor?

+a) 2.850E-01 A

-b) 3.135E-01 A

-c) 3.449E-01 A

-d) 3.793E-01 A

-e) 4.173E-01 A

5) When a 2.59 V battery operates a 2.89 W bulb, how many electrons pass through it each second?

-a) 5.756E+18 electrons

-b) 6.331E+18 electrons

+c) 6.964E+18 electrons

-d) 7.661E+18 electrons

-e) 8.427E+18 electrons

6) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?

-a) 2.094E+02 km

+b) 2.304E+02 km

-c) 2.534E+02 km

-d) 2.788E+02 km

-e) 3.066E+02 km

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.7 m, z=z₀=1.8 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 9.2m² ,and those in the zx plane have area 8.1m². An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 2.134E+01 N·m²/C

-b) 2.347E+01 N·m²/C

+c) 2.582E+01 N·m²/C

-d) 2.840E+01 N·m²/C

-e) 3.124E+01 N·m²/C

8)

Two sources of emf ε₁=38.8 V, and ε₂=14.9 V are oriented as shownin the circuit. The resistances are R₁=5.83 kΩ and R₂=1.77 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.57 mA and I₄=1.19 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 1.013E+01 V

-b) 1.115E+01 V

-c) 1.226E+01 V

+d) 1.349E+01 V

-e) 1.484E+01 V

9)

Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 7.035E-05 T

-b) B_y= 7.739E-05 T

-c) B_y= 8.512E-05 T

+d) B_y= 9.364E-05 T

-e) B_y= 1.030E-04 T

10) An induced emf of 1.92V is measured across a coil of 74 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.38A in 0.69s. What is the self-inductance of the coil?

-a) 1.560E-01 H

-b) 1.716E-01 H

-c) 1.888E-01 H

+d) 2.076E-01 H

-e) 2.284E-01 H

11) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$ .

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

12) Calculate the motional emf induced along a 46.2 km conductor moving at an orbital speed of 7.9 km/s perpendicular to Earth's 4.630E-05 Tesla magnetic field.

-a) 1.536E+04 V

+b) 1.690E+04 V

-c) 1.859E+04 V

-d) 2.045E+04 V

-e) 2.249E+04 V

Key: D2

1) Calculate the electric field in a 12-gauge copper wire that is 99 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

+a) 3.604E-04 V/m

-b) 3.964E-04 V/m

-c) 4.360E-04 V/m

-d) 4.796E-04 V/m

-e) 5.276E-04 V/m

2) An ac generator produces an emf of amplitude 17 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 6 mF capacitor?

-a) 5.253E-02 A

-b) 5.778E-02 A

-c) 6.356E-02 A

-d) 6.991E-02 A

+e) 7.691E-02 A

3) An empty parallel-plate capacitor with metal plates has an area of 2.21 m², separated by 1.25 mm. How much charge does it store if the voltage is 1.580E+03 V?

-a) 2.249E+01 μC

+b) 2.473E+01 μC

-c) 2.721E+01 μC

-d) 2.993E+01 μC

-e) 3.292E+01 μC

4)

Three wires sit at the corners of a square of length 0.702 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 7.576E-05 T

+b) B_y= 8.333E-05 T

-c) B_y= 9.167E-05 T

-d) B_y= 1.008E-04 T

-e) B_y= 1.109E-04 T

5) When a 4.21 V battery operates a 2.17 W bulb, how many electrons pass through it each second?

-a) 2.659E+18 electrons

-b) 2.925E+18 electrons

+c) 3.217E+18 electrons

-d) 3.539E+18 electrons

-e) 3.893E+18 electrons

6) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?

-a) 2.549E-01 H

-b) 2.804E-01 H

-c) 3.084E-01 H

+d) 3.392E-01 H

-e) 3.732E-01 H

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.3 m. The other four surfaces are rectangles in y=y₀=1.1 m, y=y₁=5.7 m, z=z₀=1.8 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 12.0m². Those in the xy plane have area 6.0m² ,and those in the zx plane have area 3.5m². An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 9.823E+00 N·m²/C

+b) 1.080E+01 N·m²/C

-c) 1.189E+01 N·m²/C

-d) 1.307E+01 N·m²/C

-e) 1.438E+01 N·m²/C

8) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3{\text{ m}}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$ .

-a) 6.877E+00 V/m²

-b) 7.565E+00 V/m²

+c) 8.321E+00 V/m²

-d) 9.153E+00 V/m²

-e) 1.007E+01 V/m²

9) Calculate the motional emf induced along a 49.5 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.310E-05 Tesla magnetic field.

-a) 1.395E+04 V

-b) 1.534E+04 V

-c) 1.688E+04 V

-d) 1.857E+04 V

+e) 2.042E+04 V

10)

Two sources of emf ε₁=30.6 V, and ε₂=12.0 V are oriented as shownin the circuit. The resistances are R₁=3.46 kΩ and R₂=2.77 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.97 mA and I₄=0.643 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 4.986E+00 V

-b) 5.484E+00 V

-c) 6.033E+00 V

-d) 6.636E+00 V

+e) 7.299E+00 V

11) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 4.69 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(8.9 i + 4.27 j + 7.52 k) x 10⁴ m/s?

-a) 5.296E-14 N

-b) 5.826E-14 N

+c) 6.408E-14 N

-d) 7.049E-14 N

-e) 7.754E-14 N

12) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?

-a) 1.003E+02 km

-b) 1.103E+02 km

-c) 1.213E+02 km

+d) 1.335E+02 km

-e) 1.468E+02 km

Key: E0

1) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 9.412E+01 N/C

-b) 1.035E+02 N/C

-c) 1.139E+02 N/C

-d) 1.253E+02 N/C

-e) 1.378E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\vec {E}}=4y^{2.0}{\hat {i}}+3x^{2.0}{\hat {j}}+3y^{3.0}{\hat {k}}$

-a) 4.820E+03 V·m

-b) 5.302E+03 V·m

+c) 5.832E+03 V·m

-d) 6.415E+03 V·m

-e) 7.057E+03 V·m

3) If a 14 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=26 V is x² + y² + z² = R², where R=

-a) 3.636E+00 m

-b) 4.000E+00 m

-c) 4.399E+00 m

+d) 4.839E+00 m

-e) 5.323E+00 m

4)

In the figure shown C₁=16.9 μF, C₂=2.86 μF, and C₃=5.1 μF. The voltage source provides ε=9.98 V. What is the energy stored in C₂?

-a) 1.764E+01 μJ

+b) 1.940E+01 μJ

-c) 2.134E+01 μJ

-d) 2.348E+01 μJ

-e) 2.583E+01 μJ

5) Calculate the electric field in a 12-gauge copper wire that is 21 m long and carries a current of 42 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 1.602E-04 V/m

-b) 1.762E-04 V/m

-c) 1.938E-04 V/m

+d) 2.132E-04 V/m

-e) 2.345E-04 V/m

6) A given battery has a 13 V emf and an internal resistance of 0.113 Ω. If it is connected to a 0.686 Ω resistor what is the power dissipated by that load?

-a) 1.501E+02 W

-b) 1.651E+02 W

+c) 1.816E+02 W

-d) 1.998E+02 W

-e) 2.197E+02 W

7) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.83 T magnetic field is directed 22° away from the wire?

-a) 1.062E+00 N/m

-b) 1.168E+00 N/m

-c) 1.285E+00 N/m

-d) 1.413E+00 N/m

+e) 1.555E+00 N/m

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.253 m and $B_{max}=\,$ 0.489 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.112 m that is centered on the axis with its plane perpendicular to the axis?

-a) 1.289E+05 A

-b) 1.418E+05 A

-c) 1.560E+05 A

-d) 1.716E+05 A

+e) 1.888E+05 A

9) A long solenoid has a radius of 0.413 m and 17 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 1 A and $\alpha =$ 21 s⁻¹.What is the induced electric fied at a distance 2.25 m from the axis at time t=0.0689 s ?

-a) 3.006E-06 V/m

-b) 3.307E-06 V/m

-c) 3.637E-06 V/m

+d) 4.001E-06 V/m

-e) 4.401E-06 V/m

10)

A long solenoid has a length 0.777 meters, radius 3.45 cm, and 557 turns. It surrounds coil of radius 6.01 meters and 10turns. If the current in the solenoid is changing at a rate of 184 A/s, what is the emf induced in the surounding coil?

-a) 1.463E-02 V

-b) 1.609E-02 V

-c) 1.770E-02 V

+d) 1.947E-02 V

-e) 2.142E-02 V

11) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.43 V;. If R =7 Ω, L= 7.40E-03H , and C=6.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

-a) 9.380E-01 &rad;

-b) 1.032E+00 &rad;

-c) 1.135E+00 &rad;

-d) 1.248E+00 &rad;

+e) 1.373E+00 &rad;

12)

A parallel plate capacitor with a capicatnce C=6.50E-06 F whose plates have an area A=4.50E+03 m² and separation d=6.10E-03 m is connected via a swith to a 4 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.70E-05?

-a) 1.456E+00 V

-b) 1.602E+00 V

-c) 1.762E+00 V

+d) 1.938E+00 V

-e) 2.132E+00 V

Key: E1

1) Calculate the electric field in a 12-gauge copper wire that is 99 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

+a) 3.604E-04 V/m

-b) 3.964E-04 V/m

-c) 4.360E-04 V/m

-d) 4.796E-04 V/m

-e) 5.276E-04 V/m

2) A given battery has a 12 V emf and an internal resistance of 0.107 Ω. If it is connected to a 0.814 Ω resistor what is the power dissipated by that load?

+a) 1.382E+02 W

-b) 1.520E+02 W

-c) 1.672E+02 W

-d) 1.839E+02 W

-e) 2.023E+02 W

3)

A parallel plate capacitor with a capicatnce C=7.10E-06 F whose plates have an area A=5.10E+03 m² and separation d=6.40E-03 m is connected via a swith to a 54 Ω resistor and a battery of voltage V₀=83 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-03?

-a) 6.111E+01 V

-b) 6.722E+01 V

-c) 7.395E+01 V

+d) 8.134E+01 V

-e) 8.947E+01 V

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.547 m and $B_{max}=\,$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.158 m that is centered on the axis with its plane perpendicular to the axis?

-a) 1.751E+05 A

-b) 1.927E+05 A

-c) 2.119E+05 A

+d) 2.331E+05 A

-e) 2.564E+05 A

5) A long solenoid has a radius of 0.757 m and 90 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 30 s⁻¹.What is the induced electric fied at a distance 2.08 m from the axis at time t=0.0442 s ?

-a) 6.527E-04 V/m

-b) 7.180E-04 V/m

-c) 7.898E-04 V/m

+d) 8.688E-04 V/m

-e) 9.556E-04 V/m

6) If a 26 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=21 V is x² + y² + z² = R², where R=

-a) 8.360E+00 m

-b) 9.196E+00 m

-c) 1.012E+01 m

+d) 1.113E+01 m

-e) 1.224E+01 m

7) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}$

-a) 7.054E+03 V·m

-b) 7.759E+03 V·m

-c) 8.535E+03 V·m

-d) 9.388E+03 V·m

+e) 1.033E+04 V·m

9) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.355 T magnetic field is directed 53° away from the wire?

-a) 8.520E-01 N/m

-b) 9.372E-01 N/m

-c) 1.031E+00 N/m

+d) 1.134E+00 N/m

-e) 1.247E+00 N/m

10)

In the figure shown C₁=19.2 μF, C₂=2.24 μF, and C₃=4.93 μF. The voltage source provides ε=11.7 V. What is the energy stored in C₂?

-a) 1.303E+01 μJ

-b) 1.434E+01 μJ

-c) 1.577E+01 μJ

-d) 1.735E+01 μJ

+e) 1.908E+01 μJ

11)

A long solenoid has a length 0.805 meters, radius 4.24 cm, and 536 turns. It surrounds coil of radius 8.5 meters and 16turns. If the current in the solenoid is changing at a rate of 278 A/s, what is the emf induced in the surounding coil?

+a) 6.604E-02 V

-b) 7.264E-02 V

-c) 7.990E-02 V

-d) 8.789E-02 V

-e) 9.668E-02 V

12) The output of an ac generator connected to an RLC series combination has a frequency of 200 Hz and an amplitude of 0.14 V;. If R =3 Ω, L= 1.70E-03H , and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

-a) 3.691E-01 &rad;

+b) 4.060E-01 &rad;

-c) 4.466E-01 &rad;

-d) 4.913E-01 &rad;

-e) 5.404E-01 &rad;

Key: E2

1) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.736 m and $B_{max}=\,$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.532 m that is centered on the axis with its plane perpendicular to the axis?

-a) 3.764E+05 A

-b) 4.140E+05 A

-c) 4.554E+05 A

+d) 5.010E+05 A

-e) 5.510E+05 A

2) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.761 T magnetic field is directed 44° away from the wire?

-a) 2.527E+00 N/m

-b) 2.780E+00 N/m

-c) 3.058E+00 N/m

-d) 3.364E+00 N/m

+e) 3.700E+00 N/m

3) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

4) If a 21 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=94 V is x² + y² + z² = R², where R=

-a) 1.371E+00 m

-b) 1.509E+00 m

-c) 1.659E+00 m

-d) 1.825E+00 m

+e) 2.008E+00 m

5) A given battery has a 12 V emf and an internal resistance of 0.107 Ω. If it is connected to a 0.814 Ω resistor what is the power dissipated by that load?

+a) 1.382E+02 W

-b) 1.520E+02 W

-c) 1.672E+02 W

-d) 1.839E+02 W

-e) 2.023E+02 W

6) The output of an ac generator connected to an RLC series combination has a frequency of 480 Hz and an amplitude of 0.63 V;. If R =7 Ω, L= 3.80E-03H , and C=5.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

+a) 9.972E-01 &rad;

-b) 1.097E+00 &rad;

-c) 1.207E+00 &rad;

-d) 1.327E+00 &rad;

-e) 1.460E+00 &rad;

7)

In the figure shown C₁=16.7 μF, C₂=2.26 μF, and C₃=4.53 μF. The voltage source provides ε=10.7 V. What is the energy stored in C₂?

-a) 1.292E+01 μJ

-b) 1.421E+01 μJ

-c) 1.563E+01 μJ

+d) 1.719E+01 μJ

-e) 1.891E+01 μJ

8)

A parallel plate capacitor with a capicatnce C=7.50E-06 F whose plates have an area A=2.90E+03 m² and separation d=3.40E-03 m is connected via a swith to a 61 Ω resistor and a battery of voltage V₀=77 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.70E-03?

-a) 5.131E+01 V

-b) 5.644E+01 V

-c) 6.209E+01 V

-d) 6.830E+01 V

+e) 7.513E+01 V

9) Calculate the electric field in a 12-gauge copper wire that is 18 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

+a) 1.117E-04 V/m

-b) 1.228E-04 V/m

-c) 1.351E-04 V/m

-d) 1.486E-04 V/m

-e) 1.635E-04 V/m

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}$

-a) 1.997E+03 V·m

+b) 2.197E+03 V·m

-c) 2.417E+03 V·m

-d) 2.659E+03 V·m

-e) 2.924E+03 V·m

11)

A long solenoid has a length 0.89 meters, radius 3.01 cm, and 505 turns. It surrounds coil of radius 8.65 meters and 18turns. If the current in the solenoid is changing at a rate of 279 A/s, what is the emf induced in the surounding coil?

-a) 2.646E-02 V

-b) 2.911E-02 V

+c) 3.202E-02 V

-d) 3.522E-02 V

-e) 3.874E-02 V

12) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 5 A and $\alpha =$ 28 s⁻¹.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?

-a) 1.616E-04 V/m

-b) 1.778E-04 V/m

-c) 1.955E-04 V/m

-d) 2.151E-04 V/m

+e) 2.366E-04 V/m

Key: F0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=1e

,

q_{2}=-8e

, and

q_{3}=2e

?

+a) 5.732E-15 N

-b) 6.305E-15 N

-c) 6.936E-15 N

-d) 7.629E-15 N

-e) 8.392E-15 N

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
${\vec {E}}=4y^{1.4}{\hat {i}}+2x^{2.3}{\hat {j}}+4y^{2.3}{\hat {k}}$

-a) 2.694E+03 V·m

-b) 2.963E+03 V·m

-c) 3.259E+03 V·m

+d) 3.585E+03 V·m

-e) 3.944E+03 V·m

3)

An electron gun has parallel plates separated by 3.68 cm and gives electrons 54 keV of energy. What force would the field between the plates exert on a 0.181 μC charge that gets between the plates?

+a) 2.656E-01 N

-b) 2.922E-01 N

-c) 3.214E-01 N

-d) 3.535E-01 N

-e) 3.889E-01 N

4)

What is the net capacitance if C₁=2.3 μF, C₂=2.84 μF, and C₃=3.41 μF in the configuration shown?

-a) 4.255E+00 μF

+b) 4.681E+00 μF

-c) 5.149E+00 μF

-d) 5.664E+00 μF

-e) 6.230E+00 μF

5) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?

-a) 2.240E+02 A

-b) 2.464E+02 A

+c) 2.711E+02 A

-d) 2.982E+02 A

-e) 3.280E+02 A

6)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 558 V. If the combined external and internal resistance is 198 &Omega and the capacitance is 80 mF, how long will it take for the capacitor's voltage to reach 345.0 V?

-a) 1.146E+01 s

-b) 1.261E+01 s

-c) 1.387E+01 s

+d) 1.525E+01 s

-e) 1.678E+01 s

7) A circular current loop of radius 2.84 cm carries a current of 3.01 mA. What is the magnitude of the torque if the dipole is oriented at 63 ° to a uniform magnetic fied of 0.174 T?

-a) 1.075E-06 N m

+b) 1.182E-06 N m

-c) 1.301E-06 N m

-d) 1.431E-06 N m

-e) 1.574E-06 N m

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.852 m and $B_{max}=\,$ 0.476 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.212 m that is centered on the axis with its plane perpendicular to the axis?

-a) 1.502E+05 A

-b) 1.652E+05 A

-c) 1.817E+05 A

-d) 1.999E+05 A

+e) 2.199E+05 A

9) A long solenoid has a radius of 0.682 m and 38 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 2 A and $\alpha =$ 27 s⁻¹.What is the induced electric fied at a distance 0.16 m from the axis at time t=0.0736 s ?

-a) 2.571E-05 V/m

+b) 2.828E-05 V/m

-c) 3.111E-05 V/m

-d) 3.422E-05 V/m

-e) 3.764E-05 V/m

10) A washer has an inner diameter of 2.3 cm and an outer diamter of 4.44 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.31mm$ , and $n=2.66$ . What is the volume of the washer?

-a) 1.089E+00 cm³

-b) 1.198E+00 cm³

+c) 1.318E+00 cm³

-d) 1.449E+00 cm³

-e) 1.594E+00 cm³

11) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.88 V. The resistance, inductance, and capacitance are R =7 Ω, L= 8.00E-03H , and C=5.50E-04 F, respectively. What is the amplitude of the current?

-a) 1.143E-01 A

+b) 1.257E-01 A

-c) 1.383E-01 A

-d) 1.521E-01 A

-e) 1.673E-01 A

12) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m²? The average power output of the Sun is 3.80E+26 W.

+a) 2.673E-07 N

-b) 2.940E-07 N

-c) 3.234E-07 N

-d) 3.558E-07 N

-e) 3.913E-07 N

Key: F1

1) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.82 V. The resistance, inductance, and capacitance are R =8 Ω, L= 6.40E-03H , and C=5.70E-04 F, respectively. What is the amplitude of the current?

-a) 7.701E-02 A

-b) 8.471E-02 A

-c) 9.318E-02 A

+d) 1.025E-01 A

-e) 1.128E-01 A

2) What is the average current involved when a truck battery sets in motion 659 C of charge in 5.48 s while starting an engine?

-a) 8.214E+01 A

-b) 9.035E+01 A

-c) 9.938E+01 A

-d) 1.093E+02 A

+e) 1.203E+02 A

3)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=1e

,

q_{2}=-7e

, and

q_{3}=2e

?

-a) 3.391E-14 N

-b) 3.731E-14 N

-c) 4.104E-14 N

+d) 4.514E-14 N

-e) 4.965E-14 N

4) A circular current loop of radius 3.04 cm carries a current of 1.94 mA. What is the magnitude of the torque if the dipole is oriented at 50 ° to a uniform magnetic fied of 0.193 T?

-a) 6.257E-07 N m

-b) 6.882E-07 N m

-c) 7.570E-07 N m

+d) 8.327E-07 N m

-e) 9.160E-07 N m

5) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.407 m and $B_{max}=\,$ 0.605 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.196 m that is centered on the axis with its plane perpendicular to the axis?

-a) 3.583E+05 A

-b) 3.941E+05 A

+c) 4.335E+05 A

-d) 4.769E+05 A

-e) 5.246E+05 A

6) What is the radiation force on an object that is 2.50E+11 m away from the sun and has cross-sectional area of 0.045 m²? The average power output of the Sun is 3.80E+26 W.

-a) 1.200E-07 N

-b) 1.320E-07 N

+c) 1.452E-07 N

-d) 1.598E-07 N

-e) 1.757E-07 N

7)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 543 V. If the combined external and internal resistance is 201 &Omega and the capacitance is 82 mF, how long will it take for the capacitor's voltage to reach 281.0 V?

-a) 9.024E+00 s

-b) 9.927E+00 s

-c) 1.092E+01 s

+d) 1.201E+01 s

-e) 1.321E+01 s

8) A washer has an inner diameter of 2.62 cm and an outer diamter of 4.79 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.08mm$ , and $n=2.68$ . What is the volume of the washer?

+a) 1.056E+00 cm³

-b) 1.161E+00 cm³

-c) 1.278E+00 cm³

-d) 1.405E+00 cm³

-e) 1.546E+00 cm³

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}$

+a) 3.429E+03 V·m

-b) 3.771E+03 V·m

-c) 4.149E+03 V·m

-d) 4.564E+03 V·m

-e) 5.020E+03 V·m

10)

An electron gun has parallel plates separated by 3.35 cm and gives electrons 26 keV of energy. What force would the field between the plates exert on a 0.682 μC charge that gets between the plates?

-a) 3.977E-01 N

-b) 4.374E-01 N

-c) 4.812E-01 N

+d) 5.293E-01 N

-e) 5.822E-01 N

11) A long solenoid has a radius of 0.749 m and 62 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 9 A and $\alpha =$ 25 s⁻¹.What is the induced electric fied at a distance 0.139 m from the axis at time t=0.071 s ?

+a) 2.065E-04 V/m

-b) 2.271E-04 V/m

-c) 2.499E-04 V/m

-d) 2.748E-04 V/m

-e) 3.023E-04 V/m

12)

What is the net capacitance if C₁=2.3 μF, C₂=2.84 μF, and C₃=3.41 μF in the configuration shown?

-a) 4.255E+00 μF

+b) 4.681E+00 μF

-c) 5.149E+00 μF

-d) 5.664E+00 μF

-e) 6.230E+00 μF

Key: F2

1) A long solenoid has a radius of 0.603 m and 51 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 2 A and $\alpha =$ 26 s⁻¹.What is the induced electric fied at a distance 0.105 m from the axis at time t=0.0659 s ?

-a) 2.154E-05 V/m

-b) 2.369E-05 V/m

-c) 2.606E-05 V/m

-d) 2.867E-05 V/m

+e) 3.154E-05 V/m

2)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=3e

?

-a) 1.473E-14 N

-b) 1.620E-14 N

-c) 1.782E-14 N

-d) 1.960E-14 N

+e) 2.156E-14 N

3)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 554 V. If the combined external and internal resistance is 228 &Omega and the capacitance is 93 mF, how long will it take for the capacitor's voltage to reach 450.0 V?

-a) 3.224E+01 s

+b) 3.547E+01 s

-c) 3.902E+01 s

-d) 4.292E+01 s

-e) 4.721E+01 s

4) A circular current loop of radius 1.56 cm carries a current of 2.57 mA. What is the magnitude of the torque if the dipole is oriented at 38 ° to a uniform magnetic fied of 0.79 T?

-a) 7.898E-07 N m

-b) 8.688E-07 N m

+c) 9.557E-07 N m

-d) 1.051E-06 N m

-e) 1.156E-06 N m

5)

What is the net capacitance if C₁=4.7 μF, C₂=4.82 μF, and C₃=3.61 μF in the configuration shown?

-a) 5.445E+00 μF

+b) 5.990E+00 μF

-c) 6.589E+00 μF

-d) 7.247E+00 μF

-e) 7.972E+00 μF

6) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.096 m²? The average power output of the Sun is 3.80E+26 W.

-a) 4.373E-08 N

-b) 4.810E-08 N

-c) 5.291E-08 N

-d) 5.820E-08 N

+e) 6.402E-08 N

7)

An electron gun has parallel plates separated by 5.31 cm and gives electrons 41 keV of energy. What force would the field between the plates exert on a 0.368 μC charge that gets between the plates?

-a) 2.348E-01 N

-b) 2.583E-01 N

+c) 2.841E-01 N

-d) 3.126E-01 N

-e) 3.438E-01 N

8) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.75 V. The resistance, inductance, and capacitance are R =5 Ω, L= 9.90E-03H , and C=6.80E-04 F, respectively. What is the amplitude of the current?

-a) 1.240E-01 A

-b) 1.364E-01 A

+c) 1.500E-01 A

-d) 1.650E-01 A

-e) 1.815E-01 A

9) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?

-a) 2.240E+02 A

-b) 2.464E+02 A

+c) 2.711E+02 A

-d) 2.982E+02 A

-e) 3.280E+02 A

10) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.62 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.66mm$ , and $n=2.61$ . What is the volume of the washer?

-a) 6.960E-01 cm³

-b) 7.656E-01 cm³

+c) 8.421E-01 cm³

-d) 9.264E-01 cm³

-e) 1.019E+00 cm³

11) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}$

-a) 9.952E+03 V·m

-b) 1.095E+04 V·m

-c) 1.204E+04 V·m

+d) 1.325E+04 V·m

-e) 1.457E+04 V·m

12) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.619 m and $B_{max}=\,$ 0.215 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.351 m that is centered on the axis with its plane perpendicular to the axis?

-a) 2.534E+05 A

-b) 2.787E+05 A

+c) 3.066E+05 A

-d) 3.373E+05 A

-e) 3.710E+05 A

Key: G0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-9e

, and

q_{3}=6e

?

-a) 5.767E+01 degrees

+b) 6.343E+01 degrees

-c) 6.978E+01 degrees

-d) 7.676E+01 degrees

-e) 8.443E+01 degrees

2) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=2 nC·m^-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

-a) 3.821E+02 N/C

-b) 4.203E+02 N/C

-c) 4.624E+02 N/C

+d) 5.086E+02 N/C

-e) 5.594E+02 N/C

3) If a 19 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=73 V is x² + y² + z² = R², where R=

-a) 1.598E+00 m

-b) 1.757E+00 m

-c) 1.933E+00 m

-d) 2.127E+00 m

+e) 2.339E+00 m

4)

In the figure shown C₁=17.7 μF, C₂=2.48 μF, and C₃=4.68 μF. The voltage source provides ε=12.7 V. What is the energy stored in C₂?

+a) 2.242E+01 μJ

-b) 2.467E+01 μJ

-c) 2.713E+01 μJ

-d) 2.985E+01 μJ

-e) 3.283E+01 μJ

5) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.58 Ω at a temperature of 24°C and that the temperature coefficient of expansion is 5.520E-03 (°C)⁻¹). What is the resistance at a temperature of 349 °C?

-a) 9.526E+00 Ω

+b) 1.000E+01 Ω

-c) 1.050E+01 Ω

-d) 1.103E+01 Ω

-e) 1.158E+01 Ω

6)

Two sources of emf ε₁=31.0 V, and ε₂=10.0 V are oriented as shownin the circuit. The resistances are R₁=4.22 kΩ and R₂=1.37 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.32 mA and I₄=1.03 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

+a) 2.290E+00 mA

-b) 2.519E+00 mA

-c) 2.771E+00 mA

-d) 3.048E+00 mA

-e) 3.353E+00 mA

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 8.55 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(1.96 i + 1.68 j + 6.92 k) x 10⁴ m/s?

-a) 4.179E-14 N

+b) 4.596E-14 N

-c) 5.056E-14 N

-d) 5.562E-14 N

-e) 6.118E-14 N

8) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?

-a) 1.283E-10 N/m

-b) 1.411E-10 N/m

-c) 1.552E-10 N/m

-d) 1.708E-10 N/m

+e) 1.878E-10 N/m

9) A recangular coil with an area of 0.449 m² and 20 turns is placed in a uniform magnetic field of 3.58 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.990E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 66 s?

-a) 7.734E+04 V

+b) 8.507E+04 V

-c) 9.358E+04 V

-d) 1.029E+05 V

-e) 1.132E+05 V

10)

A long solenoid has a length 0.667 meters, radius 4.41 cm, and 517 turns. It surrounds coil of radius 9.18 meters and 9turns. If the current in the solenoid is changing at a rate of 296 A/s, what is the emf induced in the surounding coil?

-a) 4.116E-02 V

-b) 4.528E-02 V

+c) 4.981E-02 V

-d) 5.479E-02 V

-e) 6.027E-02 V

11) The output of an ac generator connected to an RLC series combination has a frequency of 8.00E+04 Hz and an amplitude of 2 V. If R =7 Ω, L= 4.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

+a) 1.047E-04 Watts

-b) 1.151E-04 Watts

-c) 1.267E-04 Watts

-d) 1.393E-04 Watts

-e) 1.533E-04 Watts

12)

A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=3.60E+03 m² and separation d=3.50E-03 m is connected via a swith to a 28 Ω resistor and a battery of voltage V₀=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.00E-04?

-a) 3.751E+03 V/m

+b) 4.126E+03 V/m

-c) 4.539E+03 V/m

-d) 4.993E+03 V/m

-e) 5.492E+03 V/m

Key: G1

1)

Two sources of emf ε₁=20.6 V, and ε₂=9.53 V are oriented as shownin the circuit. The resistances are R₁=5.46 kΩ and R₂=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.5 mA and I₄=0.415 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

+a) 1.085E+00 mA

-b) 1.194E+00 mA

-c) 1.313E+00 mA

-d) 1.444E+00 mA

-e) 1.589E+00 mA

2) The output of an ac generator connected to an RLC series combination has a frequency of 6.00E+04 Hz and an amplitude of 2 V. If R =3 Ω, L= 7.20E-03H , and C=6.50E-06 F, what is the rms power transferred to the resistor?

-a) 2.222E-05 Watts

-b) 2.444E-05 Watts

-c) 2.689E-05 Watts

-d) 2.958E-05 Watts

+e) 3.253E-05 Watts

3) A recangular coil with an area of 0.412 m² and 18 turns is placed in a uniform magnetic field of 3.81 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 2.120E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 79 s?

-a) 4.465E+04 V

-b) 4.912E+04 V

-c) 5.403E+04 V

+d) 5.943E+04 V

-e) 6.538E+04 V

4)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=1e

,

q_{2}=-8e

, and

q_{3}=3e

?

-a) 3.629E+01 degrees

-b) 3.992E+01 degrees

-c) 4.391E+01 degrees

-d) 4.830E+01 degrees

+e) 5.313E+01 degrees

5) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=2 nC·m^-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

-a) 1.123E+02 N/C

-b) 1.235E+02 N/C

+c) 1.358E+02 N/C

-d) 1.494E+02 N/C

-e) 1.644E+02 N/C

6)

A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=4.80E+03 m² and separation d=5.80E-03 m is connected via a swith to a 93 Ω resistor and a battery of voltage V₀=48 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=9.00E-04?

-a) 5.023E+03 V/m

-b) 5.525E+03 V/m

+c) 6.078E+03 V/m

-d) 6.685E+03 V/m

-e) 7.354E+03 V/m

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.61 Ω at a temperature of 92°C and that the temperature coefficient of expansion is 4.260E-03 (°C)⁻¹). What is the resistance at a temperature of 422 °C?

+a) 6.279E+00 Ω

-b) 6.593E+00 Ω

-c) 6.923E+00 Ω

-d) 7.269E+00 Ω

-e) 7.632E+00 Ω

8)

A long solenoid has a length 0.864 meters, radius 3.37 cm, and 522 turns. It surrounds coil of radius 7.87 meters and 13turns. If the current in the solenoid is changing at a rate of 290 A/s, what is the emf induced in the surounding coil?

-a) 2.917E-02 V

+b) 3.208E-02 V

-c) 3.529E-02 V

-d) 3.882E-02 V

-e) 4.270E-02 V

9) If a 26 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=21 V is x² + y² + z² = R², where R=

-a) 8.360E+00 m

-b) 9.196E+00 m

-c) 1.012E+01 m

+d) 1.113E+01 m

-e) 1.224E+01 m

10) Two parallel wires each carry a 7.68 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.36 cm, 1.58 cm), while the other is located at (5.29 cm, 5.18 cm). What is the force per unit length between the wires?

-a) 1.973E-10 N/m

-b) 2.170E-10 N/m

-c) 2.387E-10 N/m

-d) 2.625E-10 N/m

+e) 2.888E-10 N/m

11) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.13 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(5.64 i + 1.93 j + 8.71 k) x 10⁴ m/s?

-a) 1.757E-14 N

+b) 1.933E-14 N

-c) 2.126E-14 N

-d) 2.339E-14 N

-e) 2.573E-14 N

12)

In the figure shown C₁=15.7 μF, C₂=2.87 μF, and C₃=5.46 μF. The voltage source provides ε=5.38 V. What is the energy stored in C₂?

-a) 6.890E+00 μJ

-b) 7.579E+00 μJ

-c) 8.337E+00 μJ

-d) 9.171E+00 μJ

+e) 1.009E+01 μJ

Key: G2

1) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.89 Ω at a temperature of 89°C and that the temperature coefficient of expansion is 5.340E-03 (°C)⁻¹). What is the resistance at a temperature of 566 °C?

-a) 9.763E+00 Ω

+b) 1.025E+01 Ω

-c) 1.076E+01 Ω

-d) 1.130E+01 Ω

-e) 1.187E+01 Ω

2)

Two sources of emf ε₁=31.0 V, and ε₂=10.0 V are oriented as shownin the circuit. The resistances are R₁=4.22 kΩ and R₂=1.37 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.32 mA and I₄=1.03 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

+a) 2.290E+00 mA

-b) 2.519E+00 mA

-c) 2.771E+00 mA

-d) 3.048E+00 mA

-e) 3.353E+00 mA

3)

A long solenoid has a length 0.822 meters, radius 4.37 cm, and 515 turns. It surrounds coil of radius 6.12 meters and 14turns. If the current in the solenoid is changing at a rate of 118 A/s, what is the emf induced in the surounding coil?

-a) 2.229E-02 V

+b) 2.451E-02 V

-c) 2.697E-02 V

-d) 2.966E-02 V

-e) 3.263E-02 V

4)

A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=5.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 98 Ω resistor and a battery of voltage V₀=67 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.80E-03?

-a) 5.050E+03 V/m

-b) 5.555E+03 V/m

-c) 6.111E+03 V/m

-d) 6.722E+03 V/m

+e) 7.394E+03 V/m

5) Two parallel wires each carry a 2.58 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.79 cm, 1.03 cm), while the other is located at (5.64 cm, 5.12 cm). What is the force per unit length between the wires?

-a) 2.634E-11 N/m

-b) 2.897E-11 N/m

+c) 3.187E-11 N/m

-d) 3.506E-11 N/m

-e) 3.856E-11 N/m

6) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 6.96 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(7.01 i + 5.35 j + 2.07 k) x 10⁴ m/s?

+a) 1.192E-13 N

-b) 1.311E-13 N

-c) 1.442E-13 N

-d) 1.586E-13 N

-e) 1.745E-13 N

7) If a 20 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=70 V is x² + y² + z² = R², where R=

-a) 1.754E+00 m

-b) 1.929E+00 m

-c) 2.122E+00 m

-d) 2.334E+00 m

+e) 2.568E+00 m

8) A recangular coil with an area of 0.178 m² and 17 turns is placed in a uniform magnetic field of 2.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.380E+03 s⁻¹. What is the magnitude (absolute value) of the induced emf at t = 45 s?

-a) 1.068E+04 V

-b) 1.175E+04 V

+c) 1.293E+04 V

-d) 1.422E+04 V

-e) 1.564E+04 V

9)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=5e

?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

10) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 6.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

-a) 2.007E-03 Watts

-b) 2.208E-03 Watts

-c) 2.429E-03 Watts

+d) 2.672E-03 Watts

-e) 2.939E-03 Watts

11)

In the figure shown C₁=16.3 μF, C₂=2.17 μF, and C₃=4.67 μF. The voltage source provides ε=8.35 V. What is the energy stored in C₂?

-a) 8.718E+00 μJ

-b) 9.589E+00 μJ

-c) 1.055E+01 μJ

-d) 1.160E+01 μJ

+e) 1.276E+01 μJ

12) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=2 nC·m^-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 6.411E+02 N/C

-b) 7.052E+02 N/C

+c) 7.757E+02 N/C

-d) 8.533E+02 N/C

-e) 9.386E+02 N/C

Key: H0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=4e

?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.7 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.3 m, z=z₀=1.8 m, and z=z₁=4.9 m. The surfaces in the yz plane each have area 8.1m². Those in the xy plane have area 7.0m² ,and those in the zx plane have area 8.4m². An electric field has the xyz components (0, 9.2, 7.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 6.364E+01 N·m²/C

-b) 7.000E+01 N·m²/C

+c) 7.700E+01 N·m²/C

-d) 8.470E+01 N·m²/C

-e) 9.317E+01 N·m²/C

3)

A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.29 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.33 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.

-a) 4.324E+02 V

-b) 4.757E+02 V

+c) 5.232E+02 V

-d) 5.755E+02 V

-e) 6.331E+02 V

4)

What is the net capacitance if C₁=3.13 μF, C₂=2.28 μF, and C₃=2.59 μF in the configuration shown?

-a) 3.231E+00 μF

-b) 3.554E+00 μF

+c) 3.909E+00 μF

-d) 4.300E+00 μF

-e) 4.730E+00 μF

5) Calculate the drift speed of electrons in a copper wire with a diameter of 5.33 mm carrying a 5.1 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

+a) 1.711E-05 m/s

-b) 1.882E-05 m/s

-c) 2.070E-05 m/s

-d) 2.277E-05 m/s

-e) 2.505E-05 m/s

6)

The resistances in the figure shown are R₁= 2.73 Ω, R₂= 1.4 Ω, and R₂= 2.35 Ω. V₁ and V₃ are text 0.549 V and 1.27 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.584 V. What is the absolute value of the current through R₁?

-a) 1.213E-01 A

-b) 1.334E-01 A

-c) 1.468E-01 A

+d) 1.614E-01 A

-e) 1.776E-01 A

7)

The silver ribbon shown are a=3.47 cm, b=2.98 cm, and c= 0.681 cm. The current carries a current of 289 A and it lies in a uniform magnetic field of 3.37 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

-a) 1.375E-05 V

+b) 1.513E-05 V

-c) 1.664E-05 V

-d) 1.831E-05 V

-e) 2.014E-05 V

8) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?

-a) 1.791E-05 T

-b) 1.970E-05 T

-c) 2.167E-05 T

-d) 2.384E-05 T

+e) 2.622E-05 T

9) A long solenoid has a radius of 0.521 m and 46 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 1 A and $\alpha =$ 30 s⁻¹.What is the induced electric fied at a distance 2.42 m from the axis at time t=0.0449 s ?

+a) 2.529E-05 V/m

-b) 2.782E-05 V/m

-c) 3.060E-05 V/m

-d) 3.366E-05 V/m

-e) 3.703E-05 V/m

10)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =3.56 s if ε = 6.14 V , R = 7.96 Ω, and L = 6.65 H?

-a) 5.281E-01 V

-b) 6.337E-01 V

+c) 7.605E-01 V

-d) 9.126E-01 V

-e) 1.095E+00 V

11) An ac generator produces an emf of amplitude 98 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a 2 mF capacitor?

-a) 1.232E-01 A

+b) 1.355E-01 A

-c) 1.490E-01 A

-d) 1.639E-01 A

-e) 1.803E-01 A

12)

A parallel plate capacitor with a capicatnce C=8.90E-06 F whose plates have an area A=6.90E+03 m² and separation d=6.90E-03 m is connected via a swith to a 89 Ω resistor and a battery of voltage V₀=89 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-03?

-a) 6.595E+01 V

-b) 7.255E+01 V

-c) 7.980E+01 V

+d) 8.778E+01 V

-e) 9.656E+01 V

Key: H1

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.26 mm from the center of a wire of radius 5 mm if the current is 1A?

-a) 1.494E-05 T

-b) 1.644E-05 T

+c) 1.808E-05 T

-d) 1.989E-05 T

-e) 2.188E-05 T

2)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =5.67 s if ε = 5.58 V , R = 3.81 Ω, and L = 3.85 H?

-a) 7.037E-01 V

-b) 8.444E-01 V

-c) 1.013E+00 V

-d) 1.216E+00 V

+e) 1.459E+00 V

3)

The silver ribbon shown are a=3.68 cm, b=2.66 cm, and c= 0.505 cm. The current carries a current of 113 A and it lies in a uniform magnetic field of 3.12 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

-a) 6.104E-06 V

-b) 6.714E-06 V

+c) 7.385E-06 V

-d) 8.124E-06 V

-e) 8.936E-06 V

4)

The resistances in the figure shown are R₁= 1.81 Ω, R₂= 1.18 Ω, and R₂= 2.62 Ω. V₁ and V₃ are text 0.628 V and 2.54 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.748 V. What is the absolute value of the current through R₁?

-a) 1.552E-01 A

-b) 1.707E-01 A

-c) 1.878E-01 A

-d) 2.065E-01 A

+e) 2.272E-01 A

5)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=5e

?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

6)

A parallel plate capacitor with a capicatnce C=7.10E-06 F whose plates have an area A=5.10E+03 m² and separation d=6.40E-03 m is connected via a swith to a 54 Ω resistor and a battery of voltage V₀=83 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-03?

-a) 6.111E+01 V

-b) 6.722E+01 V

-c) 7.395E+01 V

+d) 8.134E+01 V

-e) 8.947E+01 V

7)

A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.08 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.

-a) 7.017E+02 V

+b) 7.718E+02 V

-c) 8.490E+02 V

-d) 9.339E+02 V

-e) 1.027E+03 V

8)

What is the net capacitance if C₁=3.13 μF, C₂=2.28 μF, and C₃=2.59 μF in the configuration shown?

-a) 3.231E+00 μF

-b) 3.554E+00 μF

+c) 3.909E+00 μF

-d) 4.300E+00 μF

-e) 4.730E+00 μF

9) Calculate the drift speed of electrons in a copper wire with a diameter of 5.82 mm carrying a 9.11 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

-a) 1.926E-05 m/s

-b) 2.118E-05 m/s

-c) 2.330E-05 m/s

+d) 2.563E-05 m/s

-e) 2.819E-05 m/s

10) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

-a) 1.170E+00 A

+b) 1.287E+00 A

-c) 1.415E+00 A

-d) 1.557E+00 A

-e) 1.713E+00 A

11)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.1 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.2 m, z=z₀=1.1 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 8.5m². Those in the xy plane have area 2.8m² ,and those in the zx plane have area 3.7m². An electric field has the xyz components (0, 7.4, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 2.079E+01 N·m²/C

-b) 2.287E+01 N·m²/C

-c) 2.516E+01 N·m²/C

+d) 2.768E+01 N·m²/C

-e) 3.044E+01 N·m²/C

12) A long solenoid has a radius of 0.306 m and 98 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 6 A and $\alpha =$ 22 s⁻¹.What is the induced electric fied at a distance 2.52 m from the axis at time t=0.0246 s ?

-a) 1.598E-04 V/m

+b) 1.758E-04 V/m

-c) 1.934E-04 V/m

-d) 2.127E-04 V/m

-e) 2.340E-04 V/m

Key: H2

1) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.03 mm from the center of a wire of radius 3 mm if the current is 1A?

-a) 1.720E-05 T

-b) 1.892E-05 T

-c) 2.081E-05 T

+d) 2.289E-05 T

-e) 2.518E-05 T

2) An ac generator produces an emf of amplitude 90 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 16 mF capacitor?

-a) 4.351E-01 A

-b) 4.786E-01 A

-c) 5.264E-01 A

+d) 5.791E-01 A

-e) 6.370E-01 A

3)

What is the net capacitance if C₁=3.06 μF, C₂=3.09 μF, and C₃=2.48 μF in the configuration shown?

-a) 3.018E+00 μF

-b) 3.320E+00 μF

-c) 3.652E+00 μF

+d) 4.017E+00 μF

-e) 4.419E+00 μF

4)

The silver ribbon shown are a=3.55 cm, b=2.99 cm, and c= 1.03 cm. The current carries a current of 135 A and it lies in a uniform magnetic field of 1.26 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

-a) 1.193E-06 V

-b) 1.313E-06 V

-c) 1.444E-06 V

-d) 1.588E-06 V

+e) 1.747E-06 V

5) Calculate the drift speed of electrons in a copper wire with a diameter of 3.17 mm carrying a 12.0 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

+a) 1.138E-04 m/s

-b) 1.252E-04 m/s

-c) 1.377E-04 m/s

-d) 1.515E-04 m/s

-e) 1.666E-04 m/s

6)

The resistances in the figure shown are R₁= 2.67 Ω, R₂= 1.78 Ω, and R₂= 3.63 Ω. V₁ and V₃ are text 0.448 V and 2.29 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.656 V. What is the absolute value of the current through R₁?

-a) 9.287E-02 A

-b) 1.022E-01 A

-c) 1.124E-01 A

+d) 1.236E-01 A

-e) 1.360E-01 A

7)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 23 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?

+a) 2.877E+00 V

-b) 3.165E+00 V

-c) 3.481E+00 V

-d) 3.829E+00 V

-e) 4.212E+00 V

8) A long solenoid has a radius of 0.306 m and 98 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 6 A and $\alpha =$ 22 s⁻¹.What is the induced electric fied at a distance 2.52 m from the axis at time t=0.0246 s ?

-a) 1.598E-04 V/m

+b) 1.758E-04 V/m

-c) 1.934E-04 V/m

-d) 2.127E-04 V/m

-e) 2.340E-04 V/m

9)

A diploe has a charge magnitude of q=4 nC and a separation distance of d=4.16 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.

-a) 3.070E+02 V

-b) 3.377E+02 V

-c) 3.715E+02 V

-d) 4.086E+02 V

+e) 4.495E+02 V

10)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.6 m. The other four surfaces are rectangles in y=y₀=1.6 m, y=y₁=5.6 m, z=z₀=1.8 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 10.0m². Those in the xy plane have area 6.4m² ,and those in the zx plane have area 4.2m². An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 1.891E+01 N·m²/C

-b) 2.080E+01 N·m²/C

+c) 2.288E+01 N·m²/C

-d) 2.517E+01 N·m²/C

-e) 2.768E+01 N·m²/C

11)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=5e

?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

12)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =20.1 s if ε = 5.77 V , R = 1.38 Ω, and L = 5.45 H?

-a) 3.463E+00 V

+b) 4.156E+00 V

-c) 4.987E+00 V

-d) 5.984E+00 V

-e) 7.181E+00 V

Key: I0

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 3.428E+01 N/C

-b) 3.771E+01 N/C

-c) 4.148E+01 N/C

-d) 4.563E+01 N/C

+e) 5.020E+01 N/C

2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.7 (r≤R) where a=3 nC·m^-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 1.390E+03 N/C

+b) 1.530E+03 N/C

-c) 1.682E+03 N/C

-d) 1.851E+03 N/C

-e) 2.036E+03 N/C

3) Two large parallel conducting plates are separated by 6.67 mm. Equal and opposite surface charges of 7.080E-07 C/m² exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 60 V?

-a) 6.525E-01 mm

+b) 7.504E-01 mm

-c) 8.629E-01 mm

-d) 9.923E-01 mm

-e) 1.141E+00 mm

4)

What is the net capacitance if C₁=2.25 μF, C₂=4.16 μF, and C₃=2.49 μF in the configuration shown?

-a) 2.698E+00 μF

-b) 2.968E+00 μF

-c) 3.265E+00 μF

-d) 3.591E+00 μF

+e) 3.950E+00 μF

5) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 4.957E-02 Ω

-b) 5.453E-02 Ω

-c) 5.998E-02 Ω

+d) 6.598E-02 Ω

-e) 7.258E-02 Ω

6) A given battery has a 12 V emf and an internal resistance of 0.0984 Ω. If it is connected to a 0.485 Ω resistor what is the power dissipated by that load?

+a) 2.052E+02 W

-b) 2.257E+02 W

-c) 2.483E+02 W

-d) 2.731E+02 W

-e) 3.004E+02 W

7) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.449 m and a magneticfield of 0.81 T. What is their maximum kinetic energy?

-a) 5.795E+00 MeV

+b) 6.374E+00 MeV

-c) 7.012E+00 MeV

-d) 7.713E+00 MeV

-e) 8.484E+00 MeV

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.44 kA, I₂=1.1 kA, and I₃=1.99 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 1.017E-03 T-m

+b) 1.118E-03 T-m

-c) 1.230E-03 T-m

-d) 1.353E-03 T-m

-e) 1.489E-03 T-m

9) Calculate the motional emf induced along a 34.3 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.780E-05 Tesla magnetic field.

-a) 8.802E+03 V

-b) 9.682E+03 V

-c) 1.065E+04 V

-d) 1.172E+04 V

+e) 1.289E+04 V

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.56% of its maximum value if ε = 4.22 V , R = 1.89 Ω, and L = 6.57 H?

-a) -4.939E+00 s

-b) -5.433E+00 s

-c) -5.976E+00 s

-d) -6.574E+00 s

+e) -7.231E+00 s

11) An ac generator produces an emf of amplitude 5 V at a frequency of 52 Hz. What is the maximum amplitude of the current if the generator is connected to a 49 mF inductor?

-a) 2.839E-01 A

+b) 3.123E-01 A

-c) 3.435E-01 A

-d) 3.779E-01 A

-e) 4.157E-01 A

12)

A parallel plate capacitor with a capicatnce C=6.20E-06 F whose plates have an area A=5.30E+03 m² and separation d=7.50E-03 m is connected via a swith to a 95 Ω resistor and a battery of voltage V₀=15 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=9.20E-04?

-a) 8.097E+00 V

-b) 8.906E+00 V

-c) 9.797E+00 V

-d) 1.078E+01 V

+e) 1.185E+01 V

Key: I1

1) Calculate the resistance of a 12-gauge copper wire that is 59 m long and carries a current of 26 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

+a) 2.995E-01 Ω

-b) 3.294E-01 Ω

-c) 3.623E-01 Ω

-d) 3.986E-01 Ω

-e) 4.384E-01 Ω

2) Calculate the motional emf induced along a 30.3 km conductor moving at an orbital speed of 7.76 km/s perpendicular to Earth's 5.100E-05 Tesla magnetic field.

-a) 1.090E+04 V

+b) 1.199E+04 V

-c) 1.319E+04 V

-d) 1.451E+04 V

-e) 1.596E+04 V

3)

A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m² and separation d=3.40E-03 m is connected via a swith to a 15 Ω resistor and a battery of voltage V₀=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?

+a) 7.693E+01 V

-b) 8.463E+01 V

-c) 9.309E+01 V

-d) 1.024E+02 V

-e) 1.126E+02 V

4) A given battery has a 13 V emf and an internal resistance of 0.106 Ω. If it is connected to a 0.752 Ω resistor what is the power dissipated by that load?

-a) 1.569E+02 W

+b) 1.726E+02 W

-c) 1.899E+02 W

-d) 2.089E+02 W

-e) 2.298E+02 W

5) Two large parallel conducting plates are separated by 7.93 mm. Equal and opposite surface charges of 7.720E-07 C/m² exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 77 V?

-a) 6.678E-01 mm

-b) 7.679E-01 mm

+c) 8.831E-01 mm

-d) 1.016E+00 mm

-e) 1.168E+00 mm

6)

What is the net capacitance if C₁=3.97 μF, C₂=3.51 μF, and C₃=2.18 μF in the configuration shown?

-a) 3.038E+00 μF

-b) 3.341E+00 μF

-c) 3.675E+00 μF

+d) 4.043E+00 μF

-e) 4.447E+00 μF

7)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.43% of its maximum value if ε = 1.64 V , R = 8.3 Ω, and L = 1.61 H?

+a) -4.120E-01 s

-b) -4.532E-01 s

-c) -4.985E-01 s

-d) -5.483E-01 s

-e) -6.031E-01 s

8) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.8 (r≤R) where a=2 nC·m^-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

+a) 2.079E+02 N/C

-b) 2.287E+02 N/C

-c) 2.516E+02 N/C

-d) 2.767E+02 N/C

-e) 3.044E+02 N/C

9) An ac generator produces an emf of amplitude 40 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a 52 mF inductor?

-a) 7.783E-01 A

-b) 8.561E-01 A

+c) 9.417E-01 A

-d) 1.036E+00 A

-e) 1.140E+00 A

10)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.48 kA, I₂=1.47 kA, and I₃=2.6 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

+a) 1.420E-03 T-m

-b) 1.562E-03 T-m

-c) 1.718E-03 T-m

-d) 1.890E-03 T-m

-e) 2.079E-03 T-m

11) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.409 m and a magneticfield of 1.27 T. What is their maximum kinetic energy?

-a) 8.881E+00 MeV

-b) 9.769E+00 MeV

-c) 1.075E+01 MeV

-d) 1.182E+01 MeV

+e) 1.300E+01 MeV

12) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 3.428E+01 N/C

-b) 3.771E+01 N/C

-c) 4.148E+01 N/C

-d) 4.563E+01 N/C

+e) 5.020E+01 N/C

Key: I2

1) An ac generator produces an emf of amplitude 70 V at a frequency of 63 Hz. What is the maximum amplitude of the current if the generator is connected to a 34 mF inductor?

-a) 3.908E+00 A

-b) 4.298E+00 A

-c) 4.728E+00 A

+d) 5.201E+00 A

-e) 5.721E+00 A

2)

What is the net capacitance if C₁=3.13 μF, C₂=2.28 μF, and C₃=2.59 μF in the configuration shown?

-a) 3.231E+00 μF

-b) 3.554E+00 μF

+c) 3.909E+00 μF

-d) 4.300E+00 μF

-e) 4.730E+00 μF

3) Calculate the resistance of a 12-gauge copper wire that is 14 m long and carries a current of 38 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 5.873E-02 Ω

-b) 6.460E-02 Ω

+c) 7.106E-02 Ω

-d) 7.816E-02 Ω

-e) 8.598E-02 Ω

4)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=5.60E+03 m² and separation d=5.10E-03 m is connected via a swith to a 15 Ω resistor and a battery of voltage V₀=54 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.50E-04?

-a) 3.015E+01 V

-b) 3.316E+01 V

-c) 3.648E+01 V

-d) 4.013E+01 V

+e) 4.414E+01 V

5)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 2.01% of its maximum value if ε = 1.45 V , R = 4.4 Ω, and L = 2.36 H?

-a) -8.659E-01 s

-b) -9.525E-01 s

+c) -1.048E+00 s

-d) -1.153E+00 s

-e) -1.268E+00 s

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 7.000E+01 N/C

-b) 7.701E+01 N/C

+c) 8.471E+01 N/C

-d) 9.318E+01 N/C

-e) 1.025E+02 N/C

7) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=3 nC·m^-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

+a) 3.797E+01 N/C

-b) 4.177E+01 N/C

-c) 4.595E+01 N/C

-d) 5.054E+01 N/C

-e) 5.560E+01 N/C

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.31 kA, I₂=1.08 kA, and I₃=1.77 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 7.166E-04 T-m

-b) 7.883E-04 T-m

+c) 8.671E-04 T-m

-d) 9.538E-04 T-m

-e) 1.049E-03 T-m

9) Calculate the motional emf induced along a 24.6 km conductor moving at an orbital speed of 7.89 km/s perpendicular to Earth's 5.180E-05 Tesla magnetic field.

-a) 9.140E+03 V

+b) 1.005E+04 V

-c) 1.106E+04 V

-d) 1.217E+04 V

-e) 1.338E+04 V

10) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.378 m and a magneticfield of 0.835 T. What is their maximum kinetic energy?

-a) 4.365E+00 MeV

+b) 4.801E+00 MeV

-c) 5.281E+00 MeV

-d) 5.809E+00 MeV

-e) 6.390E+00 MeV

11) A given battery has a 15 V emf and an internal resistance of 0.177 Ω. If it is connected to a 0.824 Ω resistor what is the power dissipated by that load?

-a) 1.682E+02 W

+b) 1.850E+02 W

-c) 2.035E+02 W

-d) 2.239E+02 W

-e) 2.463E+02 W

12) Two large parallel conducting plates are separated by 7.77 mm. Equal and opposite surface charges of 7.310E-07 C/m² exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 73 V?

-a) 5.814E-01 mm

-b) 6.686E-01 mm

-c) 7.689E-01 mm

+d) 8.842E-01 mm

-e) 1.017E+00 mm

Key: J0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-7e

, and

q_{3}=4e

?

-a) 5.914E+01 degrees

-b) 6.506E+01 degrees

+c) 7.157E+01 degrees

-d) 7.872E+01 degrees

-e) 8.659E+01 degrees

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.3 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.2 m, z=z₀=1.8 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 8.5m² ,and those in the zx plane have area 6.0m². An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 4.730E+01 N·m²/C

+b) 5.203E+01 N·m²/C

-c) 5.723E+01 N·m²/C

-d) 6.295E+01 N·m²/C

-e) 6.925E+01 N·m²/C

3) A 12.0 V battery can move 30,000 C of charge. How many Joules does it deliver?

-a) 3.273E+05 J

+b) 3.600E+05 J

-c) 3.960E+05 J

-d) 4.356E+05 J

-e) 4.792E+05 J

4)

What is the net capacitance if C₁=3.25 μF, C₂=4.87 μF, and C₃=2.19 μF in the configuration shown?

+a) 4.139E+00 μF

-b) 4.553E+00 μF

-c) 5.008E+00 μF

-d) 5.509E+00 μF

-e) 6.060E+00 μF

5) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.06 Ω at a temperature of 80°C and that the temperature coefficient of expansion is 4.290E-03 (°C)⁻¹). What is the resistance at a temperature of 330 °C?

-a) 1.196E+01 Ω

+b) 1.256E+01 Ω

-c) 1.319E+01 Ω

-d) 1.385E+01 Ω

-e) 1.454E+01 Ω

6)

The resistances in the figure shown are R₁= 1.54 Ω, R₂= 0.927 Ω, and R₂= 2.46 Ω. V₁ and V₃ are text 0.632 V and 2.12 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.586 V. What is the absolute value of the current through R₁?

-a) 1.770E-01 A

-b) 1.947E-01 A

+c) 2.141E-01 A

-d) 2.355E-01 A

-e) 2.591E-01 A

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.78 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(1.43 i + 8.8 j + 4.16 k) x 10⁴ m/s?

+a) 1.064E-13 N

-b) 1.171E-13 N

-c) 1.288E-13 N

-d) 1.417E-13 N

-e) 1.558E-13 N

8) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.86 mm from the center of a wire of radius 3 mm if the current is 1A?

-a) 3.416E-05 T

-b) 3.758E-05 T

+c) 4.133E-05 T

-d) 4.547E-05 T

-e) 5.001E-05 T

9) A long solenoid has a radius of 0.793 m and 45 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 2 A and $\alpha =$ 29 s⁻¹.What is the induced electric fied at a distance 0.216 m from the axis at time t=0.0208 s ?

-a) 1.456E-04 V/m

-b) 1.601E-04 V/m

-c) 1.762E-04 V/m

+d) 1.938E-04 V/m

-e) 2.132E-04 V/m

10)

A long solenoid has a length 0.841 meters, radius 3.81 cm, and 516 turns. It surrounds coil of radius 9.2 meters and 11turns. If the current in the solenoid is changing at a rate of 190 A/s, what is the emf induced in the surounding coil?

-a) 1.735E-02 V

-b) 1.908E-02 V

-c) 2.099E-02 V

+d) 2.309E-02 V

-e) 2.540E-02 V

11) An ac generator produces an emf of amplitude 4 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 19 mF capacitor?

-a) 6.946E-02 A

+b) 7.640E-02 A

-c) 8.404E-02 A

-d) 9.245E-02 A

-e) 1.017E-01 A

12)

A parallel plate capacitor with a capicatnce C=6.60E-06 F whose plates have an area A=4.90E+03 m² and separation d=6.60E-03 m is connected via a swith to a 20 Ω resistor and a battery of voltage V₀=59 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.70E-04?

+a) 8.138E-01 A

-b) 8.952E-01 A

-c) 9.847E-01 A

-d) 1.083E+00 A

-e) 1.191E+00 A

Key: J1

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.6 m. The other four surfaces are rectangles in y=y₀=1.2 m, y=y₁=5.9 m, z=z₀=1.9 m, and z=z₁=5.0 m. The surfaces in the yz plane each have area 15.0m². Those in the xy plane have area 12.0m² ,and those in the zx plane have area 8.1m². An electric field has the xyz components (0, 8.1, 6.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

+a) 6.529E+01 N·m²/C

-b) 7.181E+01 N·m²/C

-c) 7.900E+01 N·m²/C

-d) 8.690E+01 N·m²/C

-e) 9.559E+01 N·m²/C

2)

What is the net capacitance if C₁=3.97 μF, C₂=3.51 μF, and C₃=2.18 μF in the configuration shown?

-a) 3.038E+00 μF

-b) 3.341E+00 μF

-c) 3.675E+00 μF

+d) 4.043E+00 μF

-e) 4.447E+00 μF

3)

A parallel plate capacitor with a capicatnce C=4.40E-06 F whose plates have an area A=1.80E+03 m² and separation d=3.60E-03 m is connected via a swith to a 87 Ω resistor and a battery of voltage V₀=61 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.70E-04?

-a) 8.320E-02 A

-b) 9.152E-02 A

-c) 1.007E-01 A

-d) 1.107E-01 A

+e) 1.218E-01 A

4) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.13 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(5.64 i + 1.93 j + 8.71 k) x 10⁴ m/s?

-a) 1.757E-14 N

+b) 1.933E-14 N

-c) 2.126E-14 N

-d) 2.339E-14 N

-e) 2.573E-14 N

5) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.66 mm from the center of a wire of radius 4 mm if the current is 1A?

+a) 3.325E-05 T

-b) 3.658E-05 T

-c) 4.023E-05 T

-d) 4.426E-05 T

-e) 4.868E-05 T

6) A long solenoid has a radius of 0.596 m and 19 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 5 A and $\alpha =$ 29 s⁻¹.What is the induced electric fied at a distance 0.209 m from the axis at time t=0.0604 s ?

+a) 6.277E-05 V/m

-b) 6.904E-05 V/m

-c) 7.595E-05 V/m

-d) 8.354E-05 V/m

-e) 9.190E-05 V/m

7) A 12.0 V battery can move 29,000 C of charge. How many Joules does it deliver?

-a) 2.615E+05 J

-b) 2.876E+05 J

-c) 3.164E+05 J

+d) 3.480E+05 J

-e) 3.828E+05 J

8) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a 99 mF capacitor?

-a) 1.644E+00 A

+b) 1.808E+00 A

-c) 1.989E+00 A

-d) 2.188E+00 A

-e) 2.407E+00 A

9)

The resistances in the figure shown are R₁= 2.74 Ω, R₂= 1.63 Ω, and R₂= 2.75 Ω. V₁ and V₃ are text 0.485 V and 2.01 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.555 V. What is the absolute value of the current through R₁?

-a) 1.114E-01 A

+b) 1.225E-01 A

-c) 1.348E-01 A

-d) 1.483E-01 A

-e) 1.631E-01 A

10)

A long solenoid has a length 0.974 meters, radius 4.72 cm, and 587 turns. It surrounds coil of radius 8.65 meters and 17turns. If the current in the solenoid is changing at a rate of 146 A/s, what is the emf induced in the surounding coil?

-a) 2.823E-02 V

-b) 3.105E-02 V

-c) 3.416E-02 V

-d) 3.757E-02 V

+e) 4.133E-02 V

11) Imagine a substance could be made into a very hot filament. Suppose the resitance is 5.89 Ω at a temperature of 43°C and that the temperature coefficient of expansion is 4.400E-03 (°C)⁻¹). What is the resistance at a temperature of 398 °C?

-a) 1.369E+01 Ω

-b) 1.437E+01 Ω

+c) 1.509E+01 Ω

-d) 1.584E+01 Ω

-e) 1.664E+01 Ω

12)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-9e

, and

q_{3}=6e

?

-a) 5.767E+01 degrees

+b) 6.343E+01 degrees

-c) 6.978E+01 degrees

-d) 7.676E+01 degrees

-e) 8.443E+01 degrees

Key: J2

1) A long solenoid has a radius of 0.851 m and 12 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 3 A and $\alpha =$ 30 s⁻¹.What is the induced electric fied at a distance 0.14 m from the axis at time t=0.0531 s ?

-a) 1.319E-05 V/m

-b) 1.451E-05 V/m

-c) 1.596E-05 V/m

-d) 1.756E-05 V/m

+e) 1.932E-05 V/m

2) A 12.0 V battery can move 11,000 C of charge. How many Joules does it deliver?

-a) 9.016E+04 J

-b) 9.917E+04 J

-c) 1.091E+05 J

-d) 1.200E+05 J

+e) 1.320E+05 J

3)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.0 m, z=z₀=1.9 m, and z=z₁=4.3 m. The surfaces in the yz plane each have area 7.9m². Those in the xy plane have area 4.0m² ,and those in the zx plane have area 2.9m². An electric field has the xyz components (0, 5.3, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 1.388E+01 N·m²/C

+b) 1.526E+01 N·m²/C

-c) 1.679E+01 N·m²/C

-d) 1.847E+01 N·m²/C

-e) 2.032E+01 N·m²/C

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.03 mm from the center of a wire of radius 3 mm if the current is 1A?

-a) 1.720E-05 T

-b) 1.892E-05 T

-c) 2.081E-05 T

+d) 2.289E-05 T

-e) 2.518E-05 T

5)

The resistances in the figure shown are R₁= 1.18 Ω, R₂= 0.878 Ω, and R₂= 2.11 Ω. V₁ and V₃ are text 0.637 V and 3.51 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.547 V. What is the absolute value of the current through R₁?

-a) 1.701E-01 A

+b) 1.871E-01 A

-c) 2.058E-01 A

-d) 2.264E-01 A

-e) 2.490E-01 A

6)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-7e

, and

q_{3}=6e

?

+a) 6.343E+01 degrees

-b) 6.978E+01 degrees

-c) 7.676E+01 degrees

-d) 8.443E+01 degrees

-e) 9.288E+01 degrees

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.23 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(3.84 i + 8.79 j + 9.05 k) x 10⁴ m/s?

-a) 7.509E-14 N

-b) 8.259E-14 N

+c) 9.085E-14 N

-d) 9.994E-14 N

-e) 1.099E-13 N

8)

What is the net capacitance if C₁=3.54 μF, C₂=3.53 μF, and C₃=3.65 μF in the configuration shown?

-a) 3.700E+00 μF

-b) 4.070E+00 μF

-c) 4.477E+00 μF

-d) 4.925E+00 μF

+e) 5.417E+00 μF

9) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.64 Ω at a temperature of 82°C and that the temperature coefficient of expansion is 4.530E-03 (°C)⁻¹). What is the resistance at a temperature of 390 °C?

-a) 7.532E+00 Ω

-b) 7.908E+00 Ω

-c) 8.303E+00 Ω

+d) 8.719E+00 Ω

-e) 9.155E+00 Ω

10)

A long solenoid has a length 0.89 meters, radius 3.01 cm, and 505 turns. It surrounds coil of radius 8.65 meters and 18turns. If the current in the solenoid is changing at a rate of 279 A/s, what is the emf induced in the surounding coil?

-a) 2.646E-02 V

-b) 2.911E-02 V

+c) 3.202E-02 V

-d) 3.522E-02 V

-e) 3.874E-02 V

11) An ac generator produces an emf of amplitude 4 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 19 mF capacitor?

-a) 6.946E-02 A

+b) 7.640E-02 A

-c) 8.404E-02 A

-d) 9.245E-02 A

-e) 1.017E-01 A

12)

A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=2.70E+03 m² and separation d=6.30E-03 m is connected via a swith to a 85 Ω resistor and a battery of voltage V₀=22 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.50E-03?

-a) 2.058E-03 A

-b) 2.263E-03 A

+c) 2.490E-03 A

-d) 2.739E-03 A

-e) 3.013E-03 A

Key: K0

1)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

+a) 5.352E+09 N/C²

-b) 5.887E+09 N/C²

-c) 6.476E+09 N/C²

-d) 7.124E+09 N/C²

-e) 7.836E+09 N/C²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.3 m, z=z₀=1.5 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 8.3m². Those in the xy plane have area 5.7m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 5.408E+01 N·m²/C

+b) 5.949E+01 N·m²/C

-c) 6.544E+01 N·m²/C

-d) 7.198E+01 N·m²/C

-e) 7.918E+01 N·m²/C

3) Assume that a 29 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P₁ and P₂ where the polar coordinates (r,φ) of P₁ are (6 cm, 0°) and P₂ is at (12 cm, 77°).

-a) 1.483E+03 V

-b) 1.632E+03 V

-c) 1.795E+03 V

-d) 1.975E+03 V

+e) 2.172E+03 V

4)

What is the net capacitance if C₁=4.13 μF, C₂=3.56 μF, and C₃=3.57 μF in the configuration shown?

+a) 5.482E+00 μF

-b) 6.030E+00 μF

-c) 6.633E+00 μF

-d) 7.296E+00 μF

-e) 8.026E+00 μF

5) A DC winch moter draws 19 amps at 175 volts as it lifts a 4.230E+03 N weight at a constant speed of 0.483 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

+a) 3.551E+00 Ω

-b) 3.906E+00 Ω

-c) 4.297E+00 Ω

-d) 4.726E+00 Ω

-e) 5.199E+00 Ω

6) A battery with a terminal voltage of 7.82 V is connected to a circuit consisting of 2 19.3 Ω resistors and one 12.2 Ω resistor. What is the voltage drop across the 12.2 Ω resistor?

-a) 1.552E+00 V

-b) 1.707E+00 V

+c) 1.878E+00 V

-d) 2.066E+00 V

-e) 2.272E+00 V

7) A circular current loop of radius 2.16 cm carries a current of 1.72 mA. What is the magnitude of the torque if the dipole is oriented at 52 ° to a uniform magnetic fied of 0.24 T?

-a) 3.582E-07 N m

-b) 3.940E-07 N m

-c) 4.334E-07 N m

+d) 4.768E-07 N m

-e) 5.245E-07 N m

8) Two parallel wires each carry a 8.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.66 cm, 1.4 cm), while the other is located at (5.64 cm, 5.66 cm). What is the force per unit length between the wires?

-a) 2.449E-10 N/m

-b) 2.694E-10 N/m

-c) 2.963E-10 N/m

+d) 3.260E-10 N/m

-e) 3.586E-10 N/m

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.419 m. The magnetic field is spatially uniform but decays in time according to $(2.48)e^{-\alpha t}$ , where $\alpha =$ 9.15 s. What is the current in the coil if the impedance of the coil is 67.8 Ω?

-a) 1.240E-01 A

+b) 1.364E-01 A

-c) 1.500E-01 A

-d) 1.650E-01 A

-e) 1.815E-01 A

10)

A long solenoid has a length 0.794 meters, radius 4.45 cm, and 568 turns. It surrounds coil of radius 6.81 meters and 9turns. If the current in the solenoid is changing at a rate of 246 A/s, what is the emf induced in the surounding coil?

+a) 3.890E-02 V

-b) 4.279E-02 V

-c) 4.707E-02 V

-d) 5.177E-02 V

-e) 5.695E-02 V

11) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

-a) 1.170E+00 A

+b) 1.287E+00 A

-c) 1.415E+00 A

-d) 1.557E+00 A

-e) 1.713E+00 A

12)

A parallel plate capacitor with a capicatnce C=2.90E-06 F whose plates have an area A=1.60E+03 m² and separation d=5.00E-03 m is connected via a swith to a 41 Ω resistor and a battery of voltage V₀=92 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=4.50E-04?

-a) 6.755E+01 V

-b) 7.431E+01 V

-c) 8.174E+01 V

+d) 8.991E+01 V

-e) 9.890E+01 V

Key: K1

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.7 m, z=z₀=1.8 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 9.2m² ,and those in the zx plane have area 8.1m². An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 2.134E+01 N·m²/C

-b) 2.347E+01 N·m²/C

+c) 2.582E+01 N·m²/C

-d) 2.840E+01 N·m²/C

-e) 3.124E+01 N·m²/C

2)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

3)

What is the net capacitance if C₁=4.12 μF, C₂=3.45 μF, and C₃=3.41 μF in the configuration shown?

-a) 4.370E+00 μF

-b) 4.807E+00 μF

+c) 5.288E+00 μF

-d) 5.816E+00 μF

-e) 6.398E+00 μF

4)

A long solenoid has a length 0.605 meters, radius 4.26 cm, and 597 turns. It surrounds coil of radius 9.08 meters and 12turns. If the current in the solenoid is changing at a rate of 250 A/s, what is the emf induced in the surounding coil?

-a) 4.551E-02 V

-b) 5.006E-02 V

-c) 5.507E-02 V

-d) 6.057E-02 V

+e) 6.663E-02 V

5) A battery with a terminal voltage of 8.14 V is connected to a circuit consisting of 2 21.5 Ω resistors and one 13.1 Ω resistor. What is the voltage drop across the 13.1 Ω resistor?

-a) 1.298E+00 V

-b) 1.428E+00 V

-c) 1.571E+00 V

-d) 1.728E+00 V

+e) 1.901E+00 V

6)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 23 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?

+a) 2.877E+00 V

-b) 3.165E+00 V

-c) 3.481E+00 V

-d) 3.829E+00 V

-e) 4.212E+00 V

7) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.419 m. The magnetic field is spatially uniform but decays in time according to $(2.48)e^{-\alpha t}$ , where $\alpha =$ 9.15 s. What is the current in the coil if the impedance of the coil is 67.8 Ω?

-a) 1.240E-01 A

+b) 1.364E-01 A

-c) 1.500E-01 A

-d) 1.650E-01 A

-e) 1.815E-01 A

8) A circular current loop of radius 2.48 cm carries a current of 3.67 mA. What is the magnitude of the torque if the dipole is oriented at 21 ° to a uniform magnetic fied of 0.402 T?

+a) 1.022E-06 N m

-b) 1.124E-06 N m

-c) 1.236E-06 N m

-d) 1.360E-06 N m

-e) 1.496E-06 N m

9) Assume that a 25 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P₁ and P₂ where the polar coordinates (r,φ) of P₁ are (5 cm, 0°) and P₂ is at (13 cm, 70°).

-a) 2.285E+03 V

-b) 2.514E+03 V

+c) 2.765E+03 V

-d) 3.042E+03 V

-e) 3.346E+03 V

10) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?

-a) 2.977E-11 N/m

-b) 3.274E-11 N/m

-c) 3.602E-11 N/m

-d) 3.962E-11 N/m

+e) 4.358E-11 N/m

11) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

+a) 5.042E+00 A

-b) 5.546E+00 A

-c) 6.100E+00 A

-d) 6.710E+00 A

-e) 7.381E+00 A

12) A DC winch moter draws 20 amps at 175 volts as it lifts a 5.180E+03 N weight at a constant speed of 0.541 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

+a) 1.744E+00 Ω

-b) 1.918E+00 Ω

-c) 2.110E+00 Ω

-d) 2.321E+00 Ω

-e) 2.553E+00 Ω

Key: K2

1)

A long solenoid has a length 0.822 meters, radius 4.37 cm, and 515 turns. It surrounds coil of radius 6.12 meters and 14turns. If the current in the solenoid is changing at a rate of 118 A/s, what is the emf induced in the surounding coil?

-a) 2.229E-02 V

+b) 2.451E-02 V

-c) 2.697E-02 V

-d) 2.966E-02 V

-e) 3.263E-02 V

2) A DC winch moter draws 19 amps at 175 volts as it lifts a 4.230E+03 N weight at a constant speed of 0.483 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

+a) 3.551E+00 Ω

-b) 3.906E+00 Ω

-c) 4.297E+00 Ω

-d) 4.726E+00 Ω

-e) 5.199E+00 Ω

3)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

4) A battery with a terminal voltage of 12.4 V is connected to a circuit consisting of 3 21.6 Ω resistors and one 12.1 Ω resistor. What is the voltage drop across the 12.1 Ω resistor?

-a) 1.333E+00 V

-b) 1.466E+00 V

-c) 1.612E+00 V

-d) 1.774E+00 V

+e) 1.951E+00 V

5)

A parallel plate capacitor with a capicatnce C=7.40E-06 F whose plates have an area A=7.20E+03 m² and separation d=8.60E-03 m is connected via a swith to a 14 Ω resistor and a battery of voltage V₀=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-04?

-a) 9.195E+00 V

-b) 1.011E+01 V

-c) 1.113E+01 V

+d) 1.224E+01 V

-e) 1.346E+01 V

6)

What is the net capacitance if C₁=4.55 μF, C₂=4.39 μF, and C₃=3.32 μF in the configuration shown?

-a) 4.173E+00 μF

-b) 4.590E+00 μF

-c) 5.049E+00 μF

+d) 5.554E+00 μF

-e) 6.110E+00 μF

7) Two parallel wires each carry a 7.59 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.98 cm, 0.969 cm), while the other is located at (5.13 cm, 5.53 cm). What is the force per unit length between the wires?

-a) 1.840E-10 N/m

-b) 2.024E-10 N/m

-c) 2.227E-10 N/m

+d) 2.449E-10 N/m

-e) 2.694E-10 N/m

8) Assume that a 29 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P₁ and P₂ where the polar coordinates (r,φ) of P₁ are (6 cm, 0°) and P₂ is at (12 cm, 77°).

-a) 1.483E+03 V

-b) 1.632E+03 V

-c) 1.795E+03 V

-d) 1.975E+03 V

+e) 2.172E+03 V

9)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.5 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.3 m, z=z₀=1.2 m, and z=z₁=4.6 m. The surfaces in the yz plane each have area 9.9m². Those in the xy plane have area 4.3m² ,and those in the zx plane have area 5.1m². An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 3.750E+01 N·m²/C

-b) 4.125E+01 N·m²/C

-c) 4.537E+01 N·m²/C

+d) 4.991E+01 N·m²/C

-e) 5.490E+01 N·m²/C

10) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.419 m. The magnetic field is spatially uniform but decays in time according to $(2.48)e^{-\alpha t}$ , where $\alpha =$ 9.15 s. What is the current in the coil if the impedance of the coil is 67.8 Ω?

-a) 1.240E-01 A

+b) 1.364E-01 A

-c) 1.500E-01 A

-d) 1.650E-01 A

-e) 1.815E-01 A

11) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a 99 mF capacitor?

-a) 1.644E+00 A

+b) 1.808E+00 A

-c) 1.989E+00 A

-d) 2.188E+00 A

-e) 2.407E+00 A

12) A circular current loop of radius 1.94 cm carries a current of 1.83 mA. What is the magnitude of the torque if the dipole is oriented at 43 ° to a uniform magnetic fied of 0.156 T?

-a) 1.903E-07 N m

-b) 2.093E-07 N m

+c) 2.302E-07 N m

-d) 2.532E-07 N m

-e) 2.785E-07 N m

Key: L0

1)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate

f(x,y)

at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

-a) 6.804E+00 V/m²

+b) 7.485E+00 V/m²

-c) 8.233E+00 V/m²

-d) 9.056E+00 V/m²

-e) 9.962E+00 V/m²

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}$

-a) 2.067E+03 V·m

-b) 2.274E+03 V·m

+c) 2.501E+03 V·m

-d) 2.752E+03 V·m

-e) 3.027E+03 V·m

3) A 12.0 V battery can move 12,000 C of charge. How many Joules does it deliver?

-a) 1.190E+05 J

-b) 1.309E+05 J

+c) 1.440E+05 J

-d) 1.584E+05 J

-e) 1.742E+05 J

4) An empty parallel-plate capacitor with metal plates has an area of 1.94 m², separated by 1.36 mm. How much charge does it store if the voltage is 8.530E+03 V?

-a) 7.359E+01 μC

-b) 8.094E+01 μC

-c) 8.904E+01 μC

-d) 9.794E+01 μC

+e) 1.077E+02 μC

5) Calculate the electric field in a 12-gauge copper wire that is 23 m long and carries a current of 64 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 2.953E-04 V/m

+b) 3.248E-04 V/m

-c) 3.573E-04 V/m

-d) 3.930E-04 V/m

-e) 4.324E-04 V/m

6)

Two sources of emf ε₁=17.3 V, and ε₂=6.46 V are oriented as shownin the circuit. The resistances are R₁=2.54 kΩ and R₂=2.79 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.1 mA and I₄=0.281 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

-a) 6.488E+00 V

+b) 7.137E+00 V

-c) 7.850E+00 V

-d) 8.635E+00 V

-e) 9.499E+00 V

7) A 62 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.351 T. What current is required to maintain this balance?

-a) 3.999E-01 A

-b) 4.398E-01 A

-c) 4.838E-01 A

-d) 5.322E-01 A

+e) 5.854E-01 A

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.38 kA, I₂=1.58 kA, and I₃=4.31 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 4.386E-03 T-m

-b) 4.825E-03 T-m

-c) 5.307E-03 T-m

-d) 5.838E-03 T-m

+e) 6.421E-03 T-m

9) A long solenoid has a radius of 0.857 m and 58 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 1 A and $\alpha =$ 21 s⁻¹.What is the induced electric fied at a distance 0.144 m from the axis at time t=0.0898 s ?

-a) 1.256E-05 V/m

-b) 1.382E-05 V/m

-c) 1.520E-05 V/m

+d) 1.672E-05 V/m

-e) 1.839E-05 V/m

10)

A long solenoid has a length 0.777 meters, radius 3.45 cm, and 557 turns. It surrounds coil of radius 6.01 meters and 10turns. If the current in the solenoid is changing at a rate of 184 A/s, what is the emf induced in the surounding coil?

-a) 1.463E-02 V

-b) 1.609E-02 V

-c) 1.770E-02 V

+d) 1.947E-02 V

-e) 2.142E-02 V

11) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 6.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

-a) 2.007E-03 Watts

-b) 2.208E-03 Watts

-c) 2.429E-03 Watts

+d) 2.672E-03 Watts

-e) 2.939E-03 Watts

12) A 59 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?

-a) 1.517E+02 km

+b) 1.669E+02 km

-c) 1.835E+02 km

-d) 2.019E+02 km

-e) 2.221E+02 km

Key: L1

1) A 33 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.869 T. What current is required to maintain this balance?

-a) 2.259E-01 A

-b) 2.485E-01 A

+c) 2.734E-01 A

-d) 3.007E-01 A

-e) 3.308E-01 A

2)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate

f(x,y)

at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

-a) 3.610E+00 V/m²

+b) 3.971E+00 V/m²

-c) 4.368E+00 V/m²

-d) 4.804E+00 V/m²

-e) 5.285E+00 V/m²

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
${\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}$

-a) 2.210E+04 V·m

+b) 2.431E+04 V·m

-c) 2.674E+04 V·m

-d) 2.941E+04 V·m

-e) 3.235E+04 V·m

4)

Two sources of emf ε₁=27.9 V, and ε₂=11.1 V are oriented as shownin the circuit. The resistances are R₁=2.82 kΩ and R₂=2.25 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.1 mA and I₄=0.676 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

-a) 8.334E+00 V

-b) 9.167E+00 V

+c) 1.008E+01 V

-d) 1.109E+01 V

-e) 1.220E+01 V

5) An empty parallel-plate capacitor with metal plates has an area of 2.42 m², separated by 1.33 mm. How much charge does it store if the voltage is 1.130E+03 V?

-a) 1.368E+01 μC

-b) 1.505E+01 μC

-c) 1.655E+01 μC

+d) 1.820E+01 μC

-e) 2.003E+01 μC

6) Calculate the electric field in a 12-gauge copper wire that is 21 m long and carries a current of 42 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 1.602E-04 V/m

-b) 1.762E-04 V/m

-c) 1.938E-04 V/m

+d) 2.132E-04 V/m

-e) 2.345E-04 V/m

7)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.58 kA, I₂=1.11 kA, and I₃=2.47 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 4.092E-03 T-m

-b) 4.501E-03 T-m

+c) 4.951E-03 T-m

-d) 5.446E-03 T-m

-e) 5.991E-03 T-m

8) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 84 kW?

-a) 9.780E+01 km

-b) 1.076E+02 km

-c) 1.183E+02 km

-d) 1.302E+02 km

+e) 1.432E+02 km

9)

A long solenoid has a length 0.794 meters, radius 4.45 cm, and 568 turns. It surrounds coil of radius 6.81 meters and 9turns. If the current in the solenoid is changing at a rate of 246 A/s, what is the emf induced in the surounding coil?

+a) 3.890E-02 V

-b) 4.279E-02 V

-c) 4.707E-02 V

-d) 5.177E-02 V

-e) 5.695E-02 V

10) A long solenoid has a radius of 0.603 m and 51 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 2 A and $\alpha =$ 26 s⁻¹.What is the induced electric fied at a distance 0.105 m from the axis at time t=0.0659 s ?

-a) 2.154E-05 V/m

-b) 2.369E-05 V/m

-c) 2.606E-05 V/m

-d) 2.867E-05 V/m

+e) 3.154E-05 V/m

11) The output of an ac generator connected to an RLC series combination has a frequency of 7.60E+04 Hz and an amplitude of 5 V. If R =6 Ω, L= 3.70E-03H , and C=5.80E-06 F, what is the rms power transferred to the resistor?

-a) 7.239E-04 Watts

-b) 7.963E-04 Watts

-c) 8.759E-04 Watts

+d) 9.635E-04 Watts

-e) 1.060E-03 Watts

12) A 12.0 V battery can move 36,000 C of charge. How many Joules does it deliver?

-a) 3.570E+05 J

-b) 3.927E+05 J

+c) 4.320E+05 J

-d) 4.752E+05 J

-e) 5.227E+05 J

Key: L2

1)

E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx

is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate

f(x,y)

at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

-a) 6.804E+00 V/m²

+b) 7.485E+00 V/m²

-c) 8.233E+00 V/m²

-d) 9.056E+00 V/m²

-e) 9.962E+00 V/m²

2) A long solenoid has a radius of 0.861 m and 28 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 1 A and $\alpha =$ 20 s⁻¹.What is the induced electric fied at a distance 0.106 m from the axis at time t=0.055 s ?

-a) 1.026E-05 V/m

-b) 1.129E-05 V/m

+c) 1.242E-05 V/m

-d) 1.366E-05 V/m

-e) 1.502E-05 V/m

3)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.42 kA, I₂=0.904 kA, and I₃=1.34 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 2.696E-03 T-m

-b) 2.966E-03 T-m

-c) 3.263E-03 T-m

+d) 3.589E-03 T-m

-e) 3.948E-03 T-m

4) An empty parallel-plate capacitor with metal plates has an area of 1.73 m², separated by 1.16 mm. How much charge does it store if the voltage is 1.130E+03 V?

-a) 1.121E+01 μC

-b) 1.233E+01 μC

-c) 1.357E+01 μC

+d) 1.492E+01 μC

-e) 1.641E+01 μC

5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}$

-a) 1.969E+02 V·m

-b) 2.166E+02 V·m

-c) 2.383E+02 V·m

-d) 2.621E+02 V·m

+e) 2.883E+02 V·m

6) A 62 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.351 T. What current is required to maintain this balance?

-a) 3.999E-01 A

-b) 4.398E-01 A

-c) 4.838E-01 A

-d) 5.322E-01 A

+e) 5.854E-01 A

7) A 12.0 V battery can move 24,000 C of charge. How many Joules does it deliver?

-a) 1.967E+05 J

-b) 2.164E+05 J

-c) 2.380E+05 J

-d) 2.618E+05 J

+e) 2.880E+05 J

8) A 41 kW radio transmitter on Earth sends it signal to a satellite 100 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?

-a) 1.405E+02 km

+b) 1.546E+02 km

-c) 1.701E+02 km

-d) 1.871E+02 km

-e) 2.058E+02 km

9)

Two sources of emf ε₁=42.2 V, and ε₂=17.8 V are oriented as shownin the circuit. The resistances are R₁=4.2 kΩ and R₂=2.83 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.5 mA and I₄=0.749 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

-a) 1.056E+01 V

-b) 1.161E+01 V

-c) 1.277E+01 V

+d) 1.405E+01 V

-e) 1.545E+01 V

10)

A long solenoid has a length 0.841 meters, radius 3.81 cm, and 516 turns. It surrounds coil of radius 9.2 meters and 11turns. If the current in the solenoid is changing at a rate of 190 A/s, what is the emf induced in the surounding coil?

-a) 1.735E-02 V

-b) 1.908E-02 V

-c) 2.099E-02 V

+d) 2.309E-02 V

-e) 2.540E-02 V

11) The output of an ac generator connected to an RLC series combination has a frequency of 5.00E+04 Hz and an amplitude of 5 V. If R =6 Ω, L= 2.50E-03H , and C=5.20E-06 F, what is the rms power transferred to the resistor?

+a) 5.097E-03 Watts

-b) 5.607E-03 Watts

-c) 6.167E-03 Watts

-d) 6.784E-03 Watts

-e) 7.463E-03 Watts

12) Calculate the electric field in a 12-gauge copper wire that is 64 m long and carries a current of 76 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 2.635E-04 V/m

-b) 2.898E-04 V/m

-c) 3.188E-04 V/m

-d) 3.507E-04 V/m

+e) 3.857E-04 V/m

Key: M0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=5e

?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.3 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=4.6 m, z=z₀=1.6 m, and z=z₁=5.8 m. The surfaces in the yz plane each have area 13.0m². Those in the xy plane have area 7.1m² ,and those in the zx plane have area 9.7m². An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 8.415E+01 N·m²/C

-b) 9.256E+01 N·m²/C

-c) 1.018E+02 N·m²/C

+d) 1.120E+02 N·m²/C

-e) 1.232E+02 N·m²/C

3) When a 5.65 V battery operates a 2.73 W bulb, how many electrons pass through it each second?

+a) 3.016E+18 electrons

-b) 3.317E+18 electrons

-c) 3.649E+18 electrons

-d) 4.014E+18 electrons

-e) 4.415E+18 electrons

4)

In the figure shown C₁=18.7 μF, C₂=2.15 μF, and C₃=4.88 μF. The voltage source provides ε=11.9 V. What is the energy stored in C₂?

-a) 1.270E+01 μJ

-b) 1.397E+01 μJ

-c) 1.537E+01 μJ

-d) 1.690E+01 μJ

+e) 1.859E+01 μJ

5) A DC winch moter draws 26 amps at 177 volts as it lifts a 4.820E+03 N weight at a constant speed of 0.696 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

-a) 1.677E+00 Ω

+b) 1.845E+00 Ω

-c) 2.030E+00 Ω

-d) 2.233E+00 Ω

-e) 2.456E+00 Ω

6) Three resistors, R₁ = 1.52 Ω, and R₂ = R₂ = 3.38 Ω, are connected in parallel to a 5.82 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

-a) 1.842E+01 W

-b) 2.026E+01 W

+c) 2.228E+01 W

-d) 2.451E+01 W

-e) 2.696E+01 W

7) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.96 mT and 2.010E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

-a) 2.768E+05 m/s

-b) 3.045E+05 m/s

-c) 3.349E+05 m/s

-d) 3.684E+05 m/s

+e) 4.052E+05 m/s

8) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 17 turns per centimeter and the current applied to the solenoid is 331 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

-a)

\chi {\text{ (chi) }}=

1.593E+03

+b)

\chi {\text{ (chi) }}=

1.753E+03

-c)

\chi {\text{ (chi) }}=

1.928E+03

-d)

\chi {\text{ (chi) }}=

2.121E+03

-e)

\chi {\text{ (chi) }}=

2.333E+03

9)

A cylinder of height 3.82 cm and radius 5.6 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.89 cm from point O and moves at a speed of 4.25 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

-a) 7.280E+01 cm³/s

-b) 8.008E+01 cm³/s

+c) 8.808E+01 cm³/s

-d) 9.689E+01 cm³/s

-e) 1.066E+02 cm³/s

10)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =0.919 s if ε = 6.65 V , R = 6.34 Ω, and L = 1.14 H?

-a) 6.033E-01 V

-b) 7.240E-01 V

-c) 8.688E-01 V

+d) 1.043E+00 V

-e) 1.251E+00 V

11) An ac generator produces an emf of amplitude 8 V at a frequency of 80 Hz. What is the maximum amplitude of the current if the generator is connected to a 14 mF inductor?

-a) 8.541E-01 A

-b) 9.395E-01 A

-c) 1.033E+00 A

+d) 1.137E+00 A

-e) 1.251E+00 A

12)

A parallel plate capacitor with a capicatnce C=9.10E-06 F whose plates have an area A=8.50E+03 m² and separation d=8.30E-03 m is connected via a swith to a 67 Ω resistor and a battery of voltage V₀=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.40E-03?

-a) 5.946E+00 V

-b) 6.541E+00 V

+c) 7.195E+00 V

-d) 7.914E+00 V

-e) 8.706E+00 V

Key: M1

1) An ac generator produces an emf of amplitude 37 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 86 mF inductor?

-a) 4.677E-01 A

-b) 5.145E-01 A

-c) 5.659E-01 A

-d) 6.225E-01 A

+e) 6.847E-01 A

2)

A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

+a) 1.892E+01 cm³/s

-b) 2.081E+01 cm³/s

-c) 2.289E+01 cm³/s

-d) 2.518E+01 cm³/s

-e) 2.770E+01 cm³/s

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 18 turns per centimeter and the current applied to the solenoid is 582 mA, the net magnetic field is measured to be 1.15 T. What is the magnetic susceptibility for this case?

-a)

\chi {\text{ (chi) }}=

7.211E+02

-b)

\chi {\text{ (chi) }}=

7.932E+02

+c)

\chi {\text{ (chi) }}=

8.726E+02

-d)

\chi {\text{ (chi) }}=

9.598E+02

-e)

\chi {\text{ (chi) }}=

1.056E+03

4)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=5e

?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

5)

A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m² and separation d=3.20E-03 m is connected via a swith to a 61 Ω resistor and a battery of voltage V₀=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?

+a) 5.017E+01 V

-b) 5.519E+01 V

-c) 6.071E+01 V

-d) 6.678E+01 V

-e) 7.345E+01 V

6)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =13.6 s if ε = 6.56 V , R = 2.44 Ω, and L = 8.76 H?

+a) 2.627E+00 V

-b) 3.153E+00 V

-c) 3.783E+00 V

-d) 4.540E+00 V

-e) 5.448E+00 V

7) When a 3.63 V battery operates a 1.34 W bulb, how many electrons pass through it each second?

-a) 2.095E+18 electrons

+b) 2.304E+18 electrons

-c) 2.534E+18 electrons

-d) 2.788E+18 electrons

-e) 3.067E+18 electrons

8) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.96 mT and 2.010E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

-a) 2.768E+05 m/s

-b) 3.045E+05 m/s

-c) 3.349E+05 m/s

-d) 3.684E+05 m/s

+e) 4.052E+05 m/s

9) Three resistors, R₁ = 1.31 Ω, and R₂ = R₂ = 2.91 Ω, are connected in parallel to a 6.03 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

-a) 2.294E+01 W

-b) 2.523E+01 W

+c) 2.776E+01 W

-d) 3.053E+01 W

-e) 3.359E+01 W

10) A DC winch moter draws 29 amps at 153 volts as it lifts a 4.780E+03 N weight at a constant speed of 0.691 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

-a) 1.226E+00 Ω

+b) 1.348E+00 Ω

-c) 1.483E+00 Ω

-d) 1.632E+00 Ω

-e) 1.795E+00 Ω

11)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.6 m. The other four surfaces are rectangles in y=y₀=1.3 m, y=y₁=4.4 m, z=z₀=1.4 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 13.0m². Those in the xy plane have area 5.0m² ,and those in the zx plane have area 6.6m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 2.756E+01 N·m²/C

-b) 3.032E+01 N·m²/C

-c) 3.335E+01 N·m²/C

-d) 3.668E+01 N·m²/C

+e) 4.035E+01 N·m²/C

12)

In the figure shown C₁=18.1 μF, C₂=2.13 μF, and C₃=5.48 μF. The voltage source provides ε=14.6 V. What is the energy stored in C₂?

-a) 1.645E+01 μJ

-b) 1.809E+01 μJ

-c) 1.990E+01 μJ

+d) 2.189E+01 μJ

-e) 2.408E+01 μJ

Key: M2

1) A DC winch moter draws 13 amps at 159 volts as it lifts a 4.270E+03 N weight at a constant speed of 0.357 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.

+a) 3.211E+00 Ω

-b) 3.532E+00 Ω

-c) 3.885E+00 Ω

-d) 4.273E+00 Ω

-e) 4.701E+00 Ω

2)

Suppose switch S₁ is suddenly closed at time t=0 in the figure shown. What is the current at t =1.95 s if ε = 8.33 V , R = 6.96 Ω, and L = 2.66 H?

-a) 5.736E-01 V

-b) 6.884E-01 V

-c) 8.260E-01 V

-d) 9.912E-01 V

+e) 1.189E+00 V

3) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.88 mT and 7.340E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

+a) 1.504E+06 m/s

-b) 1.655E+06 m/s

-c) 1.820E+06 m/s

-d) 2.002E+06 m/s

-e) 2.202E+06 m/s

4) An ac generator produces an emf of amplitude 70 V at a frequency of 63 Hz. What is the maximum amplitude of the current if the generator is connected to a 34 mF inductor?

-a) 3.908E+00 A

-b) 4.298E+00 A

-c) 4.728E+00 A

+d) 5.201E+00 A

-e) 5.721E+00 A

5)

In the figure shown C₁=18.7 μF, C₂=2.15 μF, and C₃=4.88 μF. The voltage source provides ε=11.9 V. What is the energy stored in C₂?

-a) 1.270E+01 μJ

-b) 1.397E+01 μJ

-c) 1.537E+01 μJ

-d) 1.690E+01 μJ

+e) 1.859E+01 μJ

6) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 17 turns per centimeter and the current applied to the solenoid is 331 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

-a)

\chi {\text{ (chi) }}=

1.593E+03

+b)

\chi {\text{ (chi) }}=

1.753E+03

-c)

\chi {\text{ (chi) }}=

1.928E+03

-d)

\chi {\text{ (chi) }}=

2.121E+03

-e)

\chi {\text{ (chi) }}=

2.333E+03

7)

A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

+a) 1.892E+01 cm³/s

-b) 2.081E+01 cm³/s

-c) 2.289E+01 cm³/s

-d) 2.518E+01 cm³/s

-e) 2.770E+01 cm³/s

8)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.2 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.3 m, z=z₀=1.5 m, and z=z₁=4.7 m. The surfaces in the yz plane each have area 8.3m². Those in the xy plane have area 5.7m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 5.408E+01 N·m²/C

+b) 5.949E+01 N·m²/C

-c) 6.544E+01 N·m²/C

-d) 7.198E+01 N·m²/C

-e) 7.918E+01 N·m²/C

9) Three resistors, R₁ = 1.43 Ω, and R₂ = R₂ = 3.25 Ω, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

-a) 5.184E+01 W

+b) 5.702E+01 W

-c) 6.272E+01 W

-d) 6.900E+01 W

-e) 7.590E+01 W

10)

A parallel plate capacitor with a capicatnce C=9.10E-06 F whose plates have an area A=8.50E+03 m² and separation d=8.30E-03 m is connected via a swith to a 67 Ω resistor and a battery of voltage V₀=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.40E-03?

-a) 5.946E+00 V

-b) 6.541E+00 V

+c) 7.195E+00 V

-d) 7.914E+00 V

-e) 8.706E+00 V

11)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-9e

, and

q_{3}=5e

?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

12) When a 6.97 V battery operates a 2.6 W bulb, how many electrons pass through it each second?

-a) 1.749E+18 electrons

-b) 1.924E+18 electrons

-c) 2.117E+18 electrons

+d) 2.328E+18 electrons

-e) 2.561E+18 electrons

Key: N0

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.357E+01 N/C

-b) 2.593E+01 N/C

-c) 2.852E+01 N/C

+d) 3.137E+01 N/C

-e) 3.451E+01 N/C

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.3 m, y=y₁=4.2 m, z=z₀=1.9 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 10.0m². Those in the xy plane have area 8.1m² ,and those in the zx plane have area 10.0m². An electric field has the xyz components (0, 8.5, 6.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 7.081E+01 N·m²/C

-b) 7.789E+01 N·m²/C

+c) 8.568E+01 N·m²/C

-d) 9.425E+01 N·m²/C

-e) 1.037E+02 N·m²/C

3) When a 6.32 V battery operates a 1.94 W bulb, how many electrons pass through it each second?

-a) 1.439E+18 electrons

-b) 1.583E+18 electrons

-c) 1.742E+18 electrons

+d) 1.916E+18 electrons

-e) 2.107E+18 electrons

4)

What is the net capacitance if C₁=2.3 μF, C₂=2.84 μF, and C₃=3.41 μF in the configuration shown?

-a) 4.255E+00 μF

+b) 4.681E+00 μF

-c) 5.149E+00 μF

-d) 5.664E+00 μF

-e) 6.230E+00 μF

5) Calculate the resistance of a 12-gauge copper wire that is 45 m long and carries a current of 51 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 1.716E-01 Ω

-b) 1.888E-01 Ω

-c) 2.076E-01 Ω

+d) 2.284E-01 Ω

-e) 2.512E-01 Ω

6)

Two sources of emf ε₁=18.2 V, and ε₂=6.59 V are oriented as shownin the circuit. The resistances are R₁=5.47 kΩ and R₂=2.81 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.64 mA and I₄=0.341 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

+a) 1.299E+00 mA

-b) 1.429E+00 mA

-c) 1.572E+00 mA

-d) 1.729E+00 mA

-e) 1.902E+00 mA

7) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.295 m and a magneticfield of 1.44 T. What is their maximum kinetic energy?

-a) 6.534E+00 MeV

-b) 7.187E+00 MeV

-c) 7.906E+00 MeV

+d) 8.697E+00 MeV

-e) 9.566E+00 MeV

8)

Three wires sit at the corners of a square of length 0.467 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?

-a) B_x= 8.371E-05 T

-b) B_x= 9.208E-05 T

+c) B_x= 1.013E-04 T

-d) B_x= 1.114E-04 T

-e) B_x= 1.226E-04 T

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to $(1.95)e^{-\alpha t}$ , where $\alpha =$ 7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

-a) 7.402E-01 A

-b) 8.142E-01 A

-c) 8.956E-01 A

+d) 9.852E-01 A

-e) 1.084E+00 A

10)

A long solenoid has a length 0.841 meters, radius 3.81 cm, and 516 turns. It surrounds coil of radius 9.2 meters and 11turns. If the current in the solenoid is changing at a rate of 190 A/s, what is the emf induced in the surounding coil?

-a) 1.735E-02 V

-b) 1.908E-02 V

-c) 2.099E-02 V

+d) 2.309E-02 V

-e) 2.540E-02 V

11) A step-down transformer steps 18 kV down to 170 V. The high-voltage input is provided by a 240 Ω power line that carries 5 A of currentWhat is the output current (at the 170 V side ?)

+a) 5.294E+02 A

-b) 5.824E+02 A

-c) 6.406E+02 A

-d) 7.046E+02 A

-e) 7.751E+02 A

12) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?

-a) 1.753E+02 km

-b) 1.928E+02 km

+c) 2.121E+02 km

-d) 2.333E+02 km

-e) 2.567E+02 km

Key: N1

1) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.157 m and a magneticfield of 1.03 T. What is their maximum kinetic energy?

-a) 8.608E-01 MeV

-b) 9.468E-01 MeV

-c) 1.042E+00 MeV

-d) 1.146E+00 MeV

+e) 1.260E+00 MeV

2) A step-down transformer steps 12 kV down to 230 V. The high-voltage input is provided by a 140 Ω power line that carries 5 A of currentWhat is the output current (at the 230 V side ?)

-a) 2.156E+02 A

-b) 2.372E+02 A

+c) 2.609E+02 A

-d) 2.870E+02 A

-e) 3.157E+02 A

3)

What is the net capacitance if C₁=3.97 μF, C₂=3.51 μF, and C₃=2.18 μF in the configuration shown?

-a) 3.038E+00 μF

-b) 3.341E+00 μF

-c) 3.675E+00 μF

+d) 4.043E+00 μF

-e) 4.447E+00 μF

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.227 m. The magnetic field is spatially uniform but decays in time according to $(5.55)e^{-\alpha t}$ , where $\alpha =$ 3.92 s. What is the current in the coil if the impedance of the coil is 22.7 Ω?

-a) 1.082E-01 A

+b) 1.190E-01 A

-c) 1.309E-01 A

-d) 1.440E-01 A

-e) 1.584E-01 A

5)

Two sources of emf ε₁=24.9 V, and ε₂=10.1 V are oriented as shownin the circuit. The resistances are R₁=2.32 kΩ and R₂=2.31 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.74 mA and I₄=0.444 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

-a) 1.725E+00 mA

-b) 1.898E+00 mA

-c) 2.087E+00 mA

+d) 2.296E+00 mA

-e) 2.526E+00 mA

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 8.471E+01 N/C

-b) 9.318E+01 N/C

-c) 1.025E+02 N/C

-d) 1.127E+02 N/C

-e) 1.240E+02 N/C

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.3 m. The other four surfaces are rectangles in y=y₀=1.6 m, y=y₁=5.3 m, z=z₀=1.3 m, and z=z₁=5.6 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 4.8m² ,and those in the zx plane have area 5.6m². An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

+a) 3.074E+01 N·m²/C

-b) 3.382E+01 N·m²/C

-c) 3.720E+01 N·m²/C

-d) 4.092E+01 N·m²/C

-e) 4.501E+01 N·m²/C

8) Calculate the resistance of a 12-gauge copper wire that is 10 m long and carries a current of 69 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 4.614E-02 Ω

+b) 5.076E-02 Ω

-c) 5.583E-02 Ω

-d) 6.141E-02 Ω

-e) 6.756E-02 Ω

9)

A long solenoid has a length 0.864 meters, radius 3.37 cm, and 522 turns. It surrounds coil of radius 7.87 meters and 13turns. If the current in the solenoid is changing at a rate of 290 A/s, what is the emf induced in the surounding coil?

-a) 2.917E-02 V

+b) 3.208E-02 V

-c) 3.529E-02 V

-d) 3.882E-02 V

-e) 4.270E-02 V

10) A 59 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 76 kW?

-a) 1.008E+02 km

-b) 1.109E+02 km

-c) 1.219E+02 km

-d) 1.341E+02 km

+e) 1.475E+02 km

11) When a 7.78 V battery operates a 1.35 W bulb, how many electrons pass through it each second?

-a) 7.397E+17 electrons

-b) 8.137E+17 electrons

-c) 8.951E+17 electrons

-d) 9.846E+17 electrons

+e) 1.083E+18 electrons

12)

Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?

-a) B_x= 6.171E-05 T

+b) B_x= 6.788E-05 T

-c) B_x= 7.467E-05 T

-d) B_x= 8.213E-05 T

-e) B_x= 9.035E-05 T

Key: N2

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.3 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.2 m, z=z₀=1.8 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 8.5m² ,and those in the zx plane have area 6.0m². An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 4.730E+01 N·m²/C

+b) 5.203E+01 N·m²/C

-c) 5.723E+01 N·m²/C

-d) 6.295E+01 N·m²/C

-e) 6.925E+01 N·m²/C

2) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?

-a) 2.094E+02 km

+b) 2.304E+02 km

-c) 2.534E+02 km

-d) 2.788E+02 km

-e) 3.066E+02 km

3)

What is the net capacitance if C₁=2.25 μF, C₂=4.16 μF, and C₃=2.49 μF in the configuration shown?

-a) 2.698E+00 μF

-b) 2.968E+00 μF

-c) 3.265E+00 μF

-d) 3.591E+00 μF

+e) 3.950E+00 μF

4)

Two sources of emf ε₁=43.7 V, and ε₂=13.1 V are oriented as shownin the circuit. The resistances are R₁=5.21 kΩ and R₂=1.72 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.86 mA and I₄=0.9 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

-a) 2.691E+00 mA

+b) 2.960E+00 mA

-c) 3.256E+00 mA

-d) 3.582E+00 mA

-e) 3.940E+00 mA

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to $(1.95)e^{-\alpha t}$ , where $\alpha =$ 7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

-a) 7.402E-01 A

-b) 8.142E-01 A

-c) 8.956E-01 A

+d) 9.852E-01 A

-e) 1.084E+00 A

6) A cyclotron used to accelerate alpha particlesm=6.64 x 10⁻²⁷kg, q=3.2 x 10⁻¹⁹C) has a radius of 0.118 m and a magneticfield of 1.48 T. What is their maximum kinetic energy?

-a) 1.004E+00 MeV

-b) 1.104E+00 MeV

-c) 1.215E+00 MeV

-d) 1.336E+00 MeV

+e) 1.470E+00 MeV

7)

Three wires sit at the corners of a square of length 0.774 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?

-a) B_x= 7.270E-05 T

+b) B_x= 7.997E-05 T

-c) B_x= 8.797E-05 T

-d) B_x= 9.677E-05 T

-e) B_x= 1.064E-04 T

8) When a 6.97 V battery operates a 2.6 W bulb, how many electrons pass through it each second?

-a) 1.749E+18 electrons

-b) 1.924E+18 electrons

-c) 2.117E+18 electrons

+d) 2.328E+18 electrons

-e) 2.561E+18 electrons

9) Calculate the resistance of a 12-gauge copper wire that is 78 m long and carries a current of 82 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm².

-a) 2.974E-01 Ω

-b) 3.272E-01 Ω

-c) 3.599E-01 Ω

+d) 3.959E-01 Ω

-e) 4.355E-01 Ω

10)

A long solenoid has a length 0.784 meters, radius 3.57 cm, and 553 turns. It surrounds coil of radius 9.49 meters and 16turns. If the current in the solenoid is changing at a rate of 276 A/s, what is the emf induced in the surounding coil?

-a) 4.476E-02 V

+b) 4.924E-02 V

-c) 5.416E-02 V

-d) 5.958E-02 V

-e) 6.553E-02 V

11) A step-down transformer steps 9 kV down to 160 V. The high-voltage input is provided by a 260 Ω power line that carries 7 A of currentWhat is the output current (at the 160 V side ?)

+a) 3.938E+02 A

-b) 4.331E+02 A

-c) 4.764E+02 A

-d) 5.241E+02 A

-e) 5.765E+02 A

12) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

Key: O0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$ .

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.1 m, y=y₁=5.6 m, z=z₀=1.8 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 17.0m². Those in the xy plane have area 13.0m² ,and those in the zx plane have area 10.0m². An electric field has the xyz components (0, 7.0, 5.7) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 4.953E+01 N·m²/C

-b) 5.449E+01 N·m²/C

-c) 5.993E+01 N·m²/C

-d) 6.593E+01 N·m²/C

+e) 7.252E+01 N·m²/C

3) If a 29 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=81 V is x² + y² + z² = R², where R=

+a) 3.218E+00 m

-b) 3.540E+00 m

-c) 3.893E+00 m

-d) 4.283E+00 m

-e) 4.711E+00 m

4)

In the figure shown C₁=17.7 μF, C₂=2.48 μF, and C₃=4.68 μF. The voltage source provides ε=12.7 V. What is the energy stored in C₂?

+a) 2.242E+01 μJ

-b) 2.467E+01 μJ

-c) 2.713E+01 μJ

-d) 2.985E+01 μJ

-e) 3.283E+01 μJ

5) A make-believe metal has a density of 1.180E+04 kg/m³ and an atomic mass of 121.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

-a) 4.010E+28 e⁻/m³

-b) 4.411E+28 e⁻/m³

-c) 4.852E+28 e⁻/m³

-d) 5.337E+28 e⁻/m³

+e) 5.871E+28 e⁻/m³

6) Three resistors, R₁ = 1.2 Ω, and R₂ = R₂ = 2.75 Ω, are connected in parallel to a 6.42 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

-a) 2.581E+01 W

-b) 2.839E+01 W

-c) 3.122E+01 W

+d) 3.435E+01 W

-e) 3.778E+01 W

7) A long rigid wire carries a 3 A current. What is the magnetic force per unit length on the wire if a 0.534 T magnetic field is directed 18° away from the wire?

+a) 4.950E-01 N/m

-b) 5.445E-01 N/m

-c) 5.990E-01 N/m

-d) 6.589E-01 N/m

-e) 7.248E-01 N/m

8)

Three wires sit at the corners of a square of length 0.495 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.45 A, 1.66 A, 1.63 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 1.205E-04 T

+b) B_y= 1.325E-04 T

-c) B_y= 1.458E-04 T

-d) B_y= 1.604E-04 T

-e) B_y= 1.764E-04 T

9) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 5 A and $\alpha =$ 28 s⁻¹.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?

-a) 1.616E-04 V/m

-b) 1.778E-04 V/m

-c) 1.955E-04 V/m

-d) 2.151E-04 V/m

+e) 2.366E-04 V/m

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.44% of its maximum value if ε = 5.95 V , R = 7.26 Ω, and L = 1.29 H?

-a) -3.114E-01 s

-b) -3.425E-01 s

+c) -3.767E-01 s

-d) -4.144E-01 s

-e) -4.559E-01 s

11) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

-a) 1.170E+00 A

+b) 1.287E+00 A

-c) 1.415E+00 A

-d) 1.557E+00 A

-e) 1.713E+00 A

12) What is the radiation pressure on an object that is 8.30E+11 m away from the sun and has cross-sectional area of 0.097 m²? The average power output of the Sun is 3.80E+26 W.

+a) 2.928E-07 N/m²

-b) 3.221E-07 N/m²

-c) 3.543E-07 N/m²

-d) 3.898E-07 N/m²

-e) 4.287E-07 N/m²

Key: O1

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.1 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.2 m, z=z₀=1.1 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 8.5m². Those in the xy plane have area 2.8m² ,and those in the zx plane have area 3.7m². An electric field has the xyz components (0, 7.4, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 2.079E+01 N·m²/C

-b) 2.287E+01 N·m²/C

-c) 2.516E+01 N·m²/C

+d) 2.768E+01 N·m²/C

-e) 3.044E+01 N·m²/C

2)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 2.16% of its maximum value if ε = 4.79 V , R = 4.37 Ω, and L = 5.29 H?

-a) -2.110E+00 s

+b) -2.321E+00 s

-c) -2.553E+00 s

-d) -2.809E+00 s

-e) -3.090E+00 s

3) If a 14 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=26 V is x² + y² + z² = R², where R=

-a) 3.636E+00 m

-b) 4.000E+00 m

-c) 4.399E+00 m

+d) 4.839E+00 m

-e) 5.323E+00 m

4)

In the figure shown C₁=16.5 μF, C₂=2.7 μF, and C₃=4.82 μF. The voltage source provides ε=15.7 V. What is the energy stored in C₂?

-a) 2.188E+01 μJ

-b) 2.407E+01 μJ

-c) 2.647E+01 μJ

+d) 2.912E+01 μJ

-e) 3.203E+01 μJ

5) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.052 m²? The average power output of the Sun is 3.80E+26 W.

-a) 2.392E-06 N/m²

-b) 2.631E-06 N/m²

-c) 2.894E-06 N/m²

-d) 3.184E-06 N/m²

+e) 3.502E-06 N/m²

6) An ac generator produces an emf of amplitude 53 V at a frequency of 190 Hz. What is the maximum amplitude of the current if the generator is connected to a 85 mF capacitor?

-a) 4.445E+00 A

-b) 4.889E+00 A

+c) 5.378E+00 A

-d) 5.916E+00 A

-e) 6.507E+00 A

7) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3{\text{ m}}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$ .

-a) 6.877E+00 V/m²

-b) 7.565E+00 V/m²

+c) 8.321E+00 V/m²

-d) 9.153E+00 V/m²

-e) 1.007E+01 V/m²

8) A make-believe metal has a density of 2.670E+03 kg/m³ and an atomic mass of 40.9 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

+a) 3.930E+28 e⁻/m³

-b) 4.323E+28 e⁻/m³

-c) 4.755E+28 e⁻/m³

-d) 5.231E+28 e⁻/m³

-e) 5.754E+28 e⁻/m³

9) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.265 T magnetic field is directed 26° away from the wire?

-a) 3.840E-01 N/m

-b) 4.224E-01 N/m

+c) 4.647E-01 N/m

-d) 5.111E-01 N/m

-e) 5.623E-01 N/m

10) Three resistors, R₁ = 0.855 Ω, and R₂ = R₂ = 1.91 Ω, are connected in parallel to a 6.97 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

+a) 5.682E+01 W

-b) 6.250E+01 W

-c) 6.875E+01 W

-d) 7.563E+01 W

-e) 8.319E+01 W

11)

Three wires sit at the corners of a square of length 0.702 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 7.576E-05 T

+b) B_y= 8.333E-05 T

-c) B_y= 9.167E-05 T

-d) B_y= 1.008E-04 T

-e) B_y= 1.109E-04 T

12) A long solenoid has a radius of 0.434 m and 41 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 9 A and $\alpha =$ 28 s⁻¹.What is the induced electric fied at a distance 2.28 m from the axis at time t=0.0392 s ?

-a) 1.479E-04 V/m

-b) 1.627E-04 V/m

+c) 1.789E-04 V/m

-d) 1.968E-04 V/m

-e) 2.165E-04 V/m

Key: O2

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.0 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.7 m, z=z₀=1.2 m, and z=z₁=4.1 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 6.6m² ,and those in the zx plane have area 5.8m². An electric field has the xyz components (0, 8.4, 5.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 3.328E+01 N·m²/C

-b) 3.660E+01 N·m²/C

-c) 4.026E+01 N·m²/C

-d) 4.429E+01 N·m²/C

+e) 4.872E+01 N·m²/C

2) A long solenoid has a radius of 0.578 m and 34 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 27 s⁻¹.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0462 s ?

+a) 1.473E-04 V/m

-b) 1.621E-04 V/m

-c) 1.783E-04 V/m

-d) 1.961E-04 V/m

-e) 2.157E-04 V/m

3)

Three wires sit at the corners of a square of length 0.793 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.32 A, 1.4 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 3.480E-05 T

-b) B_y= 3.828E-05 T

-c) B_y= 4.210E-05 T

-d) B_y= 4.631E-05 T

+e) B_y= 5.095E-05 T

4) Three resistors, R₁ = 1.43 Ω, and R₂ = R₂ = 3.25 Ω, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

-a) 5.184E+01 W

+b) 5.702E+01 W

-c) 6.272E+01 W

-d) 6.900E+01 W

-e) 7.590E+01 W

5) An ac generator produces an emf of amplitude 53 V at a frequency of 190 Hz. What is the maximum amplitude of the current if the generator is connected to a 85 mF capacitor?

-a) 4.445E+00 A

-b) 4.889E+00 A

+c) 5.378E+00 A

-d) 5.916E+00 A

-e) 6.507E+00 A

6) If a 19 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=73 V is x² + y² + z² = R², where R=

-a) 1.598E+00 m

-b) 1.757E+00 m

-c) 1.933E+00 m

-d) 2.127E+00 m

+e) 2.339E+00 m

7) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.016 m²? The average power output of the Sun is 3.80E+26 W.

+a) 6.669E-07 N/m²

-b) 7.336E-07 N/m²

-c) 8.069E-07 N/m²

-d) 8.876E-07 N/m²

-e) 9.764E-07 N/m²

8) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.578 T magnetic field is directed 38° away from the wire?

+a) 2.847E+00 N/m

-b) 3.132E+00 N/m

-c) 3.445E+00 N/m

-d) 3.789E+00 N/m

-e) 4.168E+00 N/m

9) A make-believe metal has a density of 1.810E+04 kg/m³ and an atomic mass of 14.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

-a) 5.847E+29 e⁻/m³

-b) 6.432E+29 e⁻/m³

-c) 7.075E+29 e⁻/m³

+d) 7.783E+29 e⁻/m³

-e) 8.561E+29 e⁻/m³

10) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=4.3{\text{ m}}$ .

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

11)

In the figure shown C₁=18.1 μF, C₂=2.89 μF, and C₃=4.2 μF. The voltage source provides ε=9.19 V. What is the energy stored in C₂?

-a) 1.303E+01 μJ

-b) 1.434E+01 μJ

-c) 1.577E+01 μJ

-d) 1.735E+01 μJ

+e) 1.908E+01 μJ

12)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?

-a) -1.700E+00 s

-b) -1.870E+00 s

-c) -2.057E+00 s

+d) -2.262E+00 s

-e) -2.489E+00 s

Key: P0

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.571E+01 N/C

-b) 2.828E+01 N/C

-c) 3.111E+01 N/C

-d) 3.422E+01 N/C

+e) 3.765E+01 N/C

2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.7 (r≤R) where a=3 nC·m^-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 1.390E+03 N/C

+b) 1.530E+03 N/C

-c) 1.682E+03 N/C

-d) 1.851E+03 N/C

-e) 2.036E+03 N/C

3)

A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.

+a) 8.672E+02 V

-b) 9.539E+02 V

-c) 1.049E+03 V

-d) 1.154E+03 V

-e) 1.270E+03 V

4)

What is the net capacitance if C₁=2.25 μF, C₂=4.16 μF, and C₃=2.49 μF in the configuration shown?

-a) 2.698E+00 μF

-b) 2.968E+00 μF

-c) 3.265E+00 μF

-d) 3.591E+00 μF

+e) 3.950E+00 μF

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =38 C and $\tau =$ 0.0167 s. What is the current at $t=$ 0.0183 s?

-a) 5.715E+02 A

-b) 6.286E+02 A

-c) 6.915E+02 A

+d) 7.606E+02 A

-e) 8.367E+02 A

6)

Two sources of emf ε₁=38.9 V, and ε₂=16.9 V are oriented as shownin the circuit. The resistances are R₁=3.3 kΩ and R₂=2.51 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.34 mA and I₄=0.955 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 7.031E+00 V

+b) 7.734E+00 V

-c) 8.507E+00 V

-d) 9.358E+00 V

-e) 1.029E+01 V

7) A charged particle in a magnetic field of 4.480E-04 T is moving perpendicular to the magnetic field with a speed of 7.700E+05 m/s. What is the period of orbit if orbital radius is 0.368 m?

-a) 2.730E-06 s

+b) 3.003E-06 s

-c) 3.303E-06 s

-d) 3.633E-06 s

-e) 3.997E-06 s

8) Two parallel wires each carry a 7.68 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.36 cm, 1.58 cm), while the other is located at (5.29 cm, 5.18 cm). What is the force per unit length between the wires?

-a) 1.973E-10 N/m

-b) 2.170E-10 N/m

-c) 2.387E-10 N/m

-d) 2.625E-10 N/m

+e) 2.888E-10 N/m

9) A square coil has sides that are L= 0.738 m long and is tightly wound with N=717 turns of wire. The resistance of the coil is R=5.25 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0655 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 3.660E+00 A

-b) 4.027E+00 A

-c) 4.429E+00 A

+d) 4.872E+00 A

-e) 5.359E+00 A

10) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?

-a) 6.166E-04 s

-b) 6.783E-04 s

-c) 7.461E-04 s

-d) 8.207E-04 s

+e) 9.028E-04 s

11) The output of an ac generator connected to an RLC series combination has a frequency of 3.50E+04 Hz and an amplitude of 8 V. If R =7 Ω, L= 9.40E-03H , and C=8.50E-06 F, what is the rms power transferred to the resistor?

+a) 2.111E-03 Watts

-b) 2.323E-03 Watts

-c) 2.555E-03 Watts

-d) 2.810E-03 Watts

-e) 3.091E-03 Watts

12)

A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=4.00E+03 m² and separation d=4.70E-03 m is connected via a swith to a 38 Ω resistor and a battery of voltage V₀=28 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=8.10E-04?

-a) 3.351E-02 A

-b) 3.686E-02 A

-c) 4.054E-02 A

+d) 4.460E-02 A

-e) 4.906E-02 A

Key: P1

1)

A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m² and separation d=4.60E-03 m is connected via a swith to a 96 Ω resistor and a battery of voltage V₀=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?

-a) 7.315E-02 A

+b) 8.047E-02 A

-c) 8.851E-02 A

-d) 9.737E-02 A

-e) 1.071E-01 A

2)

What is the net capacitance if C₁=2.55 μF, C₂=4.13 μF, and C₃=2.5 μF in the configuration shown?

+a) 4.077E+00 μF

-b) 4.484E+00 μF

-c) 4.933E+00 μF

-d) 5.426E+00 μF

-e) 5.969E+00 μF

3)

Two sources of emf ε₁=52.7 V, and ε₂=17.5 V are oriented as shownin the circuit. The resistances are R₁=5.86 kΩ and R₂=2.08 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.48 mA and I₄=0.988 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

+a) 2.064E+01 V

-b) 2.270E+01 V

-c) 2.497E+01 V

-d) 2.747E+01 V

-e) 3.021E+01 V

4) Two parallel wires each carry a 6.53 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.82 cm, 1.17 cm), while the other is located at (4.07 cm, 5.5 cm). What is the force per unit length between the wires?

-a) 1.788E-10 N/m

+b) 1.966E-10 N/m

-c) 2.163E-10 N/m

-d) 2.379E-10 N/m

-e) 2.617E-10 N/m

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =16 C and $\tau =$ 0.0214 s. What is the current at $t=$ 0.0207 s?

-a) 2.135E+02 A

-b) 2.349E+02 A

-c) 2.584E+02 A

+d) 2.842E+02 A

-e) 3.126E+02 A

6) A charged particle in a magnetic field of 3.600E-04 T is moving perpendicular to the magnetic field with a speed of 5.960E+05 m/s. What is the period of orbit if orbital radius is 0.397 m?

-a) 3.805E-06 s

+b) 4.185E-06 s

-c) 4.604E-06 s

-d) 5.064E-06 s

-e) 5.571E-06 s

7)

A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.48 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.8 cm, y=2.24 cm)? Note that following the textbook's example, the y-value of the field point at 2.24 cm matches the disance of the positive charge above the x-axis.

-a) 5.134E+02 V

-b) 5.648E+02 V

-c) 6.212E+02 V

-d) 6.834E+02 V

+e) 7.517E+02 V

8) In an LC circuit, the self-inductance is 0.0126 H and the capacitance is 3.350E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.420E-05 C. How long does it take for the capacitor to become completely discharged?

-a) 2.204E-04 s

-b) 2.425E-04 s

-c) 2.667E-04 s

-d) 2.934E-04 s

+e) 3.227E-04 s

9) A square coil has sides that are L= 0.547 m long and is tightly wound with N=198 turns of wire. The resistance of the coil is R=4.62 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0768 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 8.953E-01 A

+b) 9.848E-01 A

-c) 1.083E+00 A

-d) 1.192E+00 A

-e) 1.311E+00 A

10) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.571E+01 N/C

-b) 2.828E+01 N/C

-c) 3.111E+01 N/C

-d) 3.422E+01 N/C

+e) 3.765E+01 N/C

11) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 6.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

-a) 2.007E-03 Watts

-b) 2.208E-03 Watts

-c) 2.429E-03 Watts

+d) 2.672E-03 Watts

-e) 2.939E-03 Watts

12) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.5 (r≤R) where a=2 nC·m^-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?

+a) 2.285E+01 N/C

-b) 2.514E+01 N/C

-c) 2.765E+01 N/C

-d) 3.042E+01 N/C

-e) 3.346E+01 N/C

Key: P2

1)

A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=6.10E+03 m² and separation d=7.40E-03 m is connected via a swith to a 18 Ω resistor and a battery of voltage V₀=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.20E-04?

-a) 6.259E-02 A

-b) 6.885E-02 A

-c) 7.573E-02 A

+d) 8.331E-02 A

-e) 9.164E-02 A

2) The output of an ac generator connected to an RLC series combination has a frequency of 4.30E+04 Hz and an amplitude of 6 V. If R =6 Ω, L= 5.20E-03H , and C=8.60E-06 F, what is the rms power transferred to the resistor?

-a) 1.511E-03 Watts

-b) 1.662E-03 Watts

-c) 1.828E-03 Watts

-d) 2.011E-03 Watts

+e) 2.212E-03 Watts

3)

A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.3 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.86 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.

-a) 6.325E+02 V

+b) 6.957E+02 V

-c) 7.653E+02 V

-d) 8.418E+02 V

-e) 9.260E+02 V

4) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =52 C and $\tau =$ 0.018 s. What is the current at $t=$ 0.0207 s?

-a) 6.872E+02 A

-b) 7.560E+02 A

-c) 8.316E+02 A

+d) 9.147E+02 A

-e) 1.006E+03 A

5) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 9.546E+01 N/C

-b) 1.050E+02 N/C

-c) 1.155E+02 N/C

+d) 1.271E+02 N/C

-e) 1.398E+02 N/C

6)

What is the net capacitance if C₁=2.55 μF, C₂=4.13 μF, and C₃=2.5 μF in the configuration shown?

+a) 4.077E+00 μF

-b) 4.484E+00 μF

-c) 4.933E+00 μF

-d) 5.426E+00 μF

-e) 5.969E+00 μF

7)

Two sources of emf ε₁=38.9 V, and ε₂=16.9 V are oriented as shownin the circuit. The resistances are R₁=3.3 kΩ and R₂=2.51 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.34 mA and I₄=0.955 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 7.031E+00 V

+b) 7.734E+00 V

-c) 8.507E+00 V

-d) 9.358E+00 V

-e) 1.029E+01 V

8) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?

-a) 2.977E-11 N/m

-b) 3.274E-11 N/m

-c) 3.602E-11 N/m

-d) 3.962E-11 N/m

+e) 4.358E-11 N/m

9) A square coil has sides that are L= 0.219 m long and is tightly wound with N=508 turns of wire. The resistance of the coil is R=8.42 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0619 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

+a) 1.791E-01 A

-b) 1.970E-01 A

-c) 2.167E-01 A

-d) 2.384E-01 A

-e) 2.622E-01 A

10) A charged particle in a magnetic field of 4.090E-04 T is moving perpendicular to the magnetic field with a speed of 5.980E+05 m/s. What is the period of orbit if orbital radius is 0.633 m?

-a) 4.543E-06 s

-b) 4.997E-06 s

-c) 5.497E-06 s

-d) 6.046E-06 s

+e) 6.651E-06 s

11) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.5 (r≤R) where a=2 nC·m^-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?

+a) 2.285E+01 N/C

-b) 2.514E+01 N/C

-c) 2.765E+01 N/C

-d) 3.042E+01 N/C

-e) 3.346E+01 N/C

12) In an LC circuit, the self-inductance is 0.0237 H and the capacitance is 6.140E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.260E-05 C. How long does it take for the capacitor to become completely discharged?

-a) 4.093E-04 s

-b) 4.502E-04 s

-c) 4.952E-04 s

-d) 5.447E-04 s

+e) 5.992E-04 s

Key: Q0

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

-a) 2.964E+00 N/C

-b) 3.260E+00 N/C

-c) 3.586E+00 N/C

+d) 3.944E+00 N/C

-e) 4.339E+00 N/C

3) A 12.0 V battery can move 49,000 C of charge. How many Joules does it deliver?

+a) 5.880E+05 J

-b) 6.468E+05 J

-c) 7.115E+05 J

-d) 7.826E+05 J

-e) 8.609E+05 J

4) An empty parallel-plate capacitor with metal plates has an area of 1.81 m², separated by 1.26 mm. How much charge does it store if the voltage is 4.610E+03 V?

-a) 4.005E+01 μC

-b) 4.405E+01 μC

-c) 4.846E+01 μC

-d) 5.330E+01 μC

+e) 5.864E+01 μC

5) A make-believe metal has a density of 1.430E+04 kg/m³ and an atomic mass of 37.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

-a) 1.882E+29 e⁻/m³

-b) 2.070E+29 e⁻/m³

+c) 2.277E+29 e⁻/m³

-d) 2.505E+29 e⁻/m³

-e) 2.756E+29 e⁻/m³

6)

The resistances in the figure shown are R₁= 1.1 Ω, R₂= 1.55 Ω, and R₂= 2.11 Ω. V₁ and V₃ are text 0.545 V and 3.22 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.744 V. What is the absolute value of the current through R₁?

-a) 1.886E-01 A

+b) 2.075E-01 A

-c) 2.282E-01 A

-d) 2.510E-01 A

-e) 2.761E-01 A

7) A 11 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.809 T. What current is required to maintain this balance?

+a) 1.432E+00 A

-b) 1.575E+00 A

-c) 1.732E+00 A

-d) 1.905E+00 A

-e) 2.096E+00 A

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.38 kA, I₂=0.839 kA, and I₃=2.27 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 4.354E-03 T-m

+b) 4.789E-03 T-m

-c) 5.268E-03 T-m

-d) 5.795E-03 T-m

-e) 6.374E-03 T-m

9) A long solenoid has a radius of 0.644 m and 20 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 27 s⁻¹.What is the induced electric fied at a distance 2.84 m from the axis at time t=0.083 s ?

-a) 3.353E-05 V/m

+b) 3.689E-05 V/m

-c) 4.058E-05 V/m

-d) 4.463E-05 V/m

-e) 4.910E-05 V/m

10) In an LC circuit, the self-inductance is 0.0262 H and the capacitance is 4.540E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 4.700E-05 C. How long does it take for the capacitor to become completely discharged?

-a) 4.070E-04 s

-b) 4.477E-04 s

-c) 4.925E-04 s

+d) 5.417E-04 s

-e) 5.959E-04 s

11) A step-down transformer steps 14 kV down to 210 V. The high-voltage input is provided by a 240 Ω power line that carries 3 A of currentWhat is the output current (at the 210 V side ?)

+a) 2.000E+02 A

-b) 2.200E+02 A

-c) 2.420E+02 A

-d) 2.662E+02 A

-e) 2.928E+02 A

12) What is the radiation force on an object that is 3.80E+11 m away from the sun and has cross-sectional area of 0.094 m²? The average power output of the Sun is 3.80E+26 W.

-a) 8.969E-08 N

-b) 9.866E-08 N

-c) 1.085E-07 N

-d) 1.194E-07 N

+e) 1.313E-07 N

Key: Q1

1) A make-believe metal has a density of 7.000E+03 kg/m³ and an atomic mass of 89.4 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

-a) 3.219E+28 e⁻/m³

-b) 3.541E+28 e⁻/m³

-c) 3.896E+28 e⁻/m³

-d) 4.285E+28 e⁻/m³

+e) 4.714E+28 e⁻/m³

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 9.546E+01 N/C

-b) 1.050E+02 N/C

-c) 1.155E+02 N/C

+d) 1.271E+02 N/C

-e) 1.398E+02 N/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.3 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.5 m from the center of the shells?

-a) 1.994E+01 N/C

-b) 2.194E+01 N/C

-c) 2.413E+01 N/C

-d) 2.655E+01 N/C

+e) 2.920E+01 N/C

4) What is the radiation force on an object that is 5.40E+11 m away from the sun and has cross-sectional area of 0.021 m²? The average power output of the Sun is 3.80E+26 W.

-a) 9.923E-09 N

-b) 1.092E-08 N

-c) 1.201E-08 N

-d) 1.321E-08 N

+e) 1.453E-08 N

5) In an LC circuit, the self-inductance is 0.0273 H and the capacitance is 6.440E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.620E-05 C. How long does it take for the capacitor to become completely discharged?

-a) 5.443E-04 s

-b) 5.988E-04 s

+c) 6.586E-04 s

-d) 7.245E-04 s

-e) 7.969E-04 s

6)

The resistances in the figure shown are R₁= 2.73 Ω, R₂= 1.4 Ω, and R₂= 2.35 Ω. V₁ and V₃ are text 0.549 V and 1.27 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.584 V. What is the absolute value of the current through R₁?

-a) 1.213E-01 A

-b) 1.334E-01 A

-c) 1.468E-01 A

+d) 1.614E-01 A

-e) 1.776E-01 A

7) A long solenoid has a radius of 0.644 m and 20 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 27 s⁻¹.What is the induced electric fied at a distance 2.84 m from the axis at time t=0.083 s ?

-a) 3.353E-05 V/m

+b) 3.689E-05 V/m

-c) 4.058E-05 V/m

-d) 4.463E-05 V/m

-e) 4.910E-05 V/m

8) A step-down transformer steps 15 kV down to 250 V. The high-voltage input is provided by a 130 Ω power line that carries 4 A of currentWhat is the output current (at the 250 V side ?)

-a) 1.983E+02 A

-b) 2.182E+02 A

+c) 2.400E+02 A

-d) 2.640E+02 A

-e) 2.904E+02 A

9) A 97 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 7 g, and the magnitude of the magnetic field is 0.753 T. What current is required to maintain this balance?

-a) 7.056E-02 A

-b) 7.762E-02 A

-c) 8.538E-02 A

+d) 9.392E-02 A

-e) 1.033E-01 A

10) An empty parallel-plate capacitor with metal plates has an area of 2.84 m², separated by 1.42 mm. How much charge does it store if the voltage is 1.510E+03 V?

-a) 1.826E+01 μC

-b) 2.009E+01 μC

-c) 2.210E+01 μC

-d) 2.431E+01 μC

+e) 2.674E+01 μC

11)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.84 kA, I₂=3.3 kA, and I₃=5.85 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 5.598E-03 T-m

-b) 6.158E-03 T-m

+c) 6.773E-03 T-m

-d) 7.451E-03 T-m

-e) 8.196E-03 T-m

12) A 12.0 V battery can move 44,000 C of charge. How many Joules does it deliver?

-a) 4.800E+05 J

+b) 5.280E+05 J

-c) 5.808E+05 J

-d) 6.389E+05 J

-e) 7.028E+05 J

Key: Q2

1) A make-believe metal has a density of 1.510E+04 kg/m³ and an atomic mass of 33.6 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.

-a) 2.236E+29 e⁻/m³

-b) 2.459E+29 e⁻/m³

+c) 2.705E+29 e⁻/m³

-d) 2.976E+29 e⁻/m³

-e) 3.274E+29 e⁻/m³

2) A step-down transformer steps 8 kV down to 220 V. The high-voltage input is provided by a 110 Ω power line that carries 8 A of currentWhat is the output current (at the 220 V side ?)

-a) 2.404E+02 A

-b) 2.645E+02 A

+c) 2.909E+02 A

-d) 3.200E+02 A

-e) 3.520E+02 A

3)

The resistances in the figure shown are R₁= 1.57 Ω, R₂= 1.25 Ω, and R₂= 3.38 Ω. V₁ and V₃ are text 0.585 V and 2.91 V, respectively. But V₂ is opposite to that shown in the figure, or, equivalently, V₂=−0.55 V. What is the absolute value of the current through R₁?

-a) 1.427E-01 A

-b) 1.569E-01 A

+c) 1.726E-01 A

-d) 1.899E-01 A

-e) 2.089E-01 A

4) A 62 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.351 T. What current is required to maintain this balance?

-a) 3.999E-01 A

-b) 4.398E-01 A

-c) 4.838E-01 A

-d) 5.322E-01 A

+e) 5.854E-01 A

5)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.38 kA, I₂=1.58 kA, and I₃=4.31 kA, take the

\omega

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 4.386E-03 T-m

-b) 4.825E-03 T-m

-c) 5.307E-03 T-m

-d) 5.838E-03 T-m

+e) 6.421E-03 T-m

6) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

-a) 1.491E+01 N/C

-b) 1.640E+01 N/C

+c) 1.804E+01 N/C

-d) 1.984E+01 N/C

-e) 2.182E+01 N/C

7) What is the radiation force on an object that is 9.90E+11 m away from the sun and has cross-sectional area of 0.083 m²? The average power output of the Sun is 3.80E+26 W.

-a) 1.167E-08 N

-b) 1.284E-08 N

-c) 1.412E-08 N

-d) 1.553E-08 N

+e) 1.708E-08 N

8) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 1.694E+02 N/C

-b) 1.864E+02 N/C

-c) 2.050E+02 N/C

-d) 2.255E+02 N/C

-e) 2.480E+02 N/C

9) A long solenoid has a radius of 0.887 m and 43 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 28 s⁻¹.What is the induced electric fied at a distance 2.66 m from the axis at time t=0.0332 s ?

+a) 6.182E-04 V/m

-b) 6.801E-04 V/m

-c) 7.481E-04 V/m

-d) 8.229E-04 V/m

-e) 9.052E-04 V/m

10) An empty parallel-plate capacitor with metal plates has an area of 1.94 m², separated by 1.27 mm. How much charge does it store if the voltage is 8.780E+03 V?

-a) 1.080E+02 μC

+b) 1.188E+02 μC

-c) 1.306E+02 μC

-d) 1.437E+02 μC

-e) 1.581E+02 μC

11) In an LC circuit, the self-inductance is 0.0795 H and the capacitance is 7.930E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 2.420E-05 C. How long does it take for the capacitor to become completely discharged?

-a) 9.370E-04 s

-b) 1.031E-03 s

-c) 1.134E-03 s

+d) 1.247E-03 s

-e) 1.372E-03 s

12) A 12.0 V battery can move 32,000 C of charge. How many Joules does it deliver?

-a) 2.885E+05 J

-b) 3.174E+05 J

-c) 3.491E+05 J

+d) 3.840E+05 J

-e) 4.224E+05 J

Key: R0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=1e

,

q_{2}=-9e

, and

q_{3}=4e

?

-a) 5.014E-14 N

-b) 5.515E-14 N

-c) 6.067E-14 N

-d) 6.674E-14 N

+e) 7.341E-14 N

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.9 m, y=y₁=5.3 m, z=z₀=1.4 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 14.0m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 9.8m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 6.270E+01 N·m²/C

-b) 6.897E+01 N·m²/C

-c) 7.586E+01 N·m²/C

-d) 8.345E+01 N·m²/C

+e) 9.179E+01 N·m²/C

3) A 7 C charge is separated from a 15 C charge by distance of 14 cm. What is the work done by increasing this separation to 20 cm?

-a) 1.519E-06 J

-b) 1.671E-06 J

-c) 1.838E-06 J

+d) 2.022E-06 J

-e) 2.224E-06 J

4)

In the figure shown C₁=15.0 μF, C₂=2.65 μF, and C₃=5.67 μF. The voltage source provides ε=7.44 V. What is the charge on C₁?

+a) 3.982E+01 μC

-b) 4.380E+01 μC

-c) 4.818E+01 μC

-d) 5.300E+01 μC

-e) 5.829E+01 μC

5) What is the average current involved when a truck battery sets in motion 738 C of charge in 3.87 s while starting an engine?

+a) 1.907E+02 A

-b) 2.098E+02 A

-c) 2.307E+02 A

-d) 2.538E+02 A

-e) 2.792E+02 A

6)

Two sources of emf ε₁=39.2 V, and ε₂=12.6 V are oriented as shownin the circuit. The resistances are R₁=3.86 kΩ and R₂=1.89 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=4.05 mA and I₄=0.701 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 8.687E+00 V

-b) 9.555E+00 V

-c) 1.051E+01 V

-d) 1.156E+01 V

+e) 1.272E+01 V

7) A circular current loop of radius 2.84 cm carries a current of 3.01 mA. What is the magnitude of the torque if the dipole is oriented at 63 ° to a uniform magnetic fied of 0.174 T?

-a) 1.075E-06 N m

+b) 1.182E-06 N m

-c) 1.301E-06 N m

-d) 1.431E-06 N m

-e) 1.574E-06 N m

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.61 kA, I₂=2.2 kA, and I₃=5.1 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

+a) 3.644E-03 T-m

-b) 4.009E-03 T-m

-c) 4.410E-03 T-m

-d) 4.850E-03 T-m

-e) 5.336E-03 T-m

9) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 3.31 T and $\omega =$ 8.360E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.547 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

-a) 7.145E+04 V

-b) 7.860E+04 V

-c) 8.646E+04 V

+d) 9.510E+04 V

-e) 1.046E+05 V

10) An induced emf of 7.87V is measured across a coil of 66 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.05A in 0.781s. What is the self-inductance of the coil?

-a) 7.926E-01 H

+b) 8.718E-01 H

-c) 9.590E-01 H

-d) 1.055E+00 H

-e) 1.160E+00 H

11) An ac generator produces an emf of amplitude 7 V at a frequency of 95 Hz. What is the maximum amplitude of the current if the generator is connected to a 50 mF capacitor?

-a) 1.427E-01 A

-b) 1.570E-01 A

-c) 1.727E-01 A

-d) 1.899E-01 A

+e) 2.089E-01 A

12) What is the radiation force on an object that is 1.20E+11 m away from the sun and has cross-sectional area of 0.055 m²? The average power output of the Sun is 3.80E+26 W.

-a) 5.263E-07 N

-b) 5.789E-07 N

-c) 6.368E-07 N

-d) 7.005E-07 N

+e) 7.705E-07 N

Key: R1

1) An ac generator produces an emf of amplitude 90 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 16 mF capacitor?

-a) 4.351E-01 A

-b) 4.786E-01 A

-c) 5.264E-01 A

+d) 5.791E-01 A

-e) 6.370E-01 A

2)

In the figure shown C₁=17.7 μF, C₂=2.5 μF, and C₃=5.0 μF. The voltage source provides ε=12.8 V. What is the charge on C₁?

-a) 5.066E+01 μC

-b) 5.573E+01 μC

-c) 6.130E+01 μC

+d) 6.743E+01 μC

-e) 7.417E+01 μC

3)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=3e

?

-a) 1.473E-14 N

-b) 1.620E-14 N

-c) 1.782E-14 N

-d) 1.960E-14 N

+e) 2.156E-14 N

4) A circular current loop of radius 2.99 cm carries a current of 4.54 mA. What is the magnitude of the torque if the dipole is oriented at 34 ° to a uniform magnetic fied of 0.107 T?

+a) 7.629E-07 N m

-b) 8.392E-07 N m

-c) 9.232E-07 N m

-d) 1.015E-06 N m

-e) 1.117E-06 N m

5) A 2 C charge is separated from a 10 C charge by distance of 10 cm. What is the work done by increasing this separation to 16 cm?

-a) 6.128E-07 J

+b) 6.741E-07 J

-c) 7.415E-07 J

-d) 8.156E-07 J

-e) 8.972E-07 J

6) An induced emf of 5.08V is measured across a coil of 78 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.07A in 0.681s. What is the self-inductance of the coil?

-a) 4.660E-01 H

-b) 5.127E-01 H

-c) 5.639E-01 H

-d) 6.203E-01 H

+e) 6.823E-01 H

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.5 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.9 m, z=z₀=1.1 m, and z=z₁=5.3 m. The surfaces in the yz plane each have area 15.0m². Those in the xy plane have area 8.8m² ,and those in the zx plane have area 10.0m². An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 5.439E+01 N·m²/C

-b) 5.983E+01 N·m²/C

-c) 6.581E+01 N·m²/C

+d) 7.239E+01 N·m²/C

-e) 7.963E+01 N·m²/C

8) What is the average current involved when a truck battery sets in motion 669 C of charge in 4.3 s while starting an engine?

-a) 1.063E+02 A

-b) 1.169E+02 A

-c) 1.286E+02 A

-d) 1.414E+02 A

+e) 1.556E+02 A

9) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 3.71 T and $\omega =$ 6.600E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.31 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

+a) 4.769E+04 V

-b) 5.246E+04 V

-c) 5.771E+04 V

-d) 6.348E+04 V

-e) 6.983E+04 V

10)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.82 kA, I₂=0.964 kA, and I₃=2.21 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 1.069E-03 T-m

-b) 1.176E-03 T-m

-c) 1.294E-03 T-m

-d) 1.423E-03 T-m

+e) 1.566E-03 T-m

11)

Two sources of emf ε₁=26.8 V, and ε₂=10.1 V are oriented as shownin the circuit. The resistances are R₁=2.2 kΩ and R₂=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.29 mA and I₄=0.464 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 3.436E+00 V

-b) 3.779E+00 V

-c) 4.157E+00 V

-d) 4.573E+00 V

+e) 5.030E+00 V

12) What is the radiation force on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.044 m²? The average power output of the Sun is 3.80E+26 W.

-a) 7.088E-09 N

-b) 7.796E-09 N

-c) 8.576E-09 N

+d) 9.434E-09 N

-e) 1.038E-08 N

Key: R2

1) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?

-a) 2.549E-01 H

-b) 2.804E-01 H

-c) 3.084E-01 H

+d) 3.392E-01 H

-e) 3.732E-01 H

2)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

. What is the magnitude of the net force on

q_{2}

if

q_{1}=2e

,

q_{2}=-8e

, and

q_{3}=3e

?

-a) 2.036E-14 N

-b) 2.240E-14 N

+c) 2.464E-14 N

-d) 2.710E-14 N

-e) 2.981E-14 N

3)

Two sources of emf ε₁=30.6 V, and ε₂=12.0 V are oriented as shownin the circuit. The resistances are R₁=3.46 kΩ and R₂=2.77 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.97 mA and I₄=0.643 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 4.986E+00 V

-b) 5.484E+00 V

-c) 6.033E+00 V

-d) 6.636E+00 V

+e) 7.299E+00 V

4) A 7 C charge is separated from a 15 C charge by distance of 14 cm. What is the work done by increasing this separation to 20 cm?

-a) 1.519E-06 J

-b) 1.671E-06 J

-c) 1.838E-06 J

+d) 2.022E-06 J

-e) 2.224E-06 J

5) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

-a) 1.170E+00 A

+b) 1.287E+00 A

-c) 1.415E+00 A

-d) 1.557E+00 A

-e) 1.713E+00 A

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 2.18 T and $\omega =$ 4.840E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.387 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

-a) 1.928E+04 V

-b) 2.120E+04 V

-c) 2.332E+04 V

+d) 2.566E+04 V

-e) 2.822E+04 V

7)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.9 m, y=y₁=5.3 m, z=z₀=1.4 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 14.0m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 9.8m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 6.270E+01 N·m²/C

-b) 6.897E+01 N·m²/C

-c) 7.586E+01 N·m²/C

-d) 8.345E+01 N·m²/C

+e) 9.179E+01 N·m²/C

8) What is the radiation force on an object that is 5.40E+11 m away from the sun and has cross-sectional area of 0.021 m²? The average power output of the Sun is 3.80E+26 W.

-a) 9.923E-09 N

-b) 1.092E-08 N

-c) 1.201E-08 N

-d) 1.321E-08 N

+e) 1.453E-08 N

9) A circular current loop of radius 1.56 cm carries a current of 2.57 mA. What is the magnitude of the torque if the dipole is oriented at 38 ° to a uniform magnetic fied of 0.79 T?

-a) 7.898E-07 N m

-b) 8.688E-07 N m

+c) 9.557E-07 N m

-d) 1.051E-06 N m

-e) 1.156E-06 N m

10) What is the average current involved when a truck battery sets in motion 572 C of charge in 3.33 s while starting an engine?

-a) 1.173E+02 A

-b) 1.291E+02 A

-c) 1.420E+02 A

-d) 1.562E+02 A

+e) 1.718E+02 A

11)

In the figure shown C₁=17.9 μF, C₂=2.71 μF, and C₃=4.14 μF. The voltage source provides ε=7.12 V. What is the charge on C₁?

+a) 3.527E+01 μC

-b) 3.880E+01 μC

-c) 4.268E+01 μC

-d) 4.695E+01 μC

-e) 5.164E+01 μC

12)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.51 kA, I₂=1.32 kA, and I₃=2.73 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 1.331E-03 T-m

-b) 1.464E-03 T-m

-c) 1.611E-03 T-m

+d) 1.772E-03 T-m

-e) 1.949E-03 T-m

Key: S0

1) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 4.492E+01 N/C

+b) 4.941E+01 N/C

-c) 5.435E+01 N/C

-d) 5.979E+01 N/C

-e) 6.577E+01 N/C

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.8 m, z=z₀=1.1 m, and z=z₁=5.2 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 12.0m² ,and those in the zx plane have area 11.0m². An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 5.606E+01 N·m²/C

-b) 6.167E+01 N·m²/C

-c) 6.784E+01 N·m²/C

+d) 7.462E+01 N·m²/C

-e) 8.208E+01 N·m²/C

3)

An electron gun has parallel plates separated by 4.2 cm and gives electrons 51 keV of energy. What force would the field between the plates exert on a 0.84 μC charge that gets between the plates?

-a) 8.430E-01 N

-b) 9.273E-01 N

+c) 1.020E+00 N

-d) 1.122E+00 N

-e) 1.234E+00 N

4) An empty parallel-plate capacitor with metal plates has an area of 1.94 m², separated by 1.27 mm. How much charge does it store if the voltage is 8.780E+03 V?

-a) 1.080E+02 μC

+b) 1.188E+02 μC

-c) 1.306E+02 μC

-d) 1.437E+02 μC

-e) 1.581E+02 μC

5) Calculate the drift speed of electrons in a copper wire with a diameter of 2.17 mm carrying a 19.4 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

-a) 3.569E-04 m/s

+b) 3.926E-04 m/s

-c) 4.319E-04 m/s

-d) 4.750E-04 m/s

-e) 5.226E-04 m/s

6)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 554 V. If the combined external and internal resistance is 228 &Omega and the capacitance is 93 mF, how long will it take for the capacitor's voltage to reach 450.0 V?

-a) 3.224E+01 s

+b) 3.547E+01 s

-c) 3.902E+01 s

-d) 4.292E+01 s

-e) 4.721E+01 s

7) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 3.43 mT and 4.670E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

+a) 1.362E+06 m/s

-b) 1.498E+06 m/s

-c) 1.647E+06 m/s

-d) 1.812E+06 m/s

-e) 1.993E+06 m/s

8)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.32 kA, I₂=2.0 kA, and I₃=3.66 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 1.724E-03 T-m

-b) 1.896E-03 T-m

+c) 2.086E-03 T-m

-d) 2.295E-03 T-m

-e) 2.524E-03 T-m

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to $(5.62)e^{-\alpha t}$ , where $\alpha =$ 9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

+a) 7.890E-01 A

-b) 8.679E-01 A

-c) 9.547E-01 A

-d) 1.050E+00 A

-e) 1.155E+00 A

10) A washer has an inner diameter of 2.21 cm and an outer diamter of 4.5 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.29mm$ , and $n=2.62$ . What is the volume of the washer?

-a) 1.325E+00 cm³

+b) 1.457E+00 cm³

-c) 1.603E+00 cm³

-d) 1.763E+00 cm³

-e) 1.939E+00 cm³

11) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.8 V. The resistance, inductance, and capacitance are R =7 Ω, L= 4.90E-03H , and C=8.50E-04 F, respectively. What is the amplitude of the current?

-a) 1.039E-01 A

+b) 1.143E-01 A

-c) 1.257E-01 A

-d) 1.383E-01 A

-e) 1.521E-01 A

12)

A parallel plate capacitor with a capicatnce C=6.60E-06 F whose plates have an area A=4.90E+03 m² and separation d=6.60E-03 m is connected via a swith to a 20 Ω resistor and a battery of voltage V₀=59 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.70E-04?

+a) 8.138E-01 A

-b) 8.952E-01 A

-c) 9.847E-01 A

-d) 1.083E+00 A

-e) 1.191E+00 A

Key: S1

1) A washer has an inner diameter of 2.46 cm and an outer diamter of 4.24 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.32mm$ , and $n=2.63$ . What is the volume of the washer?

-a) 7.499E-01 cm³

-b) 8.249E-01 cm³

-c) 9.074E-01 cm³

-d) 9.982E-01 cm³

+e) 1.098E+00 cm³

2)

An electron gun has parallel plates separated by 3.39 cm and gives electrons 57 keV of energy. What force would the field between the plates exert on a 0.218 μC charge that gets between the plates?

-a) 3.029E-01 N

-b) 3.332E-01 N

+c) 3.665E-01 N

-d) 4.032E-01 N

-e) 4.435E-01 N

3)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 130 V. If the combined external and internal resistance is 109 &Omega and the capacitance is 59 mF, how long will it take for the capacitor's voltage to reach 69.9 V?

-a) 3.728E+00 s

-b) 4.101E+00 s

-c) 4.511E+00 s

+d) 4.962E+00 s

-e) 5.458E+00 s

4) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.82 V. The resistance, inductance, and capacitance are R =3 Ω, L= 6.20E-03H , and C=6.70E-04 F, respectively. What is the amplitude of the current?

-a) 2.259E-01 A

-b) 2.485E-01 A

+c) 2.733E-01 A

-d) 3.007E-01 A

-e) 3.307E-01 A

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.274 m. The magnetic field is spatially uniform but decays in time according to $(1.84)e^{-\alpha t}$ , where $\alpha =$ 9.59 s. What is the current in the coil if the impedance of the coil is 33.0 Ω?

-a) 7.007E-02 A

-b) 7.708E-02 A

+c) 8.479E-02 A

-d) 9.327E-02 A

-e) 1.026E-01 A

6) An empty parallel-plate capacitor with metal plates has an area of 2.1 m², separated by 1.13 mm. How much charge does it store if the voltage is 1.680E+03 V?

+a) 2.764E+01 μC

-b) 3.041E+01 μC

-c) 3.345E+01 μC

-d) 3.679E+01 μC

-e) 4.047E+01 μC

7)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=1.00E+04 m² and separation d=9.00E-03 m is connected via a swith to a 15 Ω resistor and a battery of voltage V₀=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?

-a) 6.394E-02 A

+b) 7.033E-02 A

-c) 7.736E-02 A

-d) 8.510E-02 A

-e) 9.361E-02 A

8) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

9) Calculate the drift speed of electrons in a copper wire with a diameter of 3.3 mm carrying a 18.5 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

-a) 1.472E-04 m/s

+b) 1.619E-04 m/s

-c) 1.781E-04 m/s

-d) 1.959E-04 m/s

-e) 2.155E-04 m/s

10) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 2.62 mT and 2.120E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

+a) 8.092E+05 m/s

-b) 8.901E+05 m/s

-c) 9.791E+05 m/s

-d) 1.077E+06 m/s

-e) 1.185E+06 m/s

11)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.44 kA, I₂=1.1 kA, and I₃=1.99 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 1.017E-03 T-m

+b) 1.118E-03 T-m

-c) 1.230E-03 T-m

-d) 1.353E-03 T-m

-e) 1.489E-03 T-m

12)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.7 m. The other four surfaces are rectangles in y=y₀=1.9 m, y=y₁=4.3 m, z=z₀=1.7 m, and z=z₁=5.7 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 4.1m² ,and those in the zx plane have area 6.8m². An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

+a) 7.876E+01 N·m²/C

-b) 8.664E+01 N·m²/C

-c) 9.531E+01 N·m²/C

-d) 1.048E+02 N·m²/C

-e) 1.153E+02 N·m²/C

Key: S2

1)

An electron gun has parallel plates separated by 4.24 cm and gives electrons 48 keV of energy. What force would the field between the plates exert on a 0.48 μC charge that gets between the plates?

+a) 5.434E-01 N

-b) 5.977E-01 N

-c) 6.575E-01 N

-d) 7.233E-01 N

-e) 7.956E-01 N

2)

The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I₁ and I₃ flow out of the page, and I₂ flows into the page, as shown. Two closed paths are shown, labeled

\beta

and

\omega

. If I₁=2.66 kA, I₂=1.25 kA, and I₃=2.74 kA, take the

\beta

path and evalulate the line integral,

\oint {\vec {B}}\cdot d{\vec {\ell }}

:

-a) 1.547E-03 T-m

-b) 1.702E-03 T-m

+c) 1.872E-03 T-m

-d) 2.060E-03 T-m

-e) 2.266E-03 T-m

3) Calculate the drift speed of electrons in a copper wire with a diameter of 3.3 mm carrying a 18.5 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 10³kg/m³ and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 10²³atoms/mol.

-a) 1.472E-04 m/s

+b) 1.619E-04 m/s

-c) 1.781E-04 m/s

-d) 1.959E-04 m/s

-e) 2.155E-04 m/s

4)

In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 467 V. If the combined external and internal resistance is 172 &Omega and the capacitance is 74 mF, how long will it take for the capacitor's voltage to reach 258.0 V?

-a) 7.688E+00 s

-b) 8.457E+00 s

-c) 9.303E+00 s

+d) 1.023E+01 s

-e) 1.126E+01 s

5) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

6) A washer has an inner diameter of 2.37 cm and an outer diamter of 4.84 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.67mm$ , and $n=2.56$ . What is the volume of the washer?

+a) 1.570E+00 cm³

-b) 1.727E+00 cm³

-c) 1.900E+00 cm³

-d) 2.090E+00 cm³

-e) 2.299E+00 cm³

7) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.44 V. The resistance, inductance, and capacitance are R =7 Ω, L= 5.40E-03H , and C=5.70E-04 F, respectively. What is the amplitude of the current?

-a) 4.723E-02 A

-b) 5.195E-02 A

-c) 5.714E-02 A

+d) 6.286E-02 A

-e) 6.914E-02 A

8)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.2 m, y=y₁=4.2 m, z=z₀=1.2 m, and z=z₁=4.1 m. The surfaces in the yz plane each have area 8.7m². Those in the xy plane have area 7.2m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 4.024E+01 N·m²/C

+b) 4.426E+01 N·m²/C

-c) 4.868E+01 N·m²/C

-d) 5.355E+01 N·m²/C

-e) 5.891E+01 N·m²/C

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to $(5.62)e^{-\alpha t}$ , where $\alpha =$ 9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

+a) 7.890E-01 A

-b) 8.679E-01 A

-c) 9.547E-01 A

-d) 1.050E+00 A

-e) 1.155E+00 A

10)

A parallel plate capacitor with a capicatnce C=4.40E-06 F whose plates have an area A=1.80E+03 m² and separation d=3.60E-03 m is connected via a swith to a 87 Ω resistor and a battery of voltage V₀=61 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.70E-04?

-a) 8.320E-02 A

-b) 9.152E-02 A

-c) 1.007E-01 A

-d) 1.107E-01 A

+e) 1.218E-01 A

11) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 7.67 mT and 4.260E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

+a) 5.554E+05 m/s

-b) 6.110E+05 m/s

-c) 6.720E+05 m/s

-d) 7.393E+05 m/s

-e) 8.132E+05 m/s

12) An empty parallel-plate capacitor with metal plates has an area of 2.78 m², separated by 1.16 mm. How much charge does it store if the voltage is 8.980E+03 V?

-a) 1.432E+02 μC

-b) 1.575E+02 μC

-c) 1.732E+02 μC

+d) 1.906E+02 μC

-e) 2.096E+02 μC

Key: T0

1) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=4.2{\text{ m}}$ .

-a) 5.134E-01 V/m²

+b) 5.648E-01 V/m²

-c) 6.212E-01 V/m²

-d) 6.834E-01 V/m²

-e) 7.517E-01 V/m²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.6 m. The other four surfaces are rectangles in y=y₀=1.2 m, y=y₁=5.6 m, z=z₀=1.2 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 14.0m². Those in the xy plane have area 11.0m² ,and those in the zx plane have area 8.3m². An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 4.809E+01 N·m²/C

-b) 5.290E+01 N·m²/C

+c) 5.819E+01 N·m²/C

-d) 6.401E+01 N·m²/C

-e) 7.041E+01 N·m²/C

3)

A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.57 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.59 cm, y=1.78 cm)? Note that following the textbook's example, the y-value of the field point at 1.78 cm matches the disance of the positive charge above the x-axis.

-a) 2.727E+02 V

-b) 2.999E+02 V

-c) 3.299E+02 V

+d) 3.629E+02 V

-e) 3.992E+02 V

4)

In the figure shown C₁=18.1 μF, C₂=2.13 μF, and C₃=5.48 μF. The voltage source provides ε=14.6 V. What is the energy stored in C₂?

-a) 1.645E+01 μJ

-b) 1.809E+01 μJ

-c) 1.990E+01 μJ

+d) 2.189E+01 μJ

-e) 2.408E+01 μJ

5) What is consumer cost to operate one 89−W incandescent bulb for 10 hours per day for 1 year (365 days) if the cost of electricity is $0.141 per kilowatt-hour?

-a) $3.785E+01

-b) $4.164E+01

+c) $4.580E+01

-d) $5.038E+01

-e) $5.542E+01

6)

Two sources of emf ε₁=44.4 V, and ε₂=16.8 V are oriented as shownin the circuit. The resistances are R₁=4.58 kΩ and R₂=1.2 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=8.43 mA and I₄=1.46 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

+a) 6.970E+00 mA

-b) 7.667E+00 mA

-c) 8.434E+00 mA

-d) 9.277E+00 mA

-e) 1.020E+01 mA

7) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 9.82 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(7.64 i + 4.85 j + 6.02 k) x 10⁴ m/s?

-a) 1.386E-13 N

+b) 1.524E-13 N

-c) 1.676E-13 N

-d) 1.844E-13 N

-e) 2.029E-13 N

8) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 533 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?

+a)

\chi {\text{ (chi) }}=

7.512E+02

-b)

\chi {\text{ (chi) }}=

8.264E+02

-c)

\chi {\text{ (chi) }}=

9.090E+02

-d)

\chi {\text{ (chi) }}=

9.999E+02

-e)

\chi {\text{ (chi) }}=

1.100E+03

9) The current through the windings of a solenoid with n= 2.060E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 68 cm long and has a cross-sectional diameter of 2.96 cm. A small coil consisting of N=29turns wraped in a circle of diameter 1.74 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

-a) 1.463E-04 V

-b) 1.609E-04 V

-c) 1.770E-04 V

-d) 1.947E-04 V

+e) 2.142E-04 V

10) An induced emf of 6.78V is measured across a coil of 58 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.98A in 0.726s. What is the self-inductance of the coil?

-a) 1.022E+00 H

-b) 1.124E+00 H

+c) 1.237E+00 H

-d) 1.360E+00 H

-e) 1.496E+00 H

11) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

+a) 5.042E+00 A

-b) 5.546E+00 A

-c) 6.100E+00 A

-d) 6.710E+00 A

-e) 7.381E+00 A

12)

A parallel plate capacitor with a capicatnce C=2.90E-06 F whose plates have an area A=1.60E+03 m² and separation d=5.00E-03 m is connected via a swith to a 41 Ω resistor and a battery of voltage V₀=92 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=4.50E-04?

-a) 6.755E+01 V

-b) 7.431E+01 V

-c) 8.174E+01 V

+d) 8.991E+01 V

-e) 9.890E+01 V

Key: T1

1) An ac generator produces an emf of amplitude 7 V at a frequency of 95 Hz. What is the maximum amplitude of the current if the generator is connected to a 50 mF capacitor?

-a) 1.427E-01 A

-b) 1.570E-01 A

-c) 1.727E-01 A

-d) 1.899E-01 A

+e) 2.089E-01 A

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 533 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?

+a)

\chi {\text{ (chi) }}=

7.512E+02

-b)

\chi {\text{ (chi) }}=

8.264E+02

-c)

\chi {\text{ (chi) }}=

9.090E+02

-d)

\chi {\text{ (chi) }}=

9.999E+02

-e)

\chi {\text{ (chi) }}=

1.100E+03

3)

In the figure shown C₁=18.2 μF, C₂=2.44 μF, and C₃=5.0 μF. The voltage source provides ε=7.78 V. What is the energy stored in C₂?

-a) 1.225E+01 μJ

+b) 1.347E+01 μJ

-c) 1.482E+01 μJ

-d) 1.630E+01 μJ

-e) 1.793E+01 μJ

4)

Two sources of emf ε₁=40.6 V, and ε₂=13.5 V are oriented as shownin the circuit. The resistances are R₁=4.35 kΩ and R₂=2.44 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.73 mA and I₄=0.78 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

-a) 1.332E+00 mA

-b) 1.465E+00 mA

-c) 1.612E+00 mA

-d) 1.773E+00 mA

+e) 1.950E+00 mA

5)

A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.17 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.

-a) 5.261E+02 V

-b) 5.787E+02 V

+c) 6.365E+02 V

-d) 7.002E+02 V

-e) 7.702E+02 V

6)

A parallel plate capacitor with a capicatnce C=7.40E-06 F whose plates have an area A=5.30E+03 m² and separation d=6.30E-03 m is connected via a swith to a 5 Ω resistor and a battery of voltage V₀=58 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.10E-04?

-a) 4.548E+01 V

-b) 5.003E+01 V

+c) 5.503E+01 V

-d) 6.054E+01 V

-e) 6.659E+01 V

7) The current through the windings of a solenoid with n= 2.590E+03 turns per meter is changing at a rate dI/dt=11 A/s. The solenoid is 95 cm long and has a cross-sectional diameter of 2.29 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.15 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

-a) 6.985E-05 V

-b) 7.683E-05 V

-c) 8.452E-05 V

+d) 9.297E-05 V

-e) 1.023E-04 V

8) What is consumer cost to operate one 73−W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.113 per kilowatt-hour?

+a) $3.312E+01

-b) $3.643E+01

-c) $4.007E+01

-d) $4.408E+01

-e) $4.849E+01

9) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7{\text{ m}}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=5.8{\text{ m}}$ .

-a) 3.722E-01 V/m²

-b) 4.094E-01 V/m²

-c) 4.504E-01 V/m²

+d) 4.954E-01 V/m²

-e) 5.450E-01 V/m²

10)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.8 m. The other four surfaces are rectangles in y=y₀=1.1 m, y=y₁=4.9 m, z=z₀=1.3 m, and z=z₁=5.6 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 6.8m² ,and those in the zx plane have area 7.7m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 6.898E+01 N·m²/C

+b) 7.588E+01 N·m²/C

-c) 8.347E+01 N·m²/C

-d) 9.181E+01 N·m²/C

-e) 1.010E+02 N·m²/C

11) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 7.83 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(6.16 i + 2.1 j + 1.74 k) x 10⁴ m/s?

-a) 4.783E-14 N

+b) 5.262E-14 N

-c) 5.788E-14 N

-d) 6.367E-14 N

-e) 7.003E-14 N

12) An induced emf of 4.02V is measured across a coil of 85 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.53A in 0.438s. What is the self-inductance of the coil?

-a) 4.535E-01 H

+b) 4.988E-01 H

-c) 5.487E-01 H

-d) 6.035E-01 H

-e) 6.639E-01 H

Key: T2

1)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.8 m, z=z₀=1.3 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 13.0m². Those in the xy plane have area 9.8m² ,and those in the zx plane have area 7.4m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 8.457E+01 N·m²/C

+b) 9.303E+01 N·m²/C

-c) 1.023E+02 N·m²/C

-d) 1.126E+02 N·m²/C

-e) 1.238E+02 N·m²/C

2) An alpha-particle (q=3.2x10⁻¹⁹C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 4.6 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(1.92 i + 1.55 j + 6.22 k) x 10⁴ m/s?

-a) 2.074E-14 N

+b) 2.282E-14 N

-c) 2.510E-14 N

-d) 2.761E-14 N

-e) 3.037E-14 N

3) What is consumer cost to operate one 65−W incandescent bulb for 12 hours per day for 1 year (365 days) if the cost of electricity is $0.134 per kilowatt-hour?

-a) $2.866E+01

-b) $3.153E+01

-c) $3.468E+01

+d) $3.815E+01

-e) $4.196E+01

4)

A parallel plate capacitor with a capicatnce C=6.20E-06 F whose plates have an area A=5.30E+03 m² and separation d=7.50E-03 m is connected via a swith to a 95 Ω resistor and a battery of voltage V₀=15 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=9.20E-04?

-a) 8.097E+00 V

-b) 8.906E+00 V

-c) 9.797E+00 V

-d) 1.078E+01 V

+e) 1.185E+01 V

5) The current through the windings of a solenoid with n= 2.040E+03 turns per meter is changing at a rate dI/dt=19 A/s. The solenoid is 76 cm long and has a cross-sectional diameter of 3.23 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.67 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

-a) 2.204E-04 V

-b) 2.425E-04 V

+c) 2.667E-04 V

-d) 2.934E-04 V

-e) 3.227E-04 V

6) An ac generator produces an emf of amplitude 87 V at a frequency of 44 Hz. What is the maximum amplitude of the current if the generator is connected to a 9 mF capacitor?

-a) 1.626E-01 A

-b) 1.789E-01 A

-c) 1.968E-01 A

+d) 2.165E-01 A

-e) 2.381E-01 A

7)

Two sources of emf ε₁=44.4 V, and ε₂=16.8 V are oriented as shownin the circuit. The resistances are R₁=4.58 kΩ and R₂=1.2 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=8.43 mA and I₄=1.46 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of I₅?

+a) 6.970E+00 mA

-b) 7.667E+00 mA

-c) 8.434E+00 mA

-d) 9.277E+00 mA

-e) 1.020E+01 mA

8) An induced emf of 5.33V is measured across a coil of 77 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.57A in 0.648s. What is the self-inductance of the coil?

-a) 4.779E-01 H

+b) 5.257E-01 H

-c) 5.783E-01 H

-d) 6.361E-01 H

-e) 6.997E-01 H

9)

A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.39 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.56 cm, y=2.19 cm)? Note that following the textbook's example, the y-value of the field point at 2.19 cm matches the disance of the positive charge above the x-axis.

-a) 3.852E+02 V

-b) 4.238E+02 V

+c) 4.661E+02 V

-d) 5.127E+02 V

-e) 5.640E+02 V

10)

In the figure shown C₁=17.6 μF, C₂=2.12 μF, and C₃=4.72 μF. The voltage source provides ε=5.35 V. What is the energy stored in C₂?

-a) 6.750E+00 μJ

-b) 7.425E+00 μJ

+c) 8.168E+00 μJ

-d) 8.984E+00 μJ

-e) 9.883E+00 μJ

11) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 533 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?

+a)

\chi {\text{ (chi) }}=

7.512E+02

-b)

\chi {\text{ (chi) }}=

8.264E+02

-c)

\chi {\text{ (chi) }}=

9.090E+02

-d)

\chi {\text{ (chi) }}=

9.999E+02

-e)

\chi {\text{ (chi) }}=

1.100E+03

12) $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$ . Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$ .

-a) 2.567E+01 V/m²

-b) 2.824E+01 V/m²

-c) 3.106E+01 V/m²

-d) 3.417E+01 V/m²

+e) 3.759E+01 V/m²

Key: U0

1)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.8 (r≤R) where a=2 nC·m^-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

+a) 2.079E+02 N/C

-b) 2.287E+02 N/C

-c) 2.516E+02 N/C

-d) 2.767E+02 N/C

-e) 3.044E+02 N/C

3) A 5 C charge is separated from a 9 C charge by distance of 14 cm. What is the work done by increasing this separation to 18 cm?

-a) 4.385E-07 J

-b) 4.823E-07 J

-c) 5.306E-07 J

-d) 5.836E-07 J

+e) 6.420E-07 J

4)

In the figure shown C₁=19.0 μF, C₂=2.35 μF, and C₃=5.22 μF. The voltage source provides ε=6.01 V. What is the charge on C₁?

-a) 2.444E+01 μC

-b) 2.689E+01 μC

-c) 2.958E+01 μC

+d) 3.253E+01 μC

-e) 3.579E+01 μC

5) What is consumer cost to operate one 57−W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.146 per kilowatt-hour?

-a) $2.282E+01

-b) $2.510E+01

-c) $2.761E+01

-d) $3.038E+01

+e) $3.341E+01

6) A battery with a terminal voltage of 10.6 V is connected to a circuit consisting of 2 21.1 Ω resistors and one 12.8 Ω resistor. What is the voltage drop across the 12.8 Ω resistor?

+a) 2.467E+00 V

-b) 2.714E+00 V

-c) 2.985E+00 V

-d) 3.283E+00 V

-e) 3.612E+00 V

7) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.96 mT and 2.010E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

-a) 2.768E+05 m/s

-b) 3.045E+05 m/s

-c) 3.349E+05 m/s

-d) 3.684E+05 m/s

+e) 4.052E+05 m/s

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.253 m and $B_{max}=\,$ 0.489 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.112 m that is centered on the axis with its plane perpendicular to the axis?

-a) 1.289E+05 A

-b) 1.418E+05 A

-c) 1.560E+05 A

-d) 1.716E+05 A

+e) 1.888E+05 A

9) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 2.34 T and $\omega =$ 2.670E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.646 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

-a) 1.905E+04 V

-b) 2.096E+04 V

-c) 2.305E+04 V

+d) 2.536E+04 V

-e) 2.790E+04 V

10)

A long solenoid has a length 0.605 meters, radius 4.26 cm, and 597 turns. It surrounds coil of radius 9.08 meters and 12turns. If the current in the solenoid is changing at a rate of 250 A/s, what is the emf induced in the surounding coil?

-a) 4.551E-02 V

-b) 5.006E-02 V

-c) 5.507E-02 V

-d) 6.057E-02 V

+e) 6.663E-02 V

11) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.12 V. The resistance, inductance, and capacitance are R =3 Ω, L= 8.80E-03H , and C=6.40E-04 F, respectively. What is the amplitude of the current?

-a) 2.732E-02 A

-b) 3.005E-02 A

-c) 3.306E-02 A

-d) 3.636E-02 A

+e) 4.000E-02 A

12)

A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 23 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?

+a) 2.877E+00 V

-b) 3.165E+00 V

-c) 3.481E+00 V

-d) 3.829E+00 V

-e) 4.212E+00 V

Key: U1

1)

A parallel plate capacitor with a capicatnce C=1.80E-06 F whose plates have an area A=670.0 m² and separation d=3.30E-03 m is connected via a swith to a 40 Ω resistor and a battery of voltage V₀=97 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.40E-04?

-a) 7.731E+01 V

-b) 8.504E+01 V

+c) 9.354E+01 V

-d) 1.029E+02 V

-e) 1.132E+02 V

2) What is consumer cost to operate one 74−W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.119 per kilowatt-hour?

-a) $1.976E+01

-b) $2.173E+01

-c) $2.391E+01

-d) $2.630E+01

+e) $2.893E+01

3)

In the figure shown C₁=16.0 μF, C₂=2.27 μF, and C₃=4.4 μF. The voltage source provides ε=7.11 V. What is the charge on C₁?

-a) 2.515E+01 μC

-b) 2.766E+01 μC

-c) 3.043E+01 μC

+d) 3.347E+01 μC

-e) 3.682E+01 μC

4) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 3.58 T and $\omega =$ 4.310E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.879 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

-a) 7.043E+04 V

-b) 7.747E+04 V

+c) 8.522E+04 V

-d) 9.374E+04 V

-e) 1.031E+05 V

5) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.645 m and $B_{max}=\,$ 0.469 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.26 m that is centered on the axis with its plane perpendicular to the axis?

-a) 2.949E+05 A

-b) 3.244E+05 A

-c) 3.568E+05 A

+d) 3.925E+05 A

-e) 4.317E+05 A

6) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

-a) 8.971E+05 m/s

-b) 9.868E+05 m/s

-c) 1.085E+06 m/s

+d) 1.194E+06 m/s

-e) 1.313E+06 m/s

7)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

8) A battery with a terminal voltage of 12.4 V is connected to a circuit consisting of 3 21.6 Ω resistors and one 12.1 Ω resistor. What is the voltage drop across the 12.1 Ω resistor?

-a) 1.333E+00 V

-b) 1.466E+00 V

-c) 1.612E+00 V

-d) 1.774E+00 V

+e) 1.951E+00 V

9) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

-a) 2.274E+02 N/C

-b) 2.501E+02 N/C

+c) 2.751E+02 N/C

-d) 3.026E+02 N/C

-e) 3.329E+02 N/C

10)

A long solenoid has a length 0.923 meters, radius 4.08 cm, and 579 turns. It surrounds coil of radius 6.86 meters and 14turns. If the current in the solenoid is changing at a rate of 139 A/s, what is the emf induced in the surounding coil?

-a) 1.894E-02 V

-b) 2.083E-02 V

-c) 2.291E-02 V

+d) 2.520E-02 V

-e) 2.772E-02 V

11) A 4 C charge is separated from a 9 C charge by distance of 9 cm. What is the work done by increasing this separation to 14 cm?

-a) 8.769E-07 J

-b) 9.646E-07 J

-c) 1.061E-06 J

-d) 1.167E-06 J

+e) 1.284E-06 J

12) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.16 V. The resistance, inductance, and capacitance are R =8 Ω, L= 5.40E-03H , and C=5.40E-04 F, respectively. What is the amplitude of the current?

+a) 2.000E-02 A

-b) 2.200E-02 A

-c) 2.420E-02 A

-d) 2.662E-02 A

-e) 2.928E-02 A

Key: U2

1) A battery with a terminal voltage of 8.41 V is connected to a circuit consisting of 3 16.1 Ω resistors and one 10.9 Ω resistor. What is the voltage drop across the 10.9 Ω resistor?

-a) 1.058E+00 V

-b) 1.163E+00 V

-c) 1.280E+00 V

-d) 1.408E+00 V

+e) 1.548E+00 V

2)

In the figure shown C₁=15.4 μF, C₂=2.22 μF, and C₃=4.77 μF. The voltage source provides ε=6.8 V. What is the charge on C₁?

-a) 2.702E+01 μC

-b) 2.972E+01 μC

+c) 3.269E+01 μC

-d) 3.596E+01 μC

-e) 3.956E+01 μC

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

4) A 7 C charge is separated from a 12 C charge by distance of 9 cm. What is the work done by increasing this separation to 15 cm?

-a) 2.292E-06 J

-b) 2.521E-06 J

-c) 2.773E-06 J

-d) 3.050E-06 J

+e) 3.355E-06 J

5) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.7 (r≤R) where a=3 nC·m^-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 1.390E+03 N/C

+b) 1.530E+03 N/C

-c) 1.682E+03 N/C

-d) 1.851E+03 N/C

-e) 2.036E+03 N/C

6)

A parallel plate capacitor with a capicatnce C=7.10E-06 F whose plates have an area A=5.10E+03 m² and separation d=6.40E-03 m is connected via a swith to a 54 Ω resistor and a battery of voltage V₀=83 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-03?

-a) 6.111E+01 V

-b) 6.722E+01 V

-c) 7.395E+01 V

+d) 8.134E+01 V

-e) 8.947E+01 V

7) What is consumer cost to operate one 89−W incandescent bulb for 10 hours per day for 1 year (365 days) if the cost of electricity is $0.141 per kilowatt-hour?

-a) $3.785E+01

-b) $4.164E+01

+c) $4.580E+01

-d) $5.038E+01

-e) $5.542E+01

8) An RLC series combination is driven with an applied voltage of of V=V₀sin(ωt), where V₀=0.77 V. The resistance, inductance, and capacitance are R =3 Ω, L= 6.70E-03H , and C=7.10E-04 F, respectively. What is the amplitude of the current?

-a) 2.333E-01 A

+b) 2.567E-01 A

-c) 2.823E-01 A

-d) 3.106E-01 A

-e) 3.416E-01 A

9)

A long solenoid has a length 0.923 meters, radius 4.08 cm, and 579 turns. It surrounds coil of radius 6.86 meters and 14turns. If the current in the solenoid is changing at a rate of 139 A/s, what is the emf induced in the surounding coil?

-a) 1.894E-02 V

-b) 2.083E-02 V

-c) 2.291E-02 V

+d) 2.520E-02 V

-e) 2.772E-02 V

10) An electron beam (m=9.1 x 10⁻³¹kg, q=1.6 x 10⁻¹⁹C) enters a crossed-field velocity selector with magnetic and electric fields of 4.96 mT and 2.010E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

-a) 2.768E+05 m/s

-b) 3.045E+05 m/s

-c) 3.349E+05 m/s

-d) 3.684E+05 m/s

+e) 4.052E+05 m/s

11) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\vec {B}}(t)=B_{0}\sin \omega t$ where $B_{0}=$ 1.97 T and $\omega =$ 5.410E+03 s⁻¹. Suppose the electric field is always zero at point ${\mathcal {O}}$ , and consider a circle of radius 0.244 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $\oint {\vec {B}}\cdot d{\vec {s}}$ around the circle.

-a) 1.485E+04 V

+b) 1.634E+04 V

-c) 1.797E+04 V

-d) 1.977E+04 V

-e) 2.175E+04 V

12) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $r<a$ is,
$B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}$ ,
where $B_{max}$ is the maximum magnetic field (at $r=a$ ). If $a=$ 0.736 m and $B_{max}=\,$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius $r=$ 0.532 m that is centered on the axis with its plane perpendicular to the axis?

-a) 3.764E+05 A

-b) 4.140E+05 A

-c) 4.554E+05 A

+d) 5.010E+05 A

-e) 5.510E+05 A

Key: V0

1)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.1 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.6 m, z=z₀=1.8 m, and z=z₁=4.2 m. The surfaces in the yz plane each have area 9.4m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 5.0m². An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 2.186E+01 N·m²/C

-b) 2.404E+01 N·m²/C

+c) 2.645E+01 N·m²/C

-d) 2.909E+01 N·m²/C

-e) 3.200E+01 N·m²/C

3) When a 6.97 V battery operates a 2.6 W bulb, how many electrons pass through it each second?

-a) 1.749E+18 electrons

-b) 1.924E+18 electrons

-c) 2.117E+18 electrons

+d) 2.328E+18 electrons

-e) 2.561E+18 electrons

4)

In the figure shown C₁=20.6 μF, C₂=2.38 μF, and C₃=5.66 μF. The voltage source provides ε=12.6 V. What is the charge on C₁?

-a) 5.474E+01 μC

-b) 6.022E+01 μC

-c) 6.624E+01 μC

+d) 7.287E+01 μC

-e) 8.015E+01 μC

5) What is the average current involved when a truck battery sets in motion 669 C of charge in 4.3 s while starting an engine?

-a) 1.063E+02 A

-b) 1.169E+02 A

-c) 1.286E+02 A

-d) 1.414E+02 A

+e) 1.556E+02 A

6)

Two sources of emf ε₁=16.8 V, and ε₂=7.15 V are oriented as shownin the circuit. The resistances are R₁=3.12 kΩ and R₂=1.51 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=1.95 mA and I₄=0.603 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 4.108E+00 V

+b) 4.519E+00 V

-c) 4.970E+00 V

-d) 5.468E+00 V

-e) 6.014E+00 V

7) A charged particle in a magnetic field of 3.350E-04 T is moving perpendicular to the magnetic field with a speed of 4.350E+05 m/s. What is the period of orbit if orbital radius is 0.841 m?

-a) 1.004E-05 s

-b) 1.104E-05 s

+c) 1.215E-05 s

-d) 1.336E-05 s

-e) 1.470E-05 s

8)

Three wires sit at the corners of a square of length 0.495 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.45 A, 1.66 A, 1.63 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 1.205E-04 T

+b) B_y= 1.325E-04 T

-c) B_y= 1.458E-04 T

-d) B_y= 1.604E-04 T

-e) B_y= 1.764E-04 T

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.477 m. The magnetic field is spatially uniform but decays in time according to $(4.67)e^{-\alpha t}$ , where $\alpha =$ 8.01 s. What is the current in the coil if the impedance of the coil is 75.6 Ω?

-a) 2.215E-01 A

+b) 2.437E-01 A

-c) 2.681E-01 A

-d) 2.949E-01 A

-e) 3.244E-01 A

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?

-a) -1.700E+00 s

-b) -1.870E+00 s

-c) -2.057E+00 s

+d) -2.262E+00 s

-e) -2.489E+00 s

11) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, X_L, X_C). Since Q is calculatedat resonance, X_L, X_C and only twoimpedances are involved, Q=≡ω₀L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V₀sin(ωt), where V₀=2 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 5.40E-03H , and C=3.20E-06 F, respectively.

-a) Q = 9.395E+01

-b) Q = 1.080E+02

-c) Q = 1.242E+02

-d) Q = 1.429E+02

+e) Q = 1.643E+02

12) What is the radiation force on an object that is 5.40E+11 m away from the sun and has cross-sectional area of 0.021 m²? The average power output of the Sun is 3.80E+26 W.

-a) 9.923E-09 N

-b) 1.092E-08 N

-c) 1.201E-08 N

-d) 1.321E-08 N

+e) 1.453E-08 N

Key: V1

1)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

+a) 5.352E+09 N/C²

-b) 5.887E+09 N/C²

-c) 6.476E+09 N/C²

-d) 7.124E+09 N/C²

-e) 7.836E+09 N/C²

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to $(5.62)e^{-\alpha t}$ , where $\alpha =$ 9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

+a) 7.890E-01 A

-b) 8.679E-01 A

-c) 9.547E-01 A

-d) 1.050E+00 A

-e) 1.155E+00 A

3)

Two sources of emf ε₁=26.8 V, and ε₂=10.1 V are oriented as shownin the circuit. The resistances are R₁=2.2 kΩ and R₂=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=2.29 mA and I₄=0.464 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 3.436E+00 V

-b) 3.779E+00 V

-c) 4.157E+00 V

-d) 4.573E+00 V

+e) 5.030E+00 V

4)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?

-a) -1.700E+00 s

-b) -1.870E+00 s

-c) -2.057E+00 s

+d) -2.262E+00 s

-e) -2.489E+00 s

5) When a 7.1 V battery operates a 1.8 W bulb, how many electrons pass through it each second?

-a) 1.439E+18 electrons

+b) 1.582E+18 electrons

-c) 1.741E+18 electrons

-d) 1.915E+18 electrons

-e) 2.106E+18 electrons

6)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.8 m, z=z₀=1.1 m, and z=z₁=5.2 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 12.0m² ,and those in the zx plane have area 11.0m². An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 5.606E+01 N·m²/C

-b) 6.167E+01 N·m²/C

-c) 6.784E+01 N·m²/C

+d) 7.462E+01 N·m²/C

-e) 8.208E+01 N·m²/C

7) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m²? The average power output of the Sun is 3.80E+26 W.

-a) 5.275E-07 N

-b) 5.803E-07 N

+c) 6.383E-07 N

-d) 7.021E-07 N

-e) 7.723E-07 N

8)

In the figure shown C₁=18.0 μF, C₂=2.88 μF, and C₃=5.34 μF. The voltage source provides ε=11.9 V. What is the charge on C₁?

-a) 5.045E+01 μC

-b) 5.550E+01 μC

-c) 6.105E+01 μC

+d) 6.715E+01 μC

-e) 7.387E+01 μC

9) A charged particle in a magnetic field of 4.480E-04 T is moving perpendicular to the magnetic field with a speed of 7.700E+05 m/s. What is the period of orbit if orbital radius is 0.368 m?

-a) 2.730E-06 s

+b) 3.003E-06 s

-c) 3.303E-06 s

-d) 3.633E-06 s

-e) 3.997E-06 s

10) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, X_L, X_C). Since Q is calculatedat resonance, X_L, X_C and only twoimpedances are involved, Q=≡ω₀L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V₀sin(ωt), where V₀=3 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 4.70E-03H , and C=3.30E-06 F, respectively.

-a) Q = 1.313E+02

+b) Q = 1.510E+02

-c) Q = 1.736E+02

-d) Q = 1.996E+02

-e) Q = 2.296E+02

11)

Three wires sit at the corners of a square of length 0.699 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.87 A, 2.18 A, 1.34 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 6.999E-05 T

-b) B_y= 7.699E-05 T

+c) B_y= 8.469E-05 T

-d) B_y= 9.316E-05 T

-e) B_y= 1.025E-04 T

12) What is the average current involved when a truck battery sets in motion 760 C of charge in 5.35 s while starting an engine?

-a) 1.291E+02 A

+b) 1.421E+02 A

-c) 1.563E+02 A

-d) 1.719E+02 A

-e) 1.891E+02 A

Key: V2

1)

Two sources of emf ε₁=49.8 V, and ε₂=18.1 V are oriented as shownin the circuit. The resistances are R₁=2.78 kΩ and R₂=2.63 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.51 mA and I₄=0.969 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₁?

-a) 7.886E+00 V

-b) 8.675E+00 V

-c) 9.542E+00 V

-d) 1.050E+01 V

+e) 1.155E+01 V

2)

Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.1 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.6 m, z=z₀=1.8 m, and z=z₁=4.2 m. The surfaces in the yz plane each have area 9.4m². Those in the xy plane have area 8.2m² ,and those in the zx plane have area 5.0m². An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

-a) 2.186E+01 N·m²/C

-b) 2.404E+01 N·m²/C

+c) 2.645E+01 N·m²/C

-d) 2.909E+01 N·m²/C

-e) 3.200E+01 N·m²/C

3)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.594 m. The magnetic field is spatially uniform but decays in time according to $(2.89)e^{-\alpha t}$ , where $\alpha =$ 9.6 s. What is the current in the coil if the impedance of the coil is 6.65 Ω?

-a) 2.088E+00 A

+b) 2.297E+00 A

-c) 2.527E+00 A

-d) 2.779E+00 A

-e) 3.057E+00 A

5)

Three wires sit at the corners of a square of length 0.834 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.26 A, 1.75 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?

+a) B_y= 7.518E-05 T

-b) B_y= 8.270E-05 T

-c) B_y= 9.097E-05 T

-d) B_y= 1.001E-04 T

-e) B_y= 1.101E-04 T

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, X_L, X_C). Since Q is calculatedat resonance, X_L, X_C and only twoimpedances are involved, Q=≡ω₀L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V₀sin(ωt), where V₀=5 V. The resistance, inductance, and capacitance are R =0.21 Ω, L= 5.40E-03H , and C=3.20E-06 F, respectively.

-a) Q = 1.286E+02

-b) Q = 1.479E+02

-c) Q = 1.701E+02

+d) Q = 1.956E+02

-e) Q = 2.250E+02

7) When a 4.89 V battery operates a 1.44 W bulb, how many electrons pass through it each second?

+a) 1.838E+18 electrons

-b) 2.022E+18 electrons

-c) 2.224E+18 electrons

-d) 2.446E+18 electrons

-e) 2.691E+18 electrons

8) A charged particle in a magnetic field of 5.500E-04 T is moving perpendicular to the magnetic field with a speed of 2.930E+05 m/s. What is the period of orbit if orbital radius is 0.787 m?

+a) 1.688E-05 s

-b) 1.856E-05 s

-c) 2.042E-05 s

-d) 2.246E-05 s

-e) 2.471E-05 s

9) What is the average current involved when a truck battery sets in motion 701 C of charge in 4.98 s while starting an engine?

-a) 1.280E+02 A

+b) 1.408E+02 A

-c) 1.548E+02 A

-d) 1.703E+02 A

-e) 1.874E+02 A

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 2.59% of its maximum value if ε = 1.14 V , R = 6.17 Ω, and L = 5.45 H?

+a) -1.614E+00 s

-b) -1.775E+00 s

-c) -1.952E+00 s

-d) -2.148E+00 s

-e) -2.362E+00 s

11)

In the figure shown C₁=17.5 μF, C₂=2.63 μF, and C₃=5.76 μF. The voltage source provides ε=15.9 V. What is the charge on C₁?

-a) 8.197E+01 μC

+b) 9.017E+01 μC

-c) 9.919E+01 μC

-d) 1.091E+02 μC

-e) 1.200E+02 μC

12) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m²? The average power output of the Sun is 3.80E+26 W.

+a) 2.673E-07 N

-b) 2.940E-07 N

-c) 3.234E-07 N

-d) 3.558E-07 N

-e) 3.913E-07 N

Key: W0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=2e

,

q_{2}=-7e

, and

q_{3}=3e

?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

2) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

-a) 2.274E+02 N/C

-b) 2.501E+02 N/C

+c) 2.751E+02 N/C

-d) 3.026E+02 N/C

-e) 3.329E+02 N/C

3)

An electron gun has parallel plates separated by 2.68 cm and gives electrons 29 keV of energy. What force would the field between the plates exert on a 0.496 μC charge that gets between the plates?

+a) 5.367E-01 N

-b) 5.904E-01 N

-c) 6.494E-01 N

-d) 7.144E-01 N

-e) 7.858E-01 N

4)

In the figure shown C₁=17.5 μF, C₂=2.63 μF, and C₃=5.76 μF. The voltage source provides ε=15.9 V. What is the charge on C₁?

-a) 8.197E+01 μC

+b) 9.017E+01 μC

-c) 9.919E+01 μC

-d) 1.091E+02 μC

-e) 1.200E+02 μC

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =97 C and $\tau =$ 0.0132 s. What is the current at $t=$ 0.0225 s?

+a) 1.336E+03 A

-b) 1.470E+03 A

-c) 1.617E+03 A

-d) 1.779E+03 A

-e) 1.957E+03 A

6)

In the circuit shown V=17.8 V, R₁=2.27 Ω, R₂=6.79 Ω, and R₃=15.1 Ω. What is the power dissipated by R₂?

-a) 1.446E+01 W

-b) 1.591E+01 W

-c) 1.750E+01 W

-d) 1.925E+01 W

+e) 2.117E+01 W

7) A 14 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 11 g, and the magnitude of the magnetic field is 0.448 T. What current is required to maintain this balance?

-a) 1.174E+00 A

-b) 1.291E+00 A

-c) 1.420E+00 A

-d) 1.562E+00 A

+e) 1.719E+00 A

8) Two loops of wire carry the same current of 29 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.76 m while the other has a radius of 1.12 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.544 m from the first (smaller) loopif the disance between the loops is 1.56 m?

+a) 1.950E-02 T

-b) 2.145E-02 T

-c) 2.360E-02 T

-d) 2.596E-02 T

-e) 2.855E-02 T

9) Calculate the motional emf induced along a 37.9 km conductor moving at an orbital speed of 7.84 km/s perpendicular to Earth's 5.410E-05 Tesla magnetic field.

-a) 1.208E+04 V

-b) 1.329E+04 V

-c) 1.461E+04 V

+d) 1.608E+04 V

-e) 1.768E+04 V

10)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.65% of its maximum value if ε = 3.62 V , R = 4.07 Ω, and L = 7.19 H?

-a) -2.476E+00 s

-b) -2.724E+00 s

-c) -2.996E+00 s

-d) -3.296E+00 s

+e) -3.625E+00 s

11) An ac generator produces an emf of amplitude 75 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 22 mF inductor?

-a) 2.466E+00 A

+b) 2.713E+00 A

-c) 2.984E+00 A

-d) 3.283E+00 A

-e) 3.611E+00 A

12)

A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=6.10E+03 m² and separation d=7.40E-03 m is connected via a swith to a 18 Ω resistor and a battery of voltage V₀=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.20E-04?

-a) 6.259E-02 A

-b) 6.885E-02 A

-c) 7.573E-02 A

+d) 8.331E-02 A

-e) 9.164E-02 A

Key: W1

1)

A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=6.80E+03 m² and separation d=8.30E-03 m is connected via a swith to a 84 Ω resistor and a battery of voltage V₀=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.60E-03?

-a) 4.678E-04 A

+b) 5.145E-04 A

-c) 5.660E-04 A

-d) 6.226E-04 A

-e) 6.848E-04 A

2) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.5 (r≤R) where a=3 nC·m^-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?

-a) 2.579E+02 N/C

+b) 2.837E+02 N/C

-c) 3.121E+02 N/C

-d) 3.433E+02 N/C

-e) 3.776E+02 N/C

3)

Three small charged objects are placed as shown, where

b=2a

, and

a=4\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=1e

,

q_{2}=-8e

, and

q_{3}=4e

?

-a) 3.719E+01 degrees

-b) 4.091E+01 degrees

+c) 4.500E+01 degrees

-d) 4.950E+01 degrees

-e) 5.445E+01 degrees

4) Calculate the motional emf induced along a 42.1 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 4.730E-05 Tesla magnetic field.

-a) 1.279E+04 V

-b) 1.407E+04 V

+c) 1.547E+04 V

-d) 1.702E+04 V

-e) 1.872E+04 V

5) An ac generator produces an emf of amplitude 73 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF inductor?

-a) 1.134E+00 A

-b) 1.247E+00 A

-c) 1.372E+00 A

+d) 1.509E+00 A

-e) 1.660E+00 A

6) Two loops of wire carry the same current of 39 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.49 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.552 m from the first (smaller) loopif the disance between the loops is 1.62 m?

-a) 1.564E-02 T

-b) 1.720E-02 T

-c) 1.892E-02 T

-d) 2.081E-02 T

+e) 2.289E-02 T

7) A 14 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 11 g, and the magnitude of the magnetic field is 0.448 T. What current is required to maintain this balance?

-a) 1.174E+00 A

-b) 1.291E+00 A

-c) 1.420E+00 A

-d) 1.562E+00 A

+e) 1.719E+00 A

8)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 2.28% of its maximum value if ε = 7.39 V , R = 7.05 Ω, and L = 3.51 H?

-a) -6.429E-01 s

-b) -7.072E-01 s

-c) -7.779E-01 s

-d) -8.557E-01 s

+e) -9.412E-01 s

9)

An electron gun has parallel plates separated by 4.2 cm and gives electrons 51 keV of energy. What force would the field between the plates exert on a 0.84 μC charge that gets between the plates?

-a) 8.430E-01 N

-b) 9.273E-01 N

+c) 1.020E+00 N

-d) 1.122E+00 N

-e) 1.234E+00 N

10)

In the figure shown C₁=17.9 μF, C₂=2.71 μF, and C₃=4.14 μF. The voltage source provides ε=7.12 V. What is the charge on C₁?

+a) 3.527E+01 μC

-b) 3.880E+01 μC

-c) 4.268E+01 μC

-d) 4.695E+01 μC

-e) 5.164E+01 μC

11)

In the circuit shown V=15.4 V, R₁=2.55 Ω, R₂=5.12 Ω, and R₃=12.7 Ω. What is the power dissipated by R₂?

-a) 1.096E+01 W

-b) 1.206E+01 W

-c) 1.326E+01 W

-d) 1.459E+01 W

+e) 1.605E+01 W

12) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =30 C and $\tau =$ 0.0178 s. What is the current at $t=$ 0.0161 s?

-a) 5.125E+02 A

-b) 5.638E+02 A

-c) 6.201E+02 A

+d) 6.822E+02 A

-e) 7.504E+02 A

Key: W2

1) A 27 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.85 T. What current is required to maintain this balance?

-a) 3.106E-01 A

+b) 3.416E-01 A

-c) 3.758E-01 A

-d) 4.134E-01 A

-e) 4.547E-01 A

2) Two loops of wire carry the same current of 39 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.49 m while the other has a radius of 1.11 m. What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.552 m from the first (smaller) loopif the disance between the loops is 1.62 m?

-a) 1.564E-02 T

-b) 1.720E-02 T

-c) 1.892E-02 T

-d) 2.081E-02 T

+e) 2.289E-02 T

3)

A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m² and separation d=4.60E-03 m is connected via a swith to a 96 Ω resistor and a battery of voltage V₀=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?

-a) 7.315E-02 A

+b) 8.047E-02 A

-c) 8.851E-02 A

-d) 9.737E-02 A

-e) 1.071E-01 A

4) An ac generator produces an emf of amplitude 46 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 63 mF inductor?

-a) 4.961E-01 A

-b) 5.457E-01 A

-c) 6.002E-01 A

-d) 6.603E-01 A

+e) 7.263E-01 A

5) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=3 nC·m^-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?

-a) 4.874E+01 N/C

+b) 5.362E+01 N/C

-c) 5.898E+01 N/C

-d) 6.488E+01 N/C

-e) 7.137E+01 N/C

6) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =23 C and $\tau =$ 0.0204 s. What is the current at $t=$ 0.0106 s?

-a) 6.096E+02 A

+b) 6.706E+02 A

-c) 7.376E+02 A

-d) 8.114E+02 A

-e) 8.925E+02 A

7)

An electron gun has parallel plates separated by 2.98 cm and gives electrons 11 keV of energy. What force would the field between the plates exert on a 0.685 μC charge that gets between the plates?

-a) 1.900E-01 N

-b) 2.090E-01 N

-c) 2.299E-01 N

+d) 2.529E-01 N

-e) 2.781E-01 N

8)

In the circuit shown V=17.5 V, R₁=2.34 Ω, R₂=7.1 Ω, and R₃=15.3 Ω. What is the power dissipated by R₂?

-a) 1.784E+01 W

+b) 1.963E+01 W

-c) 2.159E+01 W

-d) 2.375E+01 W

-e) 2.612E+01 W

9) Calculate the motional emf induced along a 49.5 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.310E-05 Tesla magnetic field.

-a) 1.395E+04 V

-b) 1.534E+04 V

-c) 1.688E+04 V

-d) 1.857E+04 V

+e) 2.042E+04 V

10)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-9e

, and

q_{3}=5e

?

-a) 6.125E+01 degrees

+b) 6.738E+01 degrees

-c) 7.412E+01 degrees

-d) 8.153E+01 degrees

-e) 8.968E+01 degrees

11)

Suppose switch S₁ in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S₁ is opened as as S₂ is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?

-a) -1.700E+00 s

-b) -1.870E+00 s

-c) -2.057E+00 s

+d) -2.262E+00 s

-e) -2.489E+00 s

12)

In the figure shown C₁=15.4 μF, C₂=2.22 μF, and C₃=4.77 μF. The voltage source provides ε=6.8 V. What is the charge on C₁?

-a) 2.702E+01 μC

-b) 2.972E+01 μC

+c) 3.269E+01 μC

-d) 3.596E+01 μC

-e) 3.956E+01 μC

Key: X0

1)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-7e

, and

q_{3}=4e

?

-a) 5.377E+01 degrees

-b) 5.914E+01 degrees

-c) 6.506E+01 degrees

+d) 7.157E+01 degrees

-e) 7.872E+01 degrees

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\vec {E}}=2y^{2.0}{\hat {i}}+2x^{2.1}{\hat {j}}+3y^{2.5}{\hat {k}}$

-a) 9.027E+03 V·m

+b) 9.930E+03 V·m

-c) 1.092E+04 V·m

-d) 1.202E+04 V·m

-e) 1.322E+04 V·m

3) Calculate the final speed of a free electron accelerated from rest through a potential difference of 19 V.

-a) 1.942E+06 m/s

-b) 2.137E+06 m/s

-c) 2.350E+06 m/s

+d) 2.585E+06 m/s

-e) 2.844E+06 m/s

4)

In the figure shown C₁=16.9 μF, C₂=2.86 μF, and C₃=5.1 μF. The voltage source provides ε=9.98 V. What is the energy stored in C₂?

-a) 1.764E+01 μJ

+b) 1.940E+01 μJ

-c) 2.134E+01 μJ

-d) 2.348E+01 μJ

-e) 2.583E+01 μJ

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =23 C and $\tau =$ 0.0204 s. What is the current at $t=$ 0.0106 s?

-a) 6.096E+02 A

+b) 6.706E+02 A

-c) 7.376E+02 A

-d) 8.114E+02 A

-e) 8.925E+02 A

6) Three resistors, R₁ = 1.41 Ω, and R₂ = R₂ = 3.17 Ω, are connected in parallel to a 5.89 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

-a) 1.681E+01 W

-b) 1.849E+01 W

-c) 2.033E+01 W

-d) 2.237E+01 W

+e) 2.460E+01 W

7)

The silver ribbon shown are a=3.89 cm, b=3.43 cm, and c= 1.21 cm. The current carries a current of 77 A and it lies in a uniform magnetic field of 2.16 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

-a) 1.322E-06 V

+b) 1.454E-06 V

-c) 1.600E-06 V

-d) 1.759E-06 V

-e) 1.935E-06 V

8) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 424 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

-a)

\chi {\text{ (chi) }}=

1.092E+03

-b)

\chi {\text{ (chi) }}=

1.201E+03

-c)

\chi {\text{ (chi) }}=

1.321E+03

+d)

\chi {\text{ (chi) }}=

1.454E+03

-e)

\chi {\text{ (chi) }}=

1.599E+03

9) Calculate the motional emf induced along a 30.3 km conductor moving at an orbital speed of 7.76 km/s perpendicular to Earth's 5.100E-05 Tesla magnetic field.

-a) 1.090E+04 V

+b) 1.199E+04 V

-c) 1.319E+04 V

-d) 1.451E+04 V

-e) 1.596E+04 V

10) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.62 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.66mm$ , and $n=2.61$ . What is the volume of the washer?

-a) 6.960E-01 cm³

-b) 7.656E-01 cm³

+c) 8.421E-01 cm³

-d) 9.264E-01 cm³

-e) 1.019E+00 cm³

11) An ac generator produces an emf of amplitude 93 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF capacitor?

-a) 4.917E+00 A

-b) 5.409E+00 A

-c) 5.950E+00 A

+d) 6.545E+00 A

-e) 7.199E+00 A

12)

A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=5.60E+03 m² and separation d=8.70E-03 m is connected via a swith to a 98 Ω resistor and a battery of voltage V₀=67 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.80E-03?

-a) 5.050E+03 V/m

-b) 5.555E+03 V/m

-c) 6.111E+03 V/m

-d) 6.722E+03 V/m

+e) 7.394E+03 V/m

Key: X1

1) Three resistors, R₁ = 1.43 Ω, and R₂ = R₂ = 3.25 Ω, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

-a) 5.184E+01 W

+b) 5.702E+01 W

-c) 6.272E+01 W

-d) 6.900E+01 W

-e) 7.590E+01 W

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}$

-a) 2.067E+03 V·m

-b) 2.274E+03 V·m

+c) 2.501E+03 V·m

-d) 2.752E+03 V·m

-e) 3.027E+03 V·m

3) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.

+a) 5.102E+06 m/s

-b) 5.612E+06 m/s

-c) 6.173E+06 m/s

-d) 6.791E+06 m/s

-e) 7.470E+06 m/s

4)

A parallel plate capacitor with a capicatnce C=1.60E-06 F whose plates have an area A=890.0 m² and separation d=4.90E-03 m is connected via a swith to a 80 Ω resistor and a battery of voltage V₀=44 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.90E-04?

-a) 6.651E+03 V/m

-b) 7.316E+03 V/m

+c) 8.048E+03 V/m

-d) 8.853E+03 V/m

-e) 9.738E+03 V/m

5) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.62 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.66mm$ , and $n=2.61$ . What is the volume of the washer?

-a) 6.960E-01 cm³

-b) 7.656E-01 cm³

+c) 8.421E-01 cm³

-d) 9.264E-01 cm³

-e) 1.019E+00 cm³

6)

Three small charged objects are placed as shown, where

b=2a

, and

a=2\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-9e

, and

q_{3}=5e

?

-a) 6.125E+01 degrees

+b) 6.738E+01 degrees

-c) 7.412E+01 degrees

-d) 8.153E+01 degrees

-e) 8.968E+01 degrees

7) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =38 C and $\tau =$ 0.0167 s. What is the current at $t=$ 0.0183 s?

-a) 5.715E+02 A

-b) 6.286E+02 A

-c) 6.915E+02 A

+d) 7.606E+02 A

-e) 8.367E+02 A

8)

The silver ribbon shown are a=3.89 cm, b=2.94 cm, and c= 0.58 cm. The current carries a current of 242 A and it lies in a uniform magnetic field of 2.47 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

-a) 9.911E-06 V

+b) 1.090E-05 V

-c) 1.199E-05 V

-d) 1.319E-05 V

-e) 1.451E-05 V

9) Calculate the motional emf induced along a 30.3 km conductor moving at an orbital speed of 7.76 km/s perpendicular to Earth's 5.100E-05 Tesla magnetic field.

-a) 1.090E+04 V

+b) 1.199E+04 V

-c) 1.319E+04 V

-d) 1.451E+04 V

-e) 1.596E+04 V

10) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

+a) 5.042E+00 A

-b) 5.546E+00 A

-c) 6.100E+00 A

-d) 6.710E+00 A

-e) 7.381E+00 A

11) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 24 turns per centimeter and the current applied to the solenoid is 595 mA, the net magnetic field is measured to be 1.46 T. What is the magnetic susceptibility for this case?

-a)

\chi {\text{ (chi) }}=

6.716E+02

-b)

\chi {\text{ (chi) }}=

7.387E+02

+c)

\chi {\text{ (chi) }}=

8.126E+02

-d)

\chi {\text{ (chi) }}=

8.939E+02

-e)

\chi {\text{ (chi) }}=

9.833E+02

12)

In the figure shown C₁=19.2 μF, C₂=2.24 μF, and C₃=4.93 μF. The voltage source provides ε=11.7 V. What is the energy stored in C₂?

-a) 1.303E+01 μJ

-b) 1.434E+01 μJ

-c) 1.577E+01 μJ

-d) 1.735E+01 μJ

+e) 1.908E+01 μJ

Key: X2

1) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.14mm$ , and $n=2.86$ . What is the volume of the washer?

+a) 1.071E+00 cm³

-b) 1.178E+00 cm³

-c) 1.296E+00 cm³

-d) 1.425E+00 cm³

-e) 1.568E+00 cm³

2)

In the figure shown C₁=15.4 μF, C₂=2.6 μF, and C₃=5.17 μF. The voltage source provides ε=9.6 V. What is the energy stored in C₂?

-a) 1.508E+01 μJ

+b) 1.659E+01 μJ

-c) 1.825E+01 μJ

-d) 2.007E+01 μJ

-e) 2.208E+01 μJ

3) Three resistors, R₁ = 0.855 Ω, and R₂ = R₂ = 1.91 Ω, are connected in parallel to a 6.97 V voltage source. Calculate the power dissipated by the smaller resistor (R₁.)

+a) 5.682E+01 W

-b) 6.250E+01 W

-c) 6.875E+01 W

-d) 7.563E+01 W

-e) 8.319E+01 W

4) Calculate the motional emf induced along a 32.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 5.280E-05 Tesla magnetic field.

-a) 1.093E+04 V

-b) 1.202E+04 V

+c) 1.322E+04 V

-d) 1.454E+04 V

-e) 1.600E+04 V

5) Calculate the final speed of a free electron accelerated from rest through a potential difference of 12 V.

-a) 1.698E+06 m/s

-b) 1.868E+06 m/s

+c) 2.055E+06 m/s

-d) 2.260E+06 m/s

-e) 2.486E+06 m/s

6) An ac generator produces an emf of amplitude 58 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 66 mF capacitor?

-a) 3.976E+00 A

-b) 4.373E+00 A

+c) 4.810E+00 A

-d) 5.291E+00 A

-e) 5.821E+00 A

7) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 17 turns per centimeter and the current applied to the solenoid is 455 mA, the net magnetic field is measured to be 1.14 T. What is the magnetic susceptibility for this case?

-a)

\chi {\text{ (chi) }}=

8.804E+02

-b)

\chi {\text{ (chi) }}=

9.685E+02

-c)

\chi {\text{ (chi) }}=

1.065E+03

+d)

\chi {\text{ (chi) }}=

1.172E+03

-e)

\chi {\text{ (chi) }}=

1.289E+03

8)

The silver ribbon shown are a=3.96 cm, b=3.35 cm, and c= 1.07 cm. The current carries a current of 295 A and it lies in a uniform magnetic field of 3.4 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

-a) 9.015E-06 V

+b) 9.916E-06 V

-c) 1.091E-05 V

-d) 1.200E-05 V

-e) 1.320E-05 V

9) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =84 C and $\tau =$ 0.0199 s. What is the current at $t=$ 0.0104 s?

-a) 2.275E+03 A

+b) 2.503E+03 A

-c) 2.753E+03 A

-d) 3.029E+03 A

-e) 3.331E+03 A

10)

Three small charged objects are placed as shown, where

b=2a

, and

a=6\times 10^{-7}{\text{m}}

.what angle does the force on

q_{2}

make above the

-x

axis if

q_{1}=3e

,

q_{2}=-7e

, and

q_{3}=4e

?

-a) 5.914E+01 degrees

-b) 6.506E+01 degrees

+c) 7.157E+01 degrees

-d) 7.872E+01 degrees

-e) 8.659E+01 degrees

11)

A parallel plate capacitor with a capicatnce C=7.90E-06 F whose plates have an area A=6.10E+03 m² and separation d=6.80E-03 m is connected via a swith to a 22 Ω resistor and a battery of voltage V₀=6 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=5.20E-04?

-a) 7.619E+02 V/m

+b) 8.381E+02 V/m

-c) 9.219E+02 V/m

-d) 1.014E+03 V/m

-e) 1.115E+03 V/m

12) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
${\vec {E}}=1y^{2.4}{\hat {i}}+4x^{1.7}{\hat {j}}+4y^{2.1}{\hat {k}}$

-a) 1.206E+03 V·m

+b) 1.326E+03 V·m

-c) 1.459E+03 V·m

-d) 1.605E+03 V·m

-e) 1.765E+03 V·m

Key: Y0

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

-a) 6.925E+09 N/C²

-b) 7.617E+09 N/C²

+c) 8.379E+09 N/C²

-d) 9.217E+09 N/C²

-e) 1.014E+10 N/C²

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?

-a) 6.641E+00 N/C

-b) 7.305E+00 N/C

+c) 8.036E+00 N/C

-d) 8.839E+00 N/C

-e) 9.723E+00 N/C

3)

A Van de Graff generator has a 116 cm diameter metal sphere that produces 246 kV near its surface. What is the excess charge on the sphere?

-a) 1.193E+01 μC

-b) 1.312E+01 μC

-c) 1.443E+01 μC

+d) 1.588E+01 μC

-e) 1.746E+01 μC

4)

In the figure shown C₁=17.7 μF, C₂=2.48 μF, and C₃=4.68 μF. The voltage source provides ε=12.7 V. What is the energy stored in C₂?

+a) 2.242E+01 μJ

-b) 2.467E+01 μJ

-c) 2.713E+01 μJ

-d) 2.985E+01 μJ

-e) 3.283E+01 μJ

5) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =63 C and $\tau =$ 0.0149 s. What is the current at $t=$ 0.0172 s?

-a) 1.212E+03 A

+b) 1.333E+03 A

-c) 1.466E+03 A

-d) 1.613E+03 A

-e) 1.774E+03 A

6) A given battery has a 11 V emf and an internal resistance of 0.0998 Ω. If it is connected to a 0.417 Ω resistor what is the power dissipated by that load?

-a) 1.419E+02 W

-b) 1.561E+02 W

-c) 1.717E+02 W

+d) 1.889E+02 W

-e) 2.078E+02 W

7) A 72 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 14 g, and the magnitude of the magnetic field is 0.54 T. What current is required to maintain this balance?

-a) 2.651E-01 A

-b) 2.916E-01 A

-c) 3.208E-01 A

+d) 3.529E-01 A

-e) 3.882E-01 A

8)

Three wires sit at the corners of a square of length 0.823 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 6.718E-05 T

-b) B_y= 7.390E-05 T

+c) B_y= 8.129E-05 T

-d) B_y= 8.942E-05 T

-e) B_y= 9.836E-05 T

9) A long solenoid has a radius of 0.442 m and 41 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 4 A and $\alpha =$ 20 s⁻¹.What is the induced electric fied at a distance 0.2 m from the axis at time t=0.0833 s ?

-a) 6.438E-05 V/m

-b) 7.082E-05 V/m

+c) 7.790E-05 V/m

-d) 8.569E-05 V/m

-e) 9.426E-05 V/m

10) An induced emf of 7.48V is measured across a coil of 95 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.33A in 0.304s. What is the self-inductance of the coil?

-a) 2.914E-01 H

-b) 3.205E-01 H

-c) 3.526E-01 H

-d) 3.878E-01 H

+e) 4.266E-01 H

11) The output of an ac generator connected to an RLC series combination has a frequency of 1.00E+03 Hz and an amplitude of 0.6 V;. If R =3 Ω, L= 1.70E-03H , and C=5.40E-04 F, what is the impedance?

-a) 8.123E+00 Ω

-b) 8.935E+00 Ω

-c) 9.828E+00 Ω

+d) 1.081E+01 Ω

-e) 1.189E+01 Ω

12) What is the radiation force on an object that is 7.40E+11 m away from the sun and has cross-sectional area of 0.082 m²? The average power output of the Sun is 3.80E+26 W.

-a) 2.063E-08 N

-b) 2.270E-08 N

-c) 2.497E-08 N

-d) 2.746E-08 N

+e) 3.021E-08 N

Key: Y1

1)

Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?

+a) B_y= 4.028E-05 T

-b) B_y= 4.431E-05 T

-c) B_y= 4.874E-05 T

-d) B_y= 5.361E-05 T

-e) B_y= 5.897E-05 T

2) A long solenoid has a radius of 0.447 m and 85 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 7 A and $\alpha =$ 23 s⁻¹.What is the induced electric fied at a distance 0.212 m from the axis at time t=0.0819 s ?

-a) 1.893E-04 V/m

-b) 2.082E-04 V/m

-c) 2.290E-04 V/m

-d) 2.519E-04 V/m

+e) 2.771E-04 V/m

3) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m²? The average power output of the Sun is 3.80E+26 W.

+a) 2.673E-07 N

-b) 2.940E-07 N

-c) 3.234E-07 N

-d) 3.558E-07 N

-e) 3.913E-07 N

4) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =16 C and $\tau =$ 0.0214 s. What is the current at $t=$ 0.0207 s?

-a) 2.135E+02 A

-b) 2.349E+02 A

-c) 2.584E+02 A

+d) 2.842E+02 A

-e) 3.126E+02 A

5) A given battery has a 12 V emf and an internal resistance of 0.107 Ω. If it is connected to a 0.814 Ω resistor what is the power dissipated by that load?

+a) 1.382E+02 W

-b) 1.520E+02 W

-c) 1.672E+02 W

-d) 1.839E+02 W

-e) 2.023E+02 W

6) The output of an ac generator connected to an RLC series combination has a frequency of 680 Hz and an amplitude of 0.79 V;. If R =5 Ω, L= 2.40E-03H , and C=9.10E-04 F, what is the impedance?

-a) 8.398E+00 Ω

-b) 9.238E+00 Ω

-c) 1.016E+01 Ω

+d) 1.118E+01 Ω

-e) 1.230E+01 Ω

7)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

8) A 34 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.348 T. What current is required to maintain this balance?

+a) 6.626E-01 A

-b) 7.289E-01 A

-c) 8.018E-01 A

-d) 8.819E-01 A

-e) 9.701E-01 A

9)

In the figure shown C₁=16.3 μF, C₂=2.17 μF, and C₃=4.67 μF. The voltage source provides ε=8.35 V. What is the energy stored in C₂?

-a) 8.718E+00 μJ

-b) 9.589E+00 μJ

-c) 1.055E+01 μJ

-d) 1.160E+01 μJ

+e) 1.276E+01 μJ

10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.3 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.5 m from the center of the shells?

-a) 1.994E+01 N/C

-b) 2.194E+01 N/C

-c) 2.413E+01 N/C

-d) 2.655E+01 N/C

+e) 2.920E+01 N/C

11) An induced emf of 6.78V is measured across a coil of 58 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.98A in 0.726s. What is the self-inductance of the coil?

-a) 1.022E+00 H

-b) 1.124E+00 H

+c) 1.237E+00 H

-d) 1.360E+00 H

-e) 1.496E+00 H

12)

A Van de Graff generator has a 141 cm diameter metal sphere that produces 280 kV near its surface. What is the excess charge on the sphere?

-a) 1.500E+01 μC

-b) 1.650E+01 μC

-c) 1.815E+01 μC

-d) 1.997E+01 μC

+e) 2.196E+01 μC

Key: Y2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

-a) 2.988E+00 N/C

-b) 3.287E+00 N/C

-c) 3.616E+00 N/C

-d) 3.977E+00 N/C

+e) 4.375E+00 N/C

2) The output of an ac generator connected to an RLC series combination has a frequency of 290 Hz and an amplitude of 0.75 V;. If R =2 Ω, L= 8.00E-03H , and C=9.90E-04 F, what is the impedance?

-a) 9.675E+00 Ω

-b) 1.064E+01 Ω

-c) 1.171E+01 Ω

-d) 1.288E+01 Ω

+e) 1.416E+01 Ω

3)

In the figure shown C₁=20.7 μF, C₂=2.79 μF, and C₃=5.18 μF. The voltage source provides ε=15.0 V. What is the energy stored in C₂?

-a) 2.064E+01 μJ

-b) 2.270E+01 μJ

-c) 2.497E+01 μJ

-d) 2.747E+01 μJ

+e) 3.022E+01 μJ

4) What is the radiation force on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.044 m²? The average power output of the Sun is 3.80E+26 W.

-a) 7.088E-09 N

-b) 7.796E-09 N

-c) 8.576E-09 N

+d) 9.434E-09 N

-e) 1.038E-08 N

5) A long solenoid has a radius of 0.732 m and 55 turns per meter; its current decreases with time according to $I_{0}e^{-\alpha t}$ , where $I_{0}=$ 9 A and $\alpha =$ 25 s⁻¹.What is the induced electric fied at a distance 0.203 m from the axis at time t=0.0448 s ?

+a) 5.150E-04 V/m

-b) 5.665E-04 V/m

-c) 6.232E-04 V/m

-d) 6.855E-04 V/m

-e) 7.540E-04 V/m

6)

Three wires sit at the corners of a square of length 0.702 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I₁, I₂, I₂) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?

-a) B_y= 7.576E-05 T

+b) B_y= 8.333E-05 T

-c) B_y= 9.167E-05 T

-d) B_y= 1.008E-04 T

-e) B_y= 1.109E-04 T

7) An induced emf of 7.48V is measured across a coil of 95 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.33A in 0.304s. What is the self-inductance of the coil?

-a) 2.914E-01 H

-b) 3.205E-01 H

-c) 3.526E-01 H

-d) 3.878E-01 H

+e) 4.266E-01 H

8) The charge passing a plane intersecting a wire is $Q_{M}=\left(1-e^{t/\tau }\right)$ , where $Q_{M}$ =38 C and $\tau =$ 0.0167 s. What is the current at $t=$ 0.0183 s?

-a) 5.715E+02 A

-b) 6.286E+02 A

-c) 6.915E+02 A

+d) 7.606E+02 A

-e) 8.367E+02 A

9)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

10) A 96 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.325 T. What current is required to maintain this balance?

-a) 2.596E-01 A

-b) 2.855E-01 A

+c) 3.141E-01 A

-d) 3.455E-01 A

-e) 3.801E-01 A

11) A given battery has a 14 V emf and an internal resistance of 0.198 Ω. If it is connected to a 0.534 Ω resistor what is the power dissipated by that load?

-a) 1.776E+02 W

+b) 1.953E+02 W

-c) 2.149E+02 W

-d) 2.364E+02 W

-e) 2.600E+02 W

12)

A Van de Graff generator has a 95 cm diameter metal sphere that produces 190 kV near its surface. What is the excess charge on the sphere?

-a) 9.129E+00 μC

+b) 1.004E+01 μC

-c) 1.105E+01 μC

-d) 1.215E+01 μC

-e) 1.337E+01 μC

Key: Z0

1)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

-a) 7.415E+09 N/C²

-b) 8.156E+09 N/C²

-c) 8.972E+09 N/C²

-d) 9.869E+09 N/C²

+e) 1.086E+10 N/C²

2) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

-a) 2.274E+02 N/C

-b) 2.501E+02 N/C

+c) 2.751E+02 N/C

-d) 3.026E+02 N/C

-e) 3.329E+02 N/C

3)

Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.) The charges are q₁=3 μC, q₂=6 μC, q₃=9 μC, and q₄=12 μC. How much work was required to assemble these four charges from infinity?

-a) 7.789E+01 J

+b) 8.568E+01 J

-c) 9.425E+01 J

-d) 1.037E+02 J

-e) 1.140E+02 J

4)

What is the net capacitance if C₁=3.54 μF, C₂=3.53 μF, and C₃=3.65 μF in the configuration shown?

-a) 3.700E+00 μF

-b) 4.070E+00 μF

-c) 4.477E+00 μF

-d) 4.925E+00 μF

+e) 5.417E+00 μF

5) What is consumer cost to operate one 102−W incandescent bulb for 6 hours per day for 1 year (365 days) if the cost of electricity is $0.127 per kilowatt-hour?

-a) $2.131E+01

-b) $2.345E+01

-c) $2.579E+01

+d) $2.837E+01

-e) $3.121E+01

6)

Two sources of emf ε₁=18.6 V, and ε₂=5.63 V are oriented as shownin the circuit. The resistances are R₁=3.9 kΩ and R₂=1.1 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.41 mA and I₄=0.614 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

-a) 4.342E+00 V

-b) 4.776E+00 V

-c) 5.254E+00 V

+d) 5.779E+00 V

-e) 6.357E+00 V

7)

The silver ribbon shown are a=4.23 cm, b=3.7 cm, and c= 0.721 cm. The current carries a current of 144 A and it lies in a uniform magnetic field of 1.21 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

-a) 1.746E-06 V

-b) 1.921E-06 V

-c) 2.113E-06 V

-d) 2.324E-06 V

+e) 2.557E-06 V

8) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 344 mA, the net magnetic field is measured to be 1.12 T. What is the magnetic susceptibility for this case?

-a)

\chi {\text{ (chi) }}=

7.922E+02

-b)

\chi {\text{ (chi) }}=

8.714E+02

+c)

\chi {\text{ (chi) }}=

9.586E+02

-d)

\chi {\text{ (chi) }}=

1.054E+03

-e)

\chi {\text{ (chi) }}=

1.160E+03

9)

A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

-a) 7.479E+00 cm³/s

-b) 8.227E+00 cm³/s

-c) 9.049E+00 cm³/s

-d) 9.954E+00 cm³/s

+e) 1.095E+01 cm³/s

10) A washer has an inner diameter of 2.46 cm and an outer diamter of 4.24 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.32mm$ , and $n=2.63$ . What is the volume of the washer?

-a) 7.499E-01 cm³

-b) 8.249E-01 cm³

-c) 9.074E-01 cm³

-d) 9.982E-01 cm³

+e) 1.098E+00 cm³

11) The output of an ac generator connected to an RLC series combination has a frequency of 5.70E+04 Hz and an amplitude of 5 V. If R =9 Ω, L= 6.10E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

+a) 9.443E-04 Watts

-b) 1.039E-03 Watts

-c) 1.143E-03 Watts

-d) 1.257E-03 Watts

-e) 1.383E-03 Watts

12) A 57 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?

-a) 1.020E+02 km

-b) 1.122E+02 km

-c) 1.235E+02 km

+d) 1.358E+02 km

-e) 1.494E+02 km

Key: Z1

1) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 23 turns per centimeter and the current applied to the solenoid is 534 mA, the net magnetic field is measured to be 1.48 T. What is the magnetic susceptibility for this case?

-a)

\chi {\text{ (chi) }}=

7.917E+02

-b)

\chi {\text{ (chi) }}=

8.708E+02

+c)

\chi {\text{ (chi) }}=

9.579E+02

-d)

\chi {\text{ (chi) }}=

1.054E+03

-e)

\chi {\text{ (chi) }}=

1.159E+03

2)

Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.) The charges are q₁=4 μC, q₂=7 μC, q₃=8 μC, and q₄=10 μC. How much work was required to assemble these four charges from infinity?

+a) 1.241E+02 J

-b) 1.365E+02 J

-c) 1.501E+02 J

-d) 1.652E+02 J

-e) 1.817E+02 J

3)

The silver ribbon shown are a=4.12 cm, b=3.32 cm, and c= 1.46 cm. The current carries a current of 120 A and it lies in a uniform magnetic field of 1.39 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

+a) 1.209E-06 V

-b) 1.329E-06 V

-c) 1.462E-06 V

-d) 1.609E-06 V

-e) 1.770E-06 V

4) The output of an ac generator connected to an RLC series combination has a frequency of 5.40E+04 Hz and an amplitude of 6 V. If R =2 Ω, L= 6.80E-03H , and C=9.90E-06 F, what is the rms power transferred to the resistor?

-a) 2.452E-04 Watts

+b) 2.697E-04 Watts

-c) 2.967E-04 Watts

-d) 3.264E-04 Watts

-e) 3.590E-04 Watts

5)

Two sources of emf ε₁=36.7 V, and ε₂=13.6 V are oriented as shownin the circuit. The resistances are R₁=2.86 kΩ and R₂=2.2 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=3.02 mA and I₄=0.854 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

+a) 1.380E+01 V

-b) 1.518E+01 V

-c) 1.670E+01 V

-d) 1.837E+01 V

-e) 2.020E+01 V

6)

A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

-a) 3.093E+01 cm³/s

-b) 3.403E+01 cm³/s

+c) 3.743E+01 cm³/s

-d) 4.117E+01 cm³/s

-e) 4.529E+01 cm³/s

7) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=3.28mm$ , and $n=2.4$ . What is the volume of the washer?

+a) 1.097E+00 cm³

-b) 1.207E+00 cm³

-c) 1.328E+00 cm³

-d) 1.460E+00 cm³

-e) 1.606E+00 cm³

8) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?

-a) 1.003E+02 km

-b) 1.103E+02 km

-c) 1.213E+02 km

+d) 1.335E+02 km

-e) 1.468E+02 km

9)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

10) What is consumer cost to operate one 104−W incandescent bulb for 6 hours per day for 1 year (365 days) if the cost of electricity is $0.136 per kilowatt-hour?

-a) $2.116E+01

-b) $2.327E+01

-c) $2.560E+01

-d) $2.816E+01

+e) $3.098E+01

11)

What is the net capacitance if C₁=2.96 μF, C₂=3.95 μF, and C₃=3.74 μF in the configuration shown?

-a) 4.489E+00 μF

-b) 4.938E+00 μF

+c) 5.432E+00 μF

-d) 5.975E+00 μF

-e) 6.573E+00 μF

12) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=2 nC·m^-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

-a) 3.821E+02 N/C

-b) 4.203E+02 N/C

-c) 4.624E+02 N/C

+d) 5.086E+02 N/C

-e) 5.594E+02 N/C

Key: Z2

1)

A cylinder of height 2.91 cm and radius 8.33 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.7 cm from point O and moves at a speed of 9.14 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)

-a) 2.061E+02 cm³/s

-b) 2.267E+02 cm³/s

+c) 2.494E+02 cm³/s

-d) 2.743E+02 cm³/s

-e) 3.018E+02 cm³/s

2)

The silver ribbon shown are a=3.89 cm, b=2.94 cm, and c= 0.58 cm. The current carries a current of 242 A and it lies in a uniform magnetic field of 2.47 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.

-a) 9.911E-06 V

+b) 1.090E-05 V

-c) 1.199E-05 V

-d) 1.319E-05 V

-e) 1.451E-05 V

3)

Two sources of emf ε₁=36.7 V, and ε₂=12.1 V are oriented as shownin the circuit. The resistances are R₁=2.52 kΩ and R₂=1.22 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I₃=4.14 mA and I₄=1.19 mA enter and leave near R₂, while the current I₅ exits near R₁.What is the magnitude (absolute value) of voltage drop across R₂?

-a) 7.805E+00 V

-b) 8.586E+00 V

-c) 9.444E+00 V

-d) 1.039E+01 V

+e) 1.143E+01 V

4) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

-a) 2.274E+02 N/C

-b) 2.501E+02 N/C

+c) 2.751E+02 N/C

-d) 3.026E+02 N/C

-e) 3.329E+02 N/C

5) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 344 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?

-a)

\chi {\text{ (chi) }}=

1.185E+03

-b)

\chi {\text{ (chi) }}=

1.303E+03

+c)

\chi {\text{ (chi) }}=

1.433E+03

-d)

\chi {\text{ (chi) }}=

1.577E+03

-e)

\chi {\text{ (chi) }}=

1.734E+03

6) The output of an ac generator connected to an RLC series combination has a frequency of 4.30E+04 Hz and an amplitude of 6 V. If R =6 Ω, L= 5.20E-03H , and C=8.60E-06 F, what is the rms power transferred to the resistor?

-a) 1.511E-03 Watts

-b) 1.662E-03 Watts

-c) 1.828E-03 Watts

-d) 2.011E-03 Watts

+e) 2.212E-03 Watts

7) A washer has an inner diameter of 2.6 cm and an outer diamter of 4.17 cm. The thickness is $h=Cr^{-n}$ where $r$ is measured in cm, $C=4.38mm$ , and $n=2.62$ . What is the volume of the washer?

-a) 7.196E-01 cm³

-b) 7.916E-01 cm³

-c) 8.707E-01 cm³

+d) 9.578E-01 cm³

-e) 1.054E+00 cm³

8) A 58 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 88 kW?

-a) 1.111E+02 km

-b) 1.222E+02 km

-c) 1.344E+02 km

+d) 1.478E+02 km

-e) 1.626E+02 km

9)

What is the net capacitance if C₁=2.96 μF, C₂=3.95 μF, and C₃=3.74 μF in the configuration shown?

-a) 4.489E+00 μF

-b) 4.938E+00 μF

+c) 5.432E+00 μF

-d) 5.975E+00 μF

-e) 6.573E+00 μF

10) What is consumer cost to operate one 76−W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.144 per kilowatt-hour?

+a) $3.595E+01

-b) $3.955E+01

-c) $4.350E+01

-d) $4.785E+01

-e) $5.264E+01

11)

Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.) The charges are q₁=3 μC, q₂=5 μC, q₃=6 μC, and q₄=9 μC. How much work was required to assemble these four charges from infinity?

-a) 2.617E+01 J

-b) 2.879E+01 J

-c) 3.167E+01 J

-d) 3.484E+01 J

+e) 3.832E+01 J

12)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

-a) 7.119E+09 N/C²

-b) 7.831E+09 N/C²

+c) 8.614E+09 N/C²

-d) 9.476E+09 N/C²

-e) 1.042E+10 N/C²