# Quizbank/University Physics Semester 2/T11

University Physics Semester 2/T11 ID153341821922

Exams:

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.

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### T11 A0

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

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,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.51 m and ${\displaystyle B_{max}=\,}$ 0.649 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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?

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.407 m and ${\displaystyle B_{max}=\,}$ 0.605 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

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?

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

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?

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

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,
${\displaystyle {\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}}$

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.736 m and ${\displaystyle B_{max}=\,}$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=8.3{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =5{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=5.3{\text{ m}}}$.

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 ${\displaystyle Q_{M}=\left(1-e^{t/\tau }\right)}$, where ${\displaystyle Q_{M}}$=78 C and ${\displaystyle \tau =}$0.0244 s. What is the current at ${\displaystyle 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 ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.28mm}$, and ${\displaystyle n=2.4}$. 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 ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.14mm}$, and ${\displaystyle n=2.86}$. 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 ${\displaystyle Q_{M}=\left(1-e^{t/\tau }\right)}$, where ${\displaystyle Q_{M}}$=91 C and ${\displaystyle \tau =}$0.0156 s. What is the current at ${\displaystyle 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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=3.0{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =8{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=2.0{\text{ m}}}$.

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 ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.28mm}$, and ${\displaystyle n=2.4}$. 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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=2.0{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =9{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=1.2{\text{ m}}}$.

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 ${\displaystyle Q_{M}=\left(1-e^{t/\tau }\right)}$, where ${\displaystyle Q_{M}}$=18 C and ${\displaystyle \tau =}$0.0169 s. What is the current at ${\displaystyle 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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=7.2{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =3{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=3.6{\text{ m}}}$.

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) By= 6.833E-05 T
b) By= 7.517E-05 T
c) By= 8.268E-05 T
d) By= 9.095E-05 T
e) By= 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) By= 7.035E-05 T
b) By= 7.739E-05 T
c) By= 8.512E-05 T
d) By= 9.364E-05 T
e) By= 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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=3.0{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =8{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=2.0{\text{ m}}}$.

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) By= 7.576E-05 T
b) By= 8.333E-05 T
c) By= 9.167E-05 T
d) By= 1.008E-04 T
e) By= 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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=3.3{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =4{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=2.0{\text{ m}}}$.

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,
${\displaystyle {\vec {E}}=4y^{2.0}{\hat {i}}+3x^{2.0}{\hat {j}}+3y^{3.0}{\hat {k}}}$

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.253 m and ${\displaystyle B_{max}=\,}$ 0.489 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \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?

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.547 m and ${\displaystyle B_{max}=\,}$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \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,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

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?

#### 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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.736 m and ${\displaystyle B_{max}=\,}$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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?

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,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$5 A and ${\displaystyle \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 ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=2e}$?
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,
${\displaystyle {\vec {E}}=4y^{1.4}{\hat {i}}+2x^{2.3}{\hat {j}}+4y^{2.3}{\hat {k}}}$

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.852 m and ${\displaystyle B_{max}=\,}$ 0.476 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \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 ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.31mm}$, and ${\displaystyle n=2.66}$. 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 ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=2e}$?
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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.407 m and ${\displaystyle B_{max}=\,}$ 0.605 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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 ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.08mm}$, and ${\displaystyle n=2.68}$. 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,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \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 ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=3e}$?
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 ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.66mm}$, and ${\displaystyle n=2.61}$. 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,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

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 ${\displaystyle r is,
${\displaystyle B_{\theta }(r)=\left({\frac {2r}{a}}-{\frac {r^{2}}{a^{2}}}\right)B_{max}}$,
where ${\displaystyle B_{max}}$ is the maximum magnetic field (at ${\displaystyle r=a}$). If ${\displaystyle a=}$ 0.619 m and ${\displaystyle B_{max}=\,}$ 0.215 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 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 ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=6e}$?
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)=ar1.4 (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 ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=3e}$?
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)=ar1.4 (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 ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=5e}$?
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)=ar1.4 (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 ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=4e}$?
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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \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 ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=5e}$?
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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \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 ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=5e}$?
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)=ar1.7 (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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.44 kA, I2=1.1 kA, and I3=1.99 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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)=ar1.8 (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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.48 kA, I2=1.47 kA, and I3=2.6 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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)=ar1.2 (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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.31 kA, I2=1.08 kA, and I3=1.77 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=4e}$?
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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$5 A and ${\displaystyle \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 ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=6e}$?
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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$3 A and ${\displaystyle \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 ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=6e}$?
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 ${\displaystyle (2.48)e^{-\alpha t}}$, where ${\displaystyle \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 ${\displaystyle (2.48)e^{-\alpha t}}$, where ${\displaystyle \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 ${\displaystyle (2.48)e^{-\alpha t}}$, where ${\displaystyle \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)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.38 kA, I2=1.58 kA, and I3=4.31 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \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)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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,
${\displaystyle {\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}}$

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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.58 kA, I2=1.11 kA, and I3=2.47 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \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)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.42 kA, I2=0.904 kA, and I3=1.34 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

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 ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=5e}$?
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) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.593E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.753E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.928E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.121E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 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) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.211E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.932E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.726E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.598E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.056E+03
4)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=5e}$?
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) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.593E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.753E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.928E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.121E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 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 ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=5e}$?
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) Bx= 8.371E-05 T
b) Bx= 9.208E-05 T
c) Bx= 1.013E-04 T
d) Bx= 1.114E-04 T
e) Bx= 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 ${\displaystyle (1.95)e^{-\alpha t}}$, where ${\displaystyle \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 ${\displaystyle (5.55)e^{-\alpha t}}$, where ${\displaystyle \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) Bx= 6.171E-05 T
b) Bx= 6.788E-05 T
c) Bx= 7.467E-05 T
d) Bx= 8.213E-05 T
e) Bx= 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 ${\displaystyle (1.95)e^{-\alpha t}}$, where ${\displaystyle \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) Bx= 7.270E-05 T
b) Bx= 7.997E-05 T
c) Bx= 8.797E-05 T
d) Bx= 9.677E-05 T
e) Bx= 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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=4.3{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =2{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=2.4{\text{ m}}}$.

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) By= 1.205E-04 T
b) By= 1.325E-04 T
c) By= 1.458E-04 T
d) By= 1.604E-04 T
e) By= 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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$5 A and ${\displaystyle \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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=3.3{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =4{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=2.0{\text{ m}}}$.

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) By= 7.576E-05 T
b) By= 8.333E-05 T
c) By= 9.167E-05 T
d) By= 1.008E-04 T
e) By= 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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \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) By= 3.480E-05 T
b) By= 3.828E-05 T
c) By= 4.210E-05 T
d) By= 4.631E-05 T
e) By= 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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=6.9{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =9{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=4.3{\text{ m}}}$.

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)=ar1.7 (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 ${\displaystyle Q_{M}=\left(1-e^{t/\tau }\right)}$, where ${\displaystyle Q_{M}}$=38 C and ${\displaystyle \tau =}$0.0167 s. What is the current at ${\displaystyle 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 ${\displaystyle Q_{M}=\left(1-e^{t/\tau }\right)}$, where ${\displaystyle Q_{M}}$=16 C and ${\displaystyle \tau =}$0.0214 s. What is the current at ${\displaystyle 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)=ar1.5 (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 ${\displaystyle Q_{M}=\left(1-e^{t/\tau }\right)}$, where ${\displaystyle Q_{M}}$=52 C and ${\displaystyle \tau =}$0.018 s. What is the current at ${\displaystyle 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)=ar1.5 (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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.38 kA, I2=0.839 kA, and I3=2.27 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=3.3 kA, and I3=5.85 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.38 kA, I2=1.58 kA, and I3=4.31 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \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 ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=4e}$?
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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.61 kA, I2=2.2 kA, and I3=5.1 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.31 T and ${\displaystyle \omega =}$8.360E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, 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 ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ 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 ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=3e}$?
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 ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.71 T and ${\displaystyle \omega =}$6.600E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, 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 ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ 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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.82 kA, I2=0.964 kA, and I3=2.21 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=3e}$?
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 ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.18 T and ${\displaystyle \omega =}$4.840E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, 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 ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ 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 ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.51 kA, I2=1.32 kA, and I3=2.73 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
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 μ