# Quizbank/Electricity and Magnetism (calculus) Exams/T2(11-16)

calcPhyEMt/T2(11-16) ID153290827354 (Study guide)

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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### T2(11-16) A0

1) A charged particle in a magnetic field of 4.970E-04 T is moving perpendicular to the magnetic field with a speed of 2.950E+05 m/s. What is the period of orbit if orbital radius is 0.344 m?

a) 7.327E-06 s
b) 8.060E-06 s
c) 8.865E-06 s
d) 9.752E-06 s
e) 1.073E-05 s

2) A wire carries a current of 250 A in a circular arc with radius 2.17 cm swept through 53 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

a) 3.498E+00 Tesla
b) 3.848E+00 Tesla
c) 4.233E+00 Tesla
d) 4.656E+00 Tesla
e) 5.122E+00 Tesla

3) Two loops of wire carry the same current of 24 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.53 m while the other has a radius of 1.38 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 0.485 m from the first (smaller) loopif the disance between the loops is 1.78 m?

a) 1.294E-02 T
b) 1.424E-02 T
c) 1.566E-02 T
d) 1.723E-02 T
e) 1.895E-02 T

4) 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
5)
A cylinder of height 1.3 cm and radius 6.01 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 3.61 cm from point O and moves at a speed of 2.11 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) 1.372E+01 cm3/s
b) 1.509E+01 cm3/s
c) 1.660E+01 cm3/s
d) 1.826E+01 cm3/s
e) 2.009E+01 cm3/s

6) 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
7)
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

8) The output of an ac generator connected to an RLC series combination has a frequency of 5.50E+04 Hz and an amplitude of 2 V. If R =8 Ω, L= 9.60E-03H , and C=8.30E-06 F, what is the rms power transferred to the resistor?

a) 4.347E-05 Watts
b) 4.782E-05 Watts
c) 5.260E-05 Watts
d) 5.786E-05 Watts
e) 6.364E-05 Watts

9) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.83 V. The resistance, inductance, and capacitance are R =4 Ω, L= 4.60E-03H , and C=8.10E-04 F, respectively. What is the amplitude of the current?

a) 1.417E-01 A
b) 1.559E-01 A
c) 1.715E-01 A
d) 1.886E-01 A
e) 2.075E-01 A
10)
A parallel plate capacitor with a capicatnce C=6.90E-06 F whose plates have an area A=5.80E+03 m2 and separation d=7.40E-03 m is connected via a swith to a 78 Ω resistor and a battery of voltage V0=70 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=2.50E-03?
a) 5.890E-03 A
b) 6.479E-03 A
c) 7.126E-03 A
d) 7.839E-03 A
e) 8.623E-03 A

#### T2(11-16) A1

1) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.18 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.42mm}$, and ${\displaystyle n=2.62}$. What is the volume of the washer?

a) 1.351E+00 cm3
b) 1.486E+00 cm3
c) 1.635E+00 cm3
d) 1.798E+00 cm3
e) 1.978E+00 cm3
2)
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

3) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.16 V. The resistance, inductance, and capacitance are R =8 Ω, L= 5.40E-03H , and C=5.40E-04 F, respectively. What is the amplitude of the current?

a) 2.000E-02 A
b) 2.200E-02 A
c) 2.420E-02 A
d) 2.662E-02 A
e) 2.928E-02 A

4) A wire carries a current of 353 A in a circular arc with radius 2.44 cm swept through 86 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

a) 5.891E+00 Tesla
b) 6.481E+00 Tesla
c) 7.129E+00 Tesla
d) 7.841E+00 Tesla
e) 8.626E+00 Tesla

5) Two loops of wire carry the same current of 11 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.424 m while the other has a radius of 1.32 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 0.52 m from the first (smaller) loopif the disance between the loops is 1.25 m?

a) 7.623E-03 T
b) 8.385E-03 T
c) 9.223E-03 T
d) 1.015E-02 T
e) 1.116E-02 T
6)
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

7) 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

8) The output of an ac generator connected to an RLC series combination has a frequency of 2.70E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 9.10E-03H , and C=9.60E-06 F, what is the rms power transferred to the resistor?

a) 2.188E-03 Watts
b) 2.407E-03 Watts
c) 2.647E-03 Watts
d) 2.912E-03 Watts
e) 3.203E-03 Watts
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) A long solenoid has a radius of 0.645 m and 37 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 =}$23 s−1.What is the induced electric fied at a distance 0.189 m from the axis at time t=0.0698 s ?

a) 1.372E-04 V/m
b) 1.509E-04 V/m
c) 1.660E-04 V/m
d) 1.826E-04 V/m
e) 2.009E-04 V/m

#### T2(11-16) A2

1) A washer has an inner diameter of 2.16 cm and an outer diamter of 4.82 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.22mm}$, and ${\displaystyle n=2.8}$. What is the volume of the washer?

a) 1.342E+00 cm3
b) 1.477E+00 cm3
c) 1.624E+00 cm3
d) 1.787E+00 cm3
e) 1.965E+00 cm3

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)
A cylinder of height 1.48 cm and radius 7.74 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 3.76 cm from point O and moves at a speed of 3.09 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 3.312E+01 cm3/s
b) 3.643E+01 cm3/s
c) 4.008E+01 cm3/s
d) 4.408E+01 cm3/s
e) 4.849E+01 cm3/s

4) A wire carries a current of 297 A in a circular arc with radius 2.31 cm swept through 75 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

a) 3.774E+00 Tesla
b) 4.151E+00 Tesla
c) 4.566E+00 Tesla
d) 5.023E+00 Tesla
e) 5.525E+00 Tesla
5)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =0.741 s if ε = 7.36 V , R = 5.33 Ω, and L = 1.27 H?
a) 7.635E-01 V
b) 9.162E-01 V
c) 1.099E+00 V
d) 1.319E+00 V
e) 1.583E+00 V

6) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.62 V. The resistance, inductance, and capacitance are R =6 Ω, L= 8.10E-03H , and C=6.40E-04 F, respectively. What is the amplitude of the current?

a) 7.058E-02 A
b) 7.764E-02 A
c) 8.540E-02 A
d) 9.394E-02 A
e) 1.033E-01 A

7) 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
8)
A parallel plate capacitor with a capicatnce C=9.40E-06 F whose plates have an area A=5.00E+03 m2 and separation d=4.70E-03 m is connected via a swith to a 62 Ω resistor and a battery of voltage V0=65 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=9.70E-04?
a) 1.985E-01 A
b) 2.183E-01 A
c) 2.401E-01 A
d) 2.642E-01 A
e) 2.906E-01 A

9) 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

10) A charged particle in a magnetic field of 1.480E-04 T is moving perpendicular to the magnetic field with a speed of 4.520E+05 m/s. What is the period of orbit if orbital radius is 0.4 m?

a) 5.560E-06 s
b) 6.116E-06 s
c) 6.728E-06 s
d) 7.401E-06 s
e) 8.141E-06 s

### T2(11-16) B0

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

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 536 mA, the net magnetic field is measured to be 1.47 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.310E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.024E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.126E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.239E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.363E+03

4) A square coil has sides that are L= 0.894 m long and is tightly wound with N=255 turns of wire. The resistance of the coil is R=8.83 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=0.0682 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.301E+00 A
b) 1.431E+00 A
c) 1.574E+00 A
d) 1.732E+00 A
e) 1.905E+00 A

5) 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

6) In an LC circuit, the self-inductance is 0.0689 H and the capacitance is 2.110E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.220E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.950E-04 s
b) 5.445E-04 s
c) 5.989E-04 s
d) 6.588E-04 s
e) 7.247E-04 s
7)
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

8) 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

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

a) 4.723E-02 A
b) 5.195E-02 A
c) 5.714E-02 A
d) 6.286E-02 A
e) 6.914E-02 A
10)
A parallel plate capacitor with a capicatnce C=8.20E-06 F whose plates have an area A=6.20E+03 m2 and separation d=6.70E-03 m is connected via a swith to a 75 Ω resistor and a battery of voltage V0=17 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=6.50E-04?
a) 1.505E+03 V/m
b) 1.656E+03 V/m
c) 1.821E+03 V/m
d) 2.003E+03 V/m
e) 2.204E+03 V/m

#### T2(11-16) B1

1) A long solenoid has a radius of 0.517 m and 23 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 0.162 m from the axis at time t=0.0679 s ?

a) 6.256E-06 V/m
b) 6.882E-06 V/m
c) 7.570E-06 V/m
d) 8.327E-06 V/m
e) 9.160E-06 V/m
2)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.43 kA, I2=1.64 kA, and I3=4.81 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 2.721E-03 T-m
b) 2.993E-03 T-m
c) 3.292E-03 T-m
d) 3.621E-03 T-m
e) 3.984E-03 T-m

3) 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

4) A cyclotron used to accelerate alpha particlesm=6.64 x 10−27kg, q=3.2 x 10−19C) has a radius of 0.232 m and a magneticfield of 1.1 T. What is their maximum kinetic energy?

a) 2.853E+00 MeV
b) 3.139E+00 MeV
c) 3.453E+00 MeV
d) 3.798E+00 MeV
e) 4.178E+00 MeV

5) An ac generator produces an emf of amplitude 32 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 14 mF capacitor?

a) 3.378E-01 A
b) 3.716E-01 A
c) 4.087E-01 A
d) 4.496E-01 A
e) 4.945E-01 A

6) 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

7) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 344 mA, the net magnetic field is measured to be 1.12 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.922E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.714E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.586E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.054E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.160E+03

8) 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
9)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =3.8 s if ε = 3.36 V , R = 5.2 Ω, and L = 3.37 H?
a) 5.369E-01 V
b) 6.443E-01 V
c) 7.732E-01 V
d) 9.278E-01 V
e) 1.113E+00 V
10)
A parallel plate capacitor with a capicatnce C=2.60E-06 F whose plates have an area A=2.60E+03 m2 and separation d=9.00E-03 m is connected via a swith to a 63 Ω resistor and a battery of voltage V0=86 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=8.00E-04?
a) 7.125E+03 V/m
b) 7.837E+03 V/m
c) 8.621E+03 V/m
d) 9.483E+03 V/m
e) 1.043E+04 V/m

#### T2(11-16) B2

1)
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

2) 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

3) A long solenoid has a radius of 0.517 m and 23 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 0.162 m from the axis at time t=0.0679 s ?

a) 6.256E-06 V/m
b) 6.882E-06 V/m
c) 7.570E-06 V/m
d) 8.327E-06 V/m
e) 9.160E-06 V/m

4) 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 0.512 T. What is their maximum kinetic energy?

a) 2.574E-01 MeV
b) 2.831E-01 MeV
c) 3.114E-01 MeV
d) 3.425E-01 MeV
e) 3.768E-01 MeV

5) In an LC circuit, the self-inductance is 0.0116 H and the capacitance is 7.040E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.140E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.489E-04 s
b) 4.938E-04 s
c) 5.432E-04 s
d) 5.975E-04 s
e) 6.572E-04 s

6) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.16 V. The resistance, inductance, and capacitance are R =8 Ω, L= 5.40E-03H , and C=5.40E-04 F, respectively. What is the amplitude of the current?

a) 2.000E-02 A
b) 2.200E-02 A
c) 2.420E-02 A
d) 2.662E-02 A
e) 2.928E-02 A
7)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.47 s if ε = 7.04 V , R = 7.69 Ω, and L = 5.78 H?
a) 4.249E-01 V
b) 5.099E-01 V
c) 6.118E-01 V
d) 7.342E-01 V
e) 8.810E-01 V

8) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 525 mA, the net magnetic field is measured to be 1.44 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 5.515E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 6.066E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 6.673E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.340E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.074E+02
9)
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=2.4 kA, I2=2.64 kA, and I3=3.96 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 1.133E-03 T-m
b) 1.246E-03 T-m
c) 1.371E-03 T-m
d) 1.508E-03 T-m
e) 1.659E-03 T-m

10) An ac generator produces an emf of amplitude 50 V at a frequency of 47 Hz. What is the maximum amplitude of the current if the generator is connected to a 88 mF capacitor?

a) 1.074E+00 A
b) 1.181E+00 A
c) 1.299E+00 A
d) 1.429E+00 A
e) 1.572E+00 A

### T2(11-16) C0

1) 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

2) A solenoid has 5.500E+04 turns wound around a cylinder of diameter 1.45 cm and length 15 m. The current through the coils is 0.395 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−4.19 cm to z=+2.16 cm

a) 7.894E-05 T-m
b) 8.683E-05 T-m
c) 9.551E-05 T-m
d) 1.051E-04 T-m
e) 1.156E-04 T-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=2.66 kA, I2=1.25 kA, and I3=2.74 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 1.547E-03 T-m
b) 1.702E-03 T-m
c) 1.872E-03 T-m
d) 2.060E-03 T-m
e) 2.266E-03 T-m

4) A recangular coil with an area of 0.587 m2 and 13 turns is placed in a uniform magnetic field of 1.62 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 3.800E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 93 s?

a) 2.512E+04 V
b) 2.763E+04 V
c) 3.039E+04 V
d) 3.343E+04 V
e) 3.677E+04 V

5) 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

6) In an LC circuit, the self-inductance is 0.0776 H and the capacitance is 6.940E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.400E-05 C. How long does it take for the capacitor to become completely discharged?

a) 1.048E-03 s
b) 1.153E-03 s
c) 1.268E-03 s
d) 1.395E-03 s
e) 1.534E-03 s
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 2.54% of its maximum value if ε = 2.46 V , R = 2.8 Ω, and L = 5.67 H?
a) -2.540E+00 s
b) -2.794E+00 s
c) -3.073E+00 s
d) -3.381E+00 s
e) -3.719E+00 s

8) A step-down transformer steps 18 kV down to 260 V. The high-voltage input is provided by a 290 Ω power line that carries 3 A of currentWhat is the output current (at the 260 V side ?)

a) 1.888E+02 A
b) 2.077E+02 A
c) 2.285E+02 A
d) 2.513E+02 A
e) 2.764E+02 A

9) The output of an ac generator connected to an RLC series combination has a frequency of 5.40E+04 Hz and an amplitude of 6 V. If R =2 Ω, L= 6.80E-03H , and C=9.90E-06 F, what is the rms power transferred to the resistor?

a) 2.452E-04 Watts
b) 2.697E-04 Watts
c) 2.967E-04 Watts
d) 3.264E-04 Watts
e) 3.590E-04 Watts
10)
A parallel plate capacitor with a capicatnce C=4.30E-06 F whose plates have an area A=2.80E+03 m2 and separation d=5.70E-03 m is connected via a swith to a 7 Ω resistor and a battery of voltage V0=97 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=7.00E-05?
a) 1.049E+04 V/m
b) 1.154E+04 V/m
c) 1.269E+04 V/m
d) 1.396E+04 V/m
e) 1.535E+04 V/m

#### T2(11-16) C1

1) A solenoid has 9.350E+04 turns wound around a cylinder of diameter 1.85 cm and length 18 m. The current through the coils is 0.872 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−4.55 cm to z=+1.58 cm

a) 2.383E-04 T-m
b) 2.621E-04 T-m
c) 2.884E-04 T-m
d) 3.172E-04 T-m
e) 3.489E-04 T-m

2) 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

3) A recangular coil with an area of 0.815 m2 and 11 turns is placed in a uniform magnetic field of 3.62 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 4.700E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 59 s?

a) 1.197E+05 V
b) 1.316E+05 V
c) 1.448E+05 V
d) 1.593E+05 V
e) 1.752E+05 V
4)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 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
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=2.49 kA, I2=0.996 kA, and I3=2.61 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 1.385E-03 T-m
b) 1.524E-03 T-m
c) 1.676E-03 T-m
d) 1.844E-03 T-m
e) 2.028E-03 T-m
6)
A parallel plate capacitor with a capicatnce C=2.60E-06 F whose plates have an area A=2.60E+03 m2 and separation d=9.00E-03 m is connected via a swith to a 41 Ω resistor and a battery of voltage V0=91 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=3.00E-04?
a) 9.505E+03 V/m
b) 1.046E+04 V/m
c) 1.150E+04 V/m
d) 1.265E+04 V/m
e) 1.392E+04 V/m

7) The output of an ac generator connected to an RLC series combination has a frequency of 2.70E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 9.10E-03H , and C=9.60E-06 F, what is the rms power transferred to the resistor?

a) 2.188E-03 Watts
b) 2.407E-03 Watts
c) 2.647E-03 Watts
d) 2.912E-03 Watts
e) 3.203E-03 Watts

8) A step-down transformer steps 18 kV down to 260 V. The high-voltage input is provided by a 290 Ω power line that carries 3 A of currentWhat is the output current (at the 260 V side ?)

a) 1.888E+02 A
b) 2.077E+02 A
c) 2.285E+02 A
d) 2.513E+02 A
e) 2.764E+02 A

9) A circular current loop of radius 3.0 cm carries a current of 1.58 mA. What is the magnitude of the torque if the dipole is oriented at 63 ° to a uniform magnetic fied of 0.408 T?

a) 1.476E-06 N m
b) 1.624E-06 N m
c) 1.786E-06 N m
d) 1.965E-06 N m
e) 2.162E-06 N m

10) 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

#### T2(11-16) C2

1) A recangular coil with an area of 0.815 m2 and 11 turns is placed in a uniform magnetic field of 3.62 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 4.700E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 59 s?

a) 1.197E+05 V
b) 1.316E+05 V
c) 1.448E+05 V
d) 1.593E+05 V
e) 1.752E+05 V

2) A solenoid has 7.170E+04 turns wound around a cylinder of diameter 1.56 cm and length 9 m. The current through the coils is 0.391 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−2.73 cm to z=+2.56 cm

a) 1.414E-04 T-m
b) 1.556E-04 T-m
c) 1.711E-04 T-m
d) 1.882E-04 T-m
e) 2.071E-04 T-m

3) 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

4) 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

5) 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
6)
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 2.63% of its maximum value if ε = 8.7 V , R = 8.35 Ω, and L = 1.44 H?
a) -3.137E-01 s
b) -3.451E-01 s
c) -3.796E-01 s
d) -4.176E-01 s
e) -4.593E-01 s
7)
A parallel plate capacitor with a capicatnce C=5.20E-06 F whose plates have an area A=2.90E+03 m2 and separation d=4.90E-03 m is connected via a swith to a 93 Ω resistor and a battery of voltage V0=5 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.20E-03?
a) 6.896E+02 V/m
b) 7.585E+02 V/m
c) 8.344E+02 V/m
d) 9.178E+02 V/m
e) 1.010E+03 V/m

8) 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
9)
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=2.43 kA, I2=1.81 kA, and I3=3.23 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 1.622E-03 T-m
b) 1.784E-03 T-m
c) 1.963E-03 T-m
d) 2.159E-03 T-m
e) 2.375E-03 T-m

10) A circular current loop of radius 2.1 cm carries a current of 5.02 mA. What is the magnitude of the torque if the dipole is oriented at 26 ° to a uniform magnetic fied of 0.184 T?

a) 5.610E-07 N m
b) 6.171E-07 N m
c) 6.788E-07 N m
d) 7.467E-07 N m
e) 8.213E-07 N m

### T2(11-16) D0

1) 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 6.97 mT and 2.240E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 2.656E+05 m/s
b) 2.922E+05 m/s
c) 3.214E+05 m/s
d) 3.535E+05 m/s
e) 3.889E+05 m/s

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.9 mm from the center of a wire of radius 4 mm if the current is 1A?

a) 1.784E-05 T
b) 1.963E-05 T
c) 2.159E-05 T
d) 2.375E-05 T
e) 2.613E-05 T

3) 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

4) 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}=}$3.84 T and ${\displaystyle \omega =}$4.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.379 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) 3.333E+04 V
b) 3.666E+04 V
c) 4.033E+04 V
d) 4.436E+04 V
e) 4.879E+04 V

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

a) 7.007E-02 A
b) 7.708E-02 A
c) 8.479E-02 A
d) 9.327E-02 A
e) 1.026E-01 A
6)
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

7) 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

8) The output of an ac generator connected to an RLC series combination has a frequency of 160 Hz and an amplitude of 0.47 V;. If R =8 Ω, L= 1.30E-03H , and C=6.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) The output of an ac generator connected to an RLC series combination has a frequency of 470 Hz and an amplitude of 0.67 V;. If R =4 Ω, L= 2.40E-03H , and C=5.10E-04 F, what is the impedance?

a) 6.254E+00 Ω
b) 6.879E+00 Ω
c) 7.567E+00 Ω
d) 8.324E+00 Ω
e) 9.156E+00 Ω

10) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.048 m2? The average power output of the Sun is 3.80E+26 W.

a) 1.253E-05 N/m2
b) 1.378E-05 N/m2
c) 1.516E-05 N/m2
d) 1.667E-05 N/m2
e) 1.834E-05 N/m2

#### T2(11-16) D1

1) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.025 m2? The average power output of the Sun is 3.80E+26 W.

a) 5.511E-07 N/m2
b) 6.063E-07 N/m2
c) 6.669E-07 N/m2
d) 7.336E-07 N/m2
e) 8.069E-07 N/m2

2) The output of an ac generator connected to an RLC series combination has a frequency of 540 Hz and an amplitude of 0.18 V;. If R =3 Ω, L= 2.50E-03H , and C=8.20E-04 F, what is the impedance?

a) 7.872E+00 Ω
b) 8.659E+00 Ω
c) 9.525E+00 Ω
d) 1.048E+01 Ω
e) 1.153E+01 Ω

3) 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

4) In an LC circuit, the self-inductance is 0.0735 H and the capacitance is 2.300E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.220E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.411E-04 s
b) 4.852E-04 s
c) 5.338E-04 s
d) 5.871E-04 s
e) 6.458E-04 s

5) 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

6) An electron beam (m=9.1 x 10−31kg, q=1.6 x 10−19C) enters a crossed-field velocity selector with magnetic and electric fields of 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

7) 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
8)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.82% of its maximum value if ε = 8.65 V , R = 3.02 Ω, and L = 1.75 H?
a) -9.593E-01 s
b) -1.055E+00 s
c) -1.161E+00 s
d) -1.277E+00 s
e) -1.405E+00 s

9) The output of an ac generator connected to an RLC series combination has a frequency of 890 Hz and an amplitude of 0.58 V;. If R =9 Ω, L= 2.90E-03H , and C=8.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

10) 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}=}$2.25 T and ${\displaystyle \omega =}$8.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.227 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) 2.657E+04 V
b) 2.923E+04 V
c) 3.215E+04 V
d) 3.537E+04 V
e) 3.890E+04 V

#### T2(11-16) D2

1) The output of an ac generator connected to an RLC series combination has a frequency of 410 Hz and an amplitude of 0.82 V;. If R =7 Ω, L= 9.70E-03H , and C=9.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

2) The output of an ac generator connected to an RLC series combination has a frequency of 290 Hz and an amplitude of 0.75 V;. If R =2 Ω, L= 8.00E-03H , and C=9.90E-04 F, what is the impedance?

a) 9.675E+00 Ω
b) 1.064E+01 Ω
c) 1.171E+01 Ω
d) 1.288E+01 Ω
e) 1.416E+01 Ω

3) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.051 m2? The average power output of the Sun is 3.80E+26 W.

a) 4.555E-07 N/m2
b) 5.010E-07 N/m2
c) 5.511E-07 N/m2
d) 6.063E-07 N/m2
e) 6.669E-07 N/m2

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 ${\displaystyle a=}$ 0.571 m and ${\displaystyle B_{max}=\,}$ 0.331 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.321 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.226E+05 A
b) 3.549E+05 A
c) 3.904E+05 A
d) 4.294E+05 A
e) 4.724E+05 A
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 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

6) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.64 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.920E-05 T
b) 2.112E-05 T
c) 2.323E-05 T
d) 2.556E-05 T
e) 2.811E-05 T

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 7.67 mT and 4.260E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 5.554E+05 m/s
b) 6.110E+05 m/s
c) 6.720E+05 m/s
d) 7.393E+05 m/s
e) 8.132E+05 m/s

8) 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

9) 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

10) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.869 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.01)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.66 s. What is the current in the coil if the impedance of the coil is 32.8 Ω?

a) 9.191E-01 A
b) 1.011E+00 A
c) 1.112E+00 A
d) 1.223E+00 A
e) 1.346E+00 A

### T2(11-16) E0

1) 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

2) Two parallel wires each carry a 7.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.62 cm, 1.31 cm), while the other is located at (4.63 cm, 5.53 cm). What is the force per unit length between the wires?

a) 2.588E-10 N/m
b) 2.847E-10 N/m
c) 3.131E-10 N/m
d) 3.444E-10 N/m
e) 3.789E-10 N/m
3)
Three wires sit at the corners of a square of length 0.76 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 (1.91 A, 1.34 A, 1.05 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 5.611E-05 T
b) By= 6.172E-05 T
c) By= 6.789E-05 T
d) By= 7.468E-05 T
e) By= 8.215E-05 T

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.43 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.73)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.61 s. What is the current in the coil if the impedance of the coil is 4.89 Ω?

a) 1.134E+00 A
b) 1.248E+00 A
c) 1.373E+00 A
d) 1.510E+00 A
e) 1.661E+00 A

5) 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

6) 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
7)
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

8) The output of an ac generator connected to an RLC series combination has a frequency of 2.30E+04 Hz and an amplitude of 3 V. If R =5 Ω, L= 3.90E-03H , and C=9.00E-06 F, what is the rms power transferred to the resistor?

a) 2.339E-03 Watts
b) 2.573E-03 Watts
c) 2.830E-03 Watts
d) 3.113E-03 Watts
e) 3.424E-03 Watts

9) An ac generator produces an emf of amplitude 90 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a 20 mF inductor?

a) 5.008E+00 A
b) 5.509E+00 A
c) 6.060E+00 A
d) 6.666E+00 A
e) 7.333E+00 A
10)
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

#### T2(11-16) E1

1)
A long solenoid has a length 0.896 meters, radius 4.28 cm, and 550 turns. It surrounds coil of radius 6.65 meters and 9turns. If the current in the solenoid is changing at a rate of 204 A/s, what is the emf induced in the surounding coil?
a) 2.328E-02 V
b) 2.560E-02 V
c) 2.817E-02 V
d) 3.098E-02 V
e) 3.408E-02 V
2)
A parallel plate capacitor with a capicatnce C=9.60E-06 F whose plates have an area A=5.40E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 29 Ω resistor and a battery of voltage V0=50 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=8.30E-04?
a) 3.923E+01 V
b) 4.315E+01 V
c) 4.746E+01 V
d) 5.221E+01 V
e) 5.743E+01 V

3) 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

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) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.85 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.7mm}$, and ${\displaystyle n=2.76}$. What is the volume of the washer?

a) 1.038E+00 cm3
b) 1.142E+00 cm3
c) 1.256E+00 cm3
d) 1.381E+00 cm3
e) 1.520E+00 cm3
6)
Three wires sit at the corners of a square of length 0.703 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 (2.49 A, 1.32 A, 1.75 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 8.962E-05 T
b) By= 9.858E-05 T
c) By= 1.084E-04 T
d) By= 1.193E-04 T
e) By= 1.312E-04 T

7) 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

8) The output of an ac generator connected to an RLC series combination has a frequency of 6.10E+04 Hz and an amplitude of 9 V. If R =4 Ω, L= 3.40E-03H , and C=8.10E-06 F, what is the rms power transferred to the resistor?

a) 3.839E-03 Watts
b) 4.223E-03 Watts
c) 4.646E-03 Watts
d) 5.110E-03 Watts
e) 5.621E-03 Watts

9) 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

10) An ac generator produces an emf of amplitude 75 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 22 mF inductor?

a) 2.466E+00 A
b) 2.713E+00 A
c) 2.984E+00 A
d) 3.283E+00 A
e) 3.611E+00 A

#### T2(11-16) E2

1)
Three wires sit at the corners of a square of length 0.819 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 (2.01 A, 1.09 A, 1.56 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 4.688E-05 T
b) By= 5.156E-05 T
c) By= 5.672E-05 T
d) By= 6.239E-05 T
e) By= 6.863E-05 T

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.477 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.67)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$8.01 s. What is the current in the coil if the impedance of the coil is 75.6 Ω?

a) 2.215E-01 A
b) 2.437E-01 A
c) 2.681E-01 A
d) 2.949E-01 A
e) 3.244E-01 A

3) 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

4) 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

5) A circular current loop of radius 3.25 cm carries a current of 2.78 mA. What is the magnitude of the torque if the dipole is oriented at 55 ° to a uniform magnetic fied of 0.523 T?

a) 2.699E-06 N m
b) 2.969E-06 N m
c) 3.266E-06 N m
d) 3.593E-06 N m
e) 3.952E-06 N m
6)
A parallel plate capacitor with a capicatnce C=5.60E-06 F whose plates have an area A=3.50E+03 m2 and separation d=5.60E-03 m is connected via a swith to a 94 Ω resistor and a battery of voltage V0=21 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) 1.258E+01 V
b) 1.384E+01 V
c) 1.522E+01 V
d) 1.674E+01 V
e) 1.842E+01 V

7) 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
8)
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

9) A recangular coil with an area of 0.45 m2 and 18 turns is placed in a uniform magnetic field of 2.68 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 3.730E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 87 s?

a) 4.861E+04 V
b) 5.347E+04 V
c) 5.882E+04 V
d) 6.470E+04 V
e) 7.117E+04 V

10) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.18 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.42mm}$, and ${\displaystyle n=2.62}$. What is the volume of the washer?

a) 1.351E+00 cm3
b) 1.486E+00 cm3
c) 1.635E+00 cm3
d) 1.798E+00 cm3
e) 1.978E+00 cm3

### T2(11-16) F0

1)
The silver ribbon shown are a=3.32 cm, b=2.81 cm, and c= 0.996 cm. The current carries a current of 121 A and it lies in a uniform magnetic field of 1.23 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 1.080E-06 V
b) 1.188E-06 V
c) 1.306E-06 V
d) 1.437E-06 V
e) 1.581E-06 V

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.9 mm from the center of a wire of radius 4 mm if the current is 1A?

a) 1.784E-05 T
b) 1.963E-05 T
c) 2.159E-05 T
d) 2.375E-05 T
e) 2.613E-05 T

3) 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 ${\displaystyle a=}$ 0.549 m and ${\displaystyle B_{max}=\,}$ 0.599 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.29 m that is centered on the axis with its plane perpendicular to the axis?

a) 5.581E+05 A
b) 6.139E+05 A
c) 6.752E+05 A
d) 7.428E+05 A
e) 8.170E+05 A

4) 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

5) 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}=}$1.8 T and ${\displaystyle \omega =}$1.530E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.519 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) 7.422E+03 V
b) 8.164E+03 V
c) 8.981E+03 V
d) 9.879E+03 V
e) 1.087E+04 V

6) In an LC circuit, the self-inductance is 0.0116 H and the capacitance is 7.040E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.140E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.489E-04 s
b) 4.938E-04 s
c) 5.432E-04 s
d) 5.975E-04 s
e) 6.572E-04 s
7)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.47 s if ε = 7.04 V , R = 7.69 Ω, and L = 5.78 H?
a) 4.249E-01 V
b) 5.099E-01 V
c) 6.118E-01 V
d) 7.342E-01 V
e) 8.810E-01 V

8) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.83 V. The resistance, inductance, and capacitance are R =4 Ω, L= 4.60E-03H , and C=8.10E-04 F, respectively. What is the amplitude of the current?

a) 1.417E-01 A
b) 1.559E-01 A
c) 1.715E-01 A
d) 1.886E-01 A
e) 2.075E-01 A

9) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.21 Ω, L= 4.70E-03H , and C=3.70E-06 F, respectively.

a) Q = 1.476E+02
b) Q = 1.697E+02
c) Q = 1.952E+02
d) Q = 2.245E+02
e) Q = 2.581E+02
10)
A parallel plate capacitor with a capicatnce C=7.90E-06 F whose plates have an area A=6.10E+03 m2 and separation d=6.80E-03 m is connected via a swith to a 22 Ω resistor and a battery of voltage V0=6 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=5.20E-04?
a) 7.619E+02 V/m
b) 8.381E+02 V/m
c) 9.219E+02 V/m
d) 1.014E+03 V/m
e) 1.115E+03 V/m

#### T2(11-16) F1

1)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =6.45 s if ε = 7.01 V , R = 7.04 Ω, and L = 8.75 H?
a) 9.902E-01 V
b) 1.188E+00 V
c) 1.426E+00 V
d) 1.711E+00 V
e) 2.053E+00 V

2) In an LC circuit, the self-inductance is 0.0216 H and the capacitance is 6.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 1.240E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.846E-04 s
b) 5.330E-04 s
c) 5.863E-04 s
d) 6.449E-04 s
e) 7.094E-04 s
3)
The silver ribbon shown are a=4.81 cm, b=3.96 cm, and c= 1.3 cm. The current carries a current of 274 A and it lies in a uniform magnetic field of 3.23 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 7.202E-06 V
b) 7.922E-06 V
c) 8.714E-06 V
d) 9.586E-06 V
e) 1.054E-05 V
4)
A parallel plate capacitor with a capicatnce C=1.20E-06 F whose plates have an area A=1.00E+03 m2 and separation d=7.70E-03 m is connected via a swith to a 32 Ω resistor and a battery of voltage V0=38 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=1.40E-04?
a) 3.972E+03 V/m
b) 4.369E+03 V/m
c) 4.806E+03 V/m
d) 5.287E+03 V/m
e) 5.816E+03 V/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 ${\displaystyle a=}$ 0.549 m and ${\displaystyle B_{max}=\,}$ 0.599 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.29 m that is centered on the axis with its plane perpendicular to the axis?

a) 5.581E+05 A
b) 6.139E+05 A
c) 6.752E+05 A
d) 7.428E+05 A
e) 8.170E+05 A

6) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.43 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.944E-05 T
b) 2.138E-05 T
c) 2.352E-05 T
d) 2.587E-05 T
e) 2.846E-05 T

7) 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

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

a) 2.259E-01 A
b) 2.485E-01 A
c) 2.733E-01 A
d) 3.007E-01 A
e) 3.307E-01 A

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) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.17 Ω, L= 4.40E-03H , and C=3.40E-06 F, respectively.

a) Q = 1.391E+02
b) Q = 1.600E+02
c) Q = 1.840E+02
d) Q = 2.116E+02
e) Q = 2.434E+02

#### T2(11-16) F2

1) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=4 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 4.80E-03H , and C=2.60E-06 F, respectively.

a) Q = 1.300E+02
b) Q = 1.495E+02
c) Q = 1.719E+02
d) Q = 1.976E+02
e) Q = 2.273E+02

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.14 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 2.533E-05 T
b) 2.787E-05 T
c) 3.065E-05 T
d) 3.372E-05 T
e) 3.709E-05 T

3) 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
4)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =6.88 s if ε = 2.58 V , R = 5.69 Ω, and L = 6.94 H?
a) 4.518E-01 V
b) 5.422E-01 V
c) 6.506E-01 V
d) 7.807E-01 V
e) 9.369E-01 V

5) In an LC circuit, the self-inductance is 0.0689 H and the capacitance is 2.110E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.220E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.950E-04 s
b) 5.445E-04 s
c) 5.989E-04 s
d) 6.588E-04 s
e) 7.247E-04 s

6) A long solenoid has a radius of 0.716 m and 96 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 =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

a) 1.426E-03 V/m
b) 1.568E-03 V/m
c) 1.725E-03 V/m
d) 1.897E-03 V/m
e) 2.087E-03 V/m

7) 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}=}$3.84 T and ${\displaystyle \omega =}$4.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.379 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) 3.333E+04 V
b) 3.666E+04 V
c) 4.033E+04 V
d) 4.436E+04 V
e) 4.879E+04 V
8)
A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=980.0 m2 and separation d=6.20E-03 m is connected via a swith to a 8 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 magnitude of the electric field at time t=2.40E-05?
a) 5.154E+03 V/m
b) 5.669E+03 V/m
c) 6.236E+03 V/m
d) 6.860E+03 V/m
e) 7.545E+03 V/m
9)
The silver ribbon shown are a=3.52 cm, b=2.88 cm, and c= 0.515 cm. The current carries a current of 137 A and it lies in a uniform magnetic field of 2.02 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 5.685E-06 V
b) 6.253E-06 V
c) 6.878E-06 V
d) 7.566E-06 V
e) 8.323E-06 V

10) 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

### T2(11-16) G0

1) A long rigind wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.379 T magnetic field is directed 53° away from the wire?

a) 1.001E+00 N/m
b) 1.101E+00 N/m
c) 1.211E+00 N/m
d) 1.332E+00 N/m
e) 1.465E+00 N/m

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 359 mA, the net magnetic field is measured to be 1.32 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.124E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.237E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.360E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.497E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.646E+03
3)
Three wires sit at the corners of a square of length 0.705 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 (1.92 A, 1.14 A, 1.11 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 4.333E-05 T
b) Bx= 4.766E-05 T
c) Bx= 5.243E-05 T
d) Bx= 5.767E-05 T
e) Bx= 6.343E-05 T
4)
A cylinder of height 2.63 cm and radius 6.27 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 2.35 cm from point O and moves at a speed of 2.7 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) 4.057E+01 cm3/s
b) 4.463E+01 cm3/s
c) 4.909E+01 cm3/s
d) 5.400E+01 cm3/s
e) 5.940E+01 cm3/s

5) 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
6)
A long solenoid has a length 0.896 meters, radius 4.28 cm, and 550 turns. It surrounds coil of radius 6.65 meters and 9turns. If the current in the solenoid is changing at a rate of 204 A/s, what is the emf induced in the surounding coil?
a) 2.328E-02 V
b) 2.560E-02 V
c) 2.817E-02 V
d) 3.098E-02 V
e) 3.408E-02 V
7)
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

8) The output of an ac generator connected to an RLC series combination has a frequency of 720 Hz and an amplitude of 0.63 V;. If R =5 Ω, L= 4.20E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) A step-down transformer steps 18 kV down to 230 V. The high-voltage input is provided by a 250 Ω power line that carries 8 A of currentWhat is the output current (at the 230 V side ?)

a) 5.174E+02 A
b) 5.692E+02 A
c) 6.261E+02 A
d) 6.887E+02 A
e) 7.576E+02 A

10) 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

#### T2(11-16) G1

1)
Three wires sit at the corners of a square of length 0.75 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 (1.1 A, 1.11 A, 2.26 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 7.507E-05 T
b) Bx= 8.257E-05 T
c) Bx= 9.083E-05 T
d) Bx= 9.991E-05 T
e) Bx= 1.099E-04 T

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 23 turns per centimeter and the current applied to the solenoid is 534 mA, the net magnetic field is measured to be 1.48 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.917E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.708E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.579E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.054E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.159E+03
3)
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

4) The output of an ac generator connected to an RLC series combination has a frequency of 300 Hz and an amplitude of 0.76 V;. If R =5 Ω, L= 6.10E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

5) A step-down transformer steps 16 kV down to 210 V. The high-voltage input is provided by a 200 Ω power line that carries 7 A of currentWhat is the output current (at the 210 V side ?)

a) 4.007E+02 A
b) 4.408E+02 A
c) 4.848E+02 A
d) 5.333E+02 A
e) 5.867E+02 A

6) A long rigind wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.222 T magnetic field is directed 23° away from the wire?

a) 5.205E-01 N/m
b) 5.725E-01 N/m
c) 6.297E-01 N/m
d) 6.927E-01 N/m
e) 7.620E-01 N/m

7) 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
8)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =6.88 s if ε = 2.58 V , R = 5.69 Ω, and L = 6.94 H?
a) 4.518E-01 V
b) 5.422E-01 V
c) 6.506E-01 V
d) 7.807E-01 V
e) 9.369E-01 V

9) Calculate the motional emf induced along a 14.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.910E-05 Tesla magnetic field.

a) 3.688E+03 V
b) 4.057E+03 V
c) 4.463E+03 V
d) 4.909E+03 V
e) 5.400E+03 V
10)
A cylinder of height 2.25 cm and radius 6.77 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 3.27 cm from point O and moves at a speed of 4.07 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) 5.834E+01 cm3/s
b) 6.418E+01 cm3/s
c) 7.059E+01 cm3/s
d) 7.765E+01 cm3/s
e) 8.542E+01 cm3/s

#### T2(11-16) G2

1)
Three wires sit at the corners of a square of length 0.739 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 (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.397E-05 T
b) Bx= 7.037E-05 T
c) Bx= 7.740E-05 T
d) Bx= 8.514E-05 T
e) Bx= 9.366E-05 T

2) 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?

3) 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

4) A step-down transformer steps 18 kV down to 260 V. The high-voltage input is provided by a 290 Ω power line that carries 3 A of currentWhat is the output current (at the 260 V side ?)

a) 1.888E+02 A
b) 2.077E+02 A
c) 2.285E+02 A
d) 2.513E+02 A
e) 2.764E+02 A
5)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.47 s if ε = 7.04 V , R = 7.69 Ω, and L = 5.78 H?
a) 4.249E-01 V
b) 5.099E-01 V
c) 6.118E-01 V
d) 7.342E-01 V
e) 8.810E-01 V
6)
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
7)
A cylinder of height 2.94 cm and radius 5.05 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 2.37 cm from point O and moves at a speed of 7.29 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) 1.153E+02 cm3/s
b) 1.268E+02 cm3/s
c) 1.395E+02 cm3/s
d) 1.535E+02 cm3/s
e) 1.688E+02 cm3/s

8) 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

9) A long rigind wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.394 T magnetic field is directed 14° away from the wire?

a) 6.302E-01 N/m
b) 6.932E-01 N/m
c) 7.625E-01 N/m
d) 8.388E-01 N/m
e) 9.227E-01 N/m

10) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.036 m2? The average power output of the Sun is 3.80E+26 W.

a) 1.378E-05 N/m2
b) 1.516E-05 N/m2
c) 1.667E-05 N/m2
d) 1.834E-05 N/m2
e) 2.017E-05 N/m2

### T2(11-16) H0

1) A 42 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 0.48 T. What current is required to maintain this balance?

a) 2.812E-01 A
b) 3.093E-01 A
c) 3.403E-01 A
d) 3.743E-01 A
e) 4.117E-01 A
2)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.43 kA, I2=1.64 kA, and I3=4.81 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 2.721E-03 T-m
b) 2.993E-03 T-m
c) 3.292E-03 T-m
d) 3.621E-03 T-m
e) 3.984E-03 T-m

3) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.14 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 2.533E-05 T
b) 2.787E-05 T
c) 3.065E-05 T
d) 3.372E-05 T
e) 3.709E-05 T

4) The current through the windings of a solenoid with n= 2.210E+03 turns per meter is changing at a rate dI/dt=18 A/s. The solenoid is 65 cm long and has a cross-sectional diameter of 2.2 cm. A small coil consisting of N=36turns wraped in a circle of diameter 1.29 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 2.352E-04 V
b) 2.587E-04 V
c) 2.846E-04 V
d) 3.131E-04 V
e) 3.444E-04 V
5)
A cylinder of height 2.25 cm and radius 6.77 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 3.27 cm from point O and moves at a speed of 4.07 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) 5.834E+01 cm3/s
b) 6.418E+01 cm3/s
c) 7.059E+01 cm3/s
d) 7.765E+01 cm3/s
e) 8.542E+01 cm3/s
6)
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 2.78% of its maximum value if ε = 1.39 V , R = 2.88 Ω, and L = 4.06 H?
a) -2.296E+00 s
b) -2.525E+00 s
c) -2.778E+00 s
d) -3.056E+00 s
e) -3.361E+00 s
7)
A long solenoid has a length 0.759 meters, radius 4.51 cm, and 542 turns. It surrounds coil of radius 9.59 meters and 13turns. If the current in the solenoid is changing at a rate of 272 A/s, what is the emf induced in the surounding coil?
a) 5.791E-02 V
b) 6.370E-02 V
c) 7.007E-02 V
d) 7.708E-02 V
e) 8.478E-02 V

8) 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

9) The output of an ac generator connected to an RLC series combination has a frequency of 720 Hz and an amplitude of 0.63 V;. If R =5 Ω, L= 4.20E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

10) 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

#### T2(11-16) H1

1)
A cylinder of height 2.63 cm and radius 6.27 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 2.35 cm from point O and moves at a speed of 2.7 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) 4.057E+01 cm3/s
b) 4.463E+01 cm3/s
c) 4.909E+01 cm3/s
d) 5.400E+01 cm3/s
e) 5.940E+01 cm3/s

2) The output of an ac generator connected to an RLC series combination has a frequency of 6.10E+04 Hz and an amplitude of 8 V. If R =5 Ω, L= 9.10E-03H , and C=8.80E-06 F, what is the rms power transferred to the resistor?

a) 4.320E-04 Watts
b) 4.752E-04 Watts
c) 5.227E-04 Watts
d) 5.750E-04 Watts
e) 6.325E-04 Watts

3) 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

4) The current through the windings of a solenoid with n= 2.500E+03 turns per meter is changing at a rate dI/dt=4 A/s. The solenoid is 96 cm long and has a cross-sectional diameter of 2.39 cm. A small coil consisting of N=22turns wraped in a circle of diameter 1.44 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 3.721E-05 V
b) 4.093E-05 V
c) 4.502E-05 V
d) 4.953E-05 V
e) 5.448E-05 V

5) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.075 m2? The average power output of the Sun is 3.80E+26 W.

a) 5.002E-08 N
b) 5.502E-08 N
c) 6.052E-08 N
d) 6.657E-08 N
e) 7.323E-08 N

6) 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?

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 2.28% of its maximum value if ε = 7.39 V , R = 7.05 Ω, and L = 3.51 H?
a) -6.429E-01 s
b) -7.072E-01 s
c) -7.779E-01 s
d) -8.557E-01 s
e) -9.412E-01 s
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=2.43 kA, I2=1.64 kA, and I3=4.81 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 2.721E-03 T-m
b) 2.993E-03 T-m
c) 3.292E-03 T-m
d) 3.621E-03 T-m
e) 3.984E-03 T-m

9) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 3.33 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 2.202E-05 T
b) 2.422E-05 T
c) 2.664E-05 T
d) 2.930E-05 T
e) 3.223E-05 T
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

#### T2(11-16) H2

1)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.28% of its maximum value if ε = 7.39 V , R = 7.05 Ω, and L = 3.51 H?
a) -6.429E-01 s
b) -7.072E-01 s
c) -7.779E-01 s
d) -8.557E-01 s
e) -9.412E-01 s
2)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 1.250E-03 T-m
b) 1.375E-03 T-m
c) 1.512E-03 T-m
d) 1.663E-03 T-m
e) 1.830E-03 T-m

3) 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

4) The output of an ac generator connected to an RLC series combination has a frequency of 300 Hz and an amplitude of 0.76 V;. If R =5 Ω, L= 6.10E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

5)
A cylinder of height 2.12 cm and radius 2.28 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.52 cm from point O and moves at a speed of 8.21 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 2.976E+01 cm3/s
b) 3.274E+01 cm3/s
c) 3.601E+01 cm3/s
d) 3.961E+01 cm3/s
e) 4.358E+01 cm3/s

6) The output of an ac generator connected to an RLC series combination has a frequency of 1.90E+04 Hz and an amplitude of 3 V. If R =8 Ω, L= 9.70E-03H , and C=9.70E-06 F, what is the rms power transferred to the resistor?

a) 7.670E-04 Watts
b) 8.436E-04 Watts
c) 9.280E-04 Watts
d) 1.021E-03 Watts
e) 1.123E-03 Watts

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

a) 6.985E-05 V
b) 7.683E-05 V
c) 8.452E-05 V
d) 9.297E-05 V
e) 1.023E-04 V
8)
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

9) A 72 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 14 g, and the magnitude of the magnetic field is 0.54 T. What current is required to maintain this balance?

a) 2.651E-01 A
b) 2.916E-01 A
c) 3.208E-01 A
d) 3.529E-01 A
e) 3.882E-01 A

10) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.81 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 3.324E-05 T
b) 3.657E-05 T
c) 4.022E-05 T
d) 4.424E-05 T
e) 4.867E-05 T

### T2(11-16) I0

1) A charged particle in a magnetic field of 2.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.120E+05 m/s. What is the period of orbit if orbital radius is 0.385 m?

a) 1.141E-05 s
b) 1.255E-05 s
c) 1.381E-05 s
d) 1.519E-05 s
e) 1.671E-05 s

2) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

a) 1.285E+00 Tesla
b) 1.413E+00 Tesla
c) 1.554E+00 Tesla
d) 1.710E+00 Tesla
e) 1.881E+00 Tesla
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=2.5 kA, I2=1.53 kA, and I3=2.34 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 1.018E-03 T-m
b) 1.120E-03 T-m
c) 1.232E-03 T-m
d) 1.355E-03 T-m
e) 1.490E-03 T-m

4) The current through the windings of a solenoid with n= 1.830E+03 turns per meter is changing at a rate dI/dt=14 A/s. The solenoid is 87 cm long and has a cross-sectional diameter of 2.5 cm. A small coil consisting of N=30turns wraped in a circle of diameter 1.34 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.126E-04 V
b) 1.238E-04 V
c) 1.362E-04 V
d) 1.498E-04 V
e) 1.648E-04 V
5)
A cylinder of height 2.94 cm and radius 5.05 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 2.37 cm from point O and moves at a speed of 7.29 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) 1.153E+02 cm3/s
b) 1.268E+02 cm3/s
c) 1.395E+02 cm3/s
d) 1.535E+02 cm3/s
e) 1.688E+02 cm3/s

6) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.92mm}$, and ${\displaystyle n=2.68}$. What is the volume of the washer?

a) 1.118E+00 cm3
b) 1.229E+00 cm3
c) 1.352E+00 cm3
d) 1.487E+00 cm3
e) 1.636E+00 cm3
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 2.78% of its maximum value if ε = 1.39 V , R = 2.88 Ω, and L = 4.06 H?
a) -2.296E+00 s
b) -2.525E+00 s
c) -2.778E+00 s
d) -3.056E+00 s
e) -3.361E+00 s

8) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.83 V. The resistance, inductance, and capacitance are R =4 Ω, L= 4.60E-03H , and C=8.10E-04 F, respectively. What is the amplitude of the current?

a) 1.417E-01 A
b) 1.559E-01 A
c) 1.715E-01 A
d) 1.886E-01 A
e) 2.075E-01 A

9) An ac generator produces an emf of amplitude 24 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 96 mF inductor?

a) 3.014E-01 A
b) 3.316E-01 A
c) 3.647E-01 A
d) 4.012E-01 A
e) 4.413E-01 A
10)
A parallel plate capacitor with a capicatnce C=5.50E-06 F whose plates have an area A=3.00E+03 m2 and separation d=4.90E-03 m is connected via a swith to a 55 Ω resistor and a battery of voltage V0=37 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=9.00E-04?
a) 2.580E-02 A
b) 2.838E-02 A
c) 3.121E-02 A
d) 3.433E-02 A
e) 3.777E-02 A

#### T2(11-16) I1

1)
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=2.4 kA, I2=2.64 kA, and I3=3.96 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 1.133E-03 T-m
b) 1.246E-03 T-m
c) 1.371E-03 T-m
d) 1.508E-03 T-m
e) 1.659E-03 T-m
2)
A cylinder of height 3.5 cm and radius 5.36 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 2.79 cm from point O and moves at a speed of 3.24 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) 5.308E+01 cm3/s
b) 5.839E+01 cm3/s
c) 6.422E+01 cm3/s
d) 7.065E+01 cm3/s
e) 7.771E+01 cm3/s

3) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.12 V. The resistance, inductance, and capacitance are R =3 Ω, L= 8.80E-03H , and C=6.40E-04 F, respectively. What is the amplitude of the current?

a) 2.732E-02 A
b) 3.005E-02 A
c) 3.306E-02 A
d) 3.636E-02 A
e) 4.000E-02 A
4)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.44% 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

5) An ac generator produces an emf of amplitude 46 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 63 mF inductor?

a) 4.961E-01 A
b) 5.457E-01 A
c) 6.002E-01 A
d) 6.603E-01 A
e) 7.263E-01 A

6) A washer has an inner diameter of 2.74 cm and an outer diamter of 4.71 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.9mm}$, and ${\displaystyle n=2.85}$. What is the volume of the washer?

a) 8.141E-01 cm3
b) 8.955E-01 cm3
c) 9.850E-01 cm3
d) 1.084E+00 cm3
e) 1.192E+00 cm3

7) The current through the windings of a solenoid with n= 2.980E+03 turns per meter is changing at a rate dI/dt=9 A/s. The solenoid is 88 cm long and has a cross-sectional diameter of 2.69 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.64 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.498E-04 V
b) 1.647E-04 V
c) 1.812E-04 V
d) 1.993E-04 V
e) 2.193E-04 V

8) A wire carries a current of 106 A in a circular arc with radius 1.32 cm swept through 38 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

a) 1.589E+00 Tesla
b) 1.748E+00 Tesla
c) 1.923E+00 Tesla
d) 2.116E+00 Tesla
e) 2.327E+00 Tesla
9)
A parallel plate capacitor with a capicatnce C=6.90E-06 F whose plates have an area A=5.80E+03 m2 and separation d=7.40E-03 m is connected via a swith to a 26 Ω resistor and a battery of voltage V0=9 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=4.70E-04?
a) 1.894E-02 A
b) 2.083E-02 A
c) 2.291E-02 A
d) 2.520E-02 A
e) 2.773E-02 A

10) A charged particle in a magnetic field of 3.820E-04 T is moving perpendicular to the magnetic field with a speed of 3.890E+05 m/s. What is the period of orbit if orbital radius is 0.718 m?

a) 8.713E-06 s
b) 9.584E-06 s
c) 1.054E-05 s
d) 1.160E-05 s
e) 1.276E-05 s

#### T2(11-16) I2

1)
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

2) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.3 V. The resistance, inductance, and capacitance are R =2 Ω, L= 8.10E-03H , and C=9.40E-04 F, respectively. What is the amplitude of the current?

a) 1.364E-01 A
b) 1.500E-01 A
c) 1.650E-01 A
d) 1.815E-01 A
e) 1.997E-01 A

3) 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

4) The current through the windings of a solenoid with n= 2.980E+03 turns per meter is changing at a rate dI/dt=9 A/s. The solenoid is 88 cm long and has a cross-sectional diameter of 2.69 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.64 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.498E-04 V
b) 1.647E-04 V
c) 1.812E-04 V
d) 1.993E-04 V
e) 2.193E-04 V
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=2.45 kA, I2=2.68 kA, and I3=5.5 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 3.544E-03 T-m
b) 3.898E-03 T-m
c) 4.288E-03 T-m
d) 4.717E-03 T-m
e) 5.188E-03 T-m

6) 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
7)
A parallel plate capacitor with a capicatnce C=3.20E-06 F whose plates have an area A=2.80E+03 m2 and separation d=7.80E-03 m is connected via a swith to a 17 Ω resistor and a battery of voltage V0=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.20E-04?
a) 8.809E-02 A
b) 9.690E-02 A
c) 1.066E-01 A
d) 1.173E-01 A
e) 1.290E-01 A
8)
A cylinder of height 2.91 cm and radius 8.33 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.7 cm from point O and moves at a speed of 9.14 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 2.061E+02 cm3/s
b) 2.267E+02 cm3/s
c) 2.494E+02 cm3/s
d) 2.743E+02 cm3/s
e) 3.018E+02 cm3/s

9) A charged particle in a magnetic field of 3.410E-04 T is moving perpendicular to the magnetic field with a speed of 5.010E+05 m/s. What is the period of orbit if orbital radius is 0.508 m?

a) 5.792E-06 s
b) 6.371E-06 s
c) 7.008E-06 s
d) 7.709E-06 s
e) 8.480E-06 s

10) A wire carries a current of 353 A in a circular arc with radius 2.44 cm swept through 86 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

a) 5.891E+00 Tesla
b) 6.481E+00 Tesla
c) 7.129E+00 Tesla
d) 7.841E+00 Tesla
e) 8.626E+00 Tesla

### T2(11-16) J0

1) A charged particle in a magnetic field of 3.410E-04 T is moving perpendicular to the magnetic field with a speed of 5.010E+05 m/s. What is the period of orbit if orbital radius is 0.508 m?

a) 5.792E-06 s
b) 6.371E-06 s
c) 7.008E-06 s
d) 7.709E-06 s
e) 8.480E-06 s
2)
Three wires sit at the corners of a square of length 0.533 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 (2.17 A, 2.25 A, 2.22 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 1.037E-04 T
b) Bx= 1.141E-04 T
c) Bx= 1.255E-04 T
d) Bx= 1.381E-04 T
e) Bx= 1.519E-04 T
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=2.43 kA, I2=1.81 kA, and I3=3.23 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 1.622E-03 T-m
b) 1.784E-03 T-m
c) 1.963E-03 T-m
d) 2.159E-03 T-m
e) 2.375E-03 T-m

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

a) 7.007E-02 A
b) 7.708E-02 A
c) 8.479E-02 A
d) 9.327E-02 A
e) 1.026E-01 A

5) 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

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

a) 7.499E-01 cm3
b) 8.249E-01 cm3
c) 9.074E-01 cm3
d) 9.982E-01 cm3
e) 1.098E+00 cm3
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 2.63% of its maximum value if ε = 8.7 V , R = 8.35 Ω, and L = 1.44 H?
a) -3.137E-01 s
b) -3.451E-01 s
c) -3.796E-01 s
d) -4.176E-01 s
e) -4.593E-01 s

8) An ac generator produces an emf of amplitude 49 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

a) 8.956E-01 A
b) 9.852E-01 A
c) 1.084E+00 A
d) 1.192E+00 A
e) 1.311E+00 A

9) The output of an ac generator connected to an RLC series combination has a frequency of 360 Hz and an amplitude of 0.17 V;. If R =9 Ω, L= 2.60E-03H , and C=8.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

10) What is the radiation force on an object that is 7.40E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.

a) 2.063E-08 N
b) 2.270E-08 N
c) 2.497E-08 N
d) 2.746E-08 N
e) 3.021E-08 N

#### T2(11-16) J1

1) 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
2)
Three wires sit at the corners of a square of length 0.78 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 (2.13 A, 1.35 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.282E-05 T
b) Bx= 6.910E-05 T
c) Bx= 7.601E-05 T
d) Bx= 8.361E-05 T
e) Bx= 9.198E-05 T

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

a) 7.499E-01 cm3
b) 8.249E-01 cm3
c) 9.074E-01 cm3
d) 9.982E-01 cm3
e) 1.098E+00 cm3
4)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.59% of its maximum value if ε = 1.14 V , R = 6.17 Ω, and L = 5.45 H?
a) -1.614E+00 s
b) -1.775E+00 s
c) -1.952E+00 s
d) -2.148E+00 s
e) -2.362E+00 s
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=2.44 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

6) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.59)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.58 s. What is the current in the coil if the impedance of the coil is 13.3 Ω?

a) 4.141E-01 A
b) 4.555E-01 A
c) 5.011E-01 A
d) 5.512E-01 A
e) 6.063E-01 A

7) 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

8) A charged particle in a magnetic field of 2.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.120E+05 m/s. What is the period of orbit if orbital radius is 0.385 m?

a) 1.141E-05 s
b) 1.255E-05 s
c) 1.381E-05 s
d) 1.519E-05 s
e) 1.671E-05 s

9) 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?

10) 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

#### T2(11-16) J2

1) A washer has an inner diameter of 2.6 cm and an outer diamter of 4.17 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.38mm}$, and ${\displaystyle n=2.62}$. What is the volume of the washer?

a) 7.196E-01 cm3
b) 7.916E-01 cm3
c) 8.707E-01 cm3
d) 9.578E-01 cm3
e) 1.054E+00 cm3
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 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

3) 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
4)
Three wires sit at the corners of a square of length 0.51 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 (1.16 A, 2.46 A, 2.15 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 9.053E-05 T
b) Bx= 9.959E-05 T
c) Bx= 1.095E-04 T
d) Bx= 1.205E-04 T
e) Bx= 1.325E-04 T

5) 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

6) The output of an ac generator connected to an RLC series combination has a frequency of 300 Hz and an amplitude of 0.76 V;. If R =5 Ω, L= 6.10E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

7) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.798 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (3.7)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$4.63 s. What is the current in the coil if the impedance of the coil is 75.7 Ω?

a) 2.651E-01 A
b) 2.917E-01 A
c) 3.208E-01 A
d) 3.529E-01 A
e) 3.882E-01 A

8) A charged particle in a magnetic field of 4.910E-04 T is moving perpendicular to the magnetic field with a speed of 3.000E+05 m/s. What is the period of orbit if orbital radius is 0.507 m?

a) 1.062E-05 s
b) 1.168E-05 s
c) 1.285E-05 s
d) 1.413E-05 s
e) 1.555E-05 s

9) 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
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=2.4 kA, I2=2.64 kA, and I3=3.96 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 1.133E-03 T-m
b) 1.246E-03 T-m
c) 1.371E-03 T-m
d) 1.508E-03 T-m
e) 1.659E-03 T-m

### T2(11-16) K0

1) A cyclotron used to accelerate alpha particlesm=6.64 x 10−27kg, q=3.2 x 10−19C) has a radius of 0.448 m and a magneticfield of 0.812 T. What is their maximum kinetic energy?

a) 5.798E+00 MeV
b) 6.377E+00 MeV
c) 7.015E+00 MeV
d) 7.717E+00 MeV
e) 8.488E+00 MeV

2) A wire carries a current of 353 A in a circular arc with radius 2.44 cm swept through 86 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

a) 5.891E+00 Tesla
b) 6.481E+00 Tesla
c) 7.129E+00 Tesla
d) 7.841E+00 Tesla
e) 8.626E+00 Tesla

3) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.14 mm from the center of a wire of radius 3 mm if the current is 1A?

a) 2.533E-05 T
b) 2.787E-05 T
c) 3.065E-05 T
d) 3.372E-05 T
e) 3.709E-05 T

4) Calculate the motional emf induced along a 42.1 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 4.730E-05 Tesla magnetic field.

a) 1.279E+04 V
b) 1.407E+04 V
c) 1.547E+04 V
d) 1.702E+04 V
e) 1.872E+04 V

5) 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

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) 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

8) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.29 Ω, L= 4.80E-03H , and C=2.60E-06 F, respectively.

a) Q = 1.288E+02
b) Q = 1.482E+02
c) Q = 1.704E+02
d) Q = 1.959E+02
e) Q = 2.253E+02

9) A step-down transformer steps 15 kV down to 240 V. The high-voltage input is provided by a 200 Ω power line that carries 4 A of currentWhat is the output current (at the 240 V side ?)

a) 1.708E+02 A
b) 1.878E+02 A
c) 2.066E+02 A
d) 2.273E+02 A
e) 2.500E+02 A

10) What is the radiation pressure on an object that is 1.20E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.

a) 9.568E-06 N/m2
b) 1.053E-05 N/m2
c) 1.158E-05 N/m2
d) 1.274E-05 N/m2
e) 1.401E-05 N/m2

#### T2(11-16) K1

1) A wire carries a current of 343 A in a circular arc with radius 2.95 cm swept through 38 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

a) 1.902E+00 Tesla
b) 2.092E+00 Tesla
c) 2.301E+00 Tesla
d) 2.532E+00 Tesla
e) 2.785E+00 Tesla

2) 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

3) A cyclotron used to accelerate alpha particlesm=6.64 x 10−27kg, q=3.2 x 10−19C) has a radius of 0.355 m and a magneticfield of 1.28 T. What is their maximum kinetic energy?

a) 7.476E+00 MeV
b) 8.224E+00 MeV
c) 9.046E+00 MeV
d) 9.951E+00 MeV
e) 1.095E+01 MeV

4) Calculate the motional emf induced along a 50.7 km conductor moving at an orbital speed of 7.88 km/s perpendicular to Earth's 4.930E-05 Tesla magnetic field.

a) 1.791E+04 V
b) 1.970E+04 V
c) 2.167E+04 V
d) 2.383E+04 V
e) 2.622E+04 V

5) An induced emf of 3.78V is measured across a coil of 99 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.36A in 0.821s. What is the self-inductance of the coil?

a) 4.033E-01 H
b) 4.436E-01 H
c) 4.880E-01 H
d) 5.367E-01 H
e) 5.904E-01 H

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.29 Ω, L= 4.80E-03H , and C=2.60E-06 F, respectively.

a) Q = 1.288E+02
b) Q = 1.482E+02
c) Q = 1.704E+02
d) Q = 1.959E+02
e) Q = 2.253E+02

7) 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

8) A step-down transformer steps 12 kV down to 170 V. The high-voltage input is provided by a 140 Ω power line that carries 9 A of currentWhat is the output current (at the 170 V side ?)

a) 4.773E+02 A
b) 5.250E+02 A
c) 5.775E+02 A
d) 6.353E+02 A
e) 6.988E+02 A

9) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.9 mm from the center of a wire of radius 4 mm if the current is 1A?

a) 1.784E-05 T
b) 1.963E-05 T
c) 2.159E-05 T
d) 2.375E-05 T
e) 2.613E-05 T

10) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.036 m2? The average power output of the Sun is 3.80E+26 W.

a) 1.378E-05 N/m2
b) 1.516E-05 N/m2
c) 1.667E-05 N/m2
d) 1.834E-05 N/m2
e) 2.017E-05 N/m2

#### T2(11-16) K2

1) What is the radiation pressure on an object that is 6.90E+11 m away from the sun and has cross-sectional area of 0.041 m2? The average power output of the Sun is 3.80E+26 W.

a) 3.502E-07 N/m2
b) 3.852E-07 N/m2
c) 4.237E-07 N/m2
d) 4.661E-07 N/m2
e) 5.127E-07 N/m2

2) A cyclotron used to accelerate alpha particlesm=6.64 x 10−27kg, q=3.2 x 10−19C) has a radius of 0.419 m and a magneticfield of 1.45 T. What is their maximum kinetic energy?

a) 1.336E+01 MeV
b) 1.470E+01 MeV
c) 1.617E+01 MeV
d) 1.779E+01 MeV
e) 1.957E+01 MeV

3) 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

4) A wire carries a current of 385 A in a circular arc with radius 1.53 cm swept through 58 degrees. Assuming that the rest of the current is 100% shielded by mu-metal, what is the magnetic field at the center of the arc?

a) 5.711E+00 Tesla
b) 6.283E+00 Tesla
c) 6.911E+00 Tesla
d) 7.602E+00 Tesla
e) 8.362E+00 Tesla

5) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.43 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.944E-05 T
b) 2.138E-05 T
c) 2.352E-05 T
d) 2.587E-05 T
e) 2.846E-05 T

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=2 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 5.40E-03H , and C=3.20E-06 F, respectively.

a) Q = 9.395E+01
b) Q = 1.080E+02
c) Q = 1.242E+02
d) Q = 1.429E+02
e) Q = 1.643E+02

7) 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

8) 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

9) 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

10) Calculate the motional emf induced along a 21.3 km conductor moving at an orbital speed of 7.75 km/s perpendicular to Earth's 5.320E-05 Tesla magnetic field.

a) 6.598E+03 V
b) 7.258E+03 V
c) 7.984E+03 V
d) 8.782E+03 V
e) 9.660E+03 V

### T2(11-16) L0

1) 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

2) Two loops of wire carry the same current of 14 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.835 m while the other has a radius of 1.29 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 0.607 m from the first (smaller) loopif the disance between the loops is 1.61 m?

a) 6.099E-03 T
b) 6.709E-03 T
c) 7.380E-03 T
d) 8.118E-03 T
e) 8.930E-03 T

3) 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 ${\displaystyle a=}$ 0.645 m and ${\displaystyle B_{max}=\,}$ 0.469 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.26 m that is centered on the axis with its plane perpendicular to the axis?

a) 2.949E+05 A
b) 3.244E+05 A
c) 3.568E+05 A
d) 3.925E+05 A
e) 4.317E+05 A

4) A long solenoid has a radius of 0.442 m and 41 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$4 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 0.2 m from the axis at time t=0.0833 s ?

a) 6.438E-05 V/m
b) 7.082E-05 V/m
c) 7.790E-05 V/m
d) 8.569E-05 V/m
e) 9.426E-05 V/m

5) A long solenoid has a radius of 0.716 m and 96 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 =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

a) 1.426E-03 V/m
b) 1.568E-03 V/m
c) 1.725E-03 V/m
d) 1.897E-03 V/m
e) 2.087E-03 V/m

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

a) 4.535E-01 H
b) 4.988E-01 H
c) 5.487E-01 H
d) 6.035E-01 H
e) 6.639E-01 H
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 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

8) The output of an ac generator connected to an RLC series combination has a frequency of 720 Hz and an amplitude of 0.63 V;. If R =5 Ω, L= 4.20E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) 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

10) 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

#### T2(11-16) L1

1) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.075 m2? The average power output of the Sun is 3.80E+26 W.

a) 5.002E-08 N
b) 5.502E-08 N
c) 6.052E-08 N
d) 6.657E-08 N
e) 7.323E-08 N

2) The output of an ac generator connected to an RLC series combination has a frequency of 860 Hz and an amplitude of 0.59 V;. If R =9 Ω, L= 8.40E-03H , and C=8.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

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

a) 1.386E-13 N
b) 1.524E-13 N
c) 1.676E-13 N
d) 1.844E-13 N
e) 2.029E-13 N

4) Two loops of wire carry the same current of 20 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.776 m while the other has a radius of 1.2 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 0.517 m from the first (smaller) loopif the disance between the loops is 1.37 m?

a) 1.127E-02 T
b) 1.240E-02 T
c) 1.364E-02 T
d) 1.500E-02 T
e) 1.650E-02 T

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 ${\displaystyle a=}$ 0.852 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

6) An ac generator produces an emf of amplitude 58 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 66 mF capacitor?

a) 3.976E+00 A
b) 4.373E+00 A
c) 4.810E+00 A
d) 5.291E+00 A
e) 5.821E+00 A

7) An induced emf of 1.7V is measured across a coil of 81 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.07A in 0.174s. What is the self-inductance of the coil?

a) 3.458E-02 H
b) 3.804E-02 H
c) 4.184E-02 H
d) 4.602E-02 H
e) 5.062E-02 H

8) A long solenoid has a radius of 0.732 m and 55 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 0.203 m from the axis at time t=0.0448 s ?

a) 5.150E-04 V/m
b) 5.665E-04 V/m
c) 6.232E-04 V/m
d) 6.855E-04 V/m
e) 7.540E-04 V/m
9)
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 2.23% of its maximum value if ε = 3.13 V , R = 3.59 Ω, and L = 3.38 H?
a) -1.345E+00 s
b) -1.480E+00 s
c) -1.628E+00 s
d) -1.790E+00 s
e) -1.969E+00 s

10) 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

#### T2(11-16) L2

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 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)
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 2.63% of its maximum value if ε = 8.7 V , R = 8.35 Ω, and L = 1.44 H?
a) -3.137E-01 s
b) -3.451E-01 s
c) -3.796E-01 s
d) -4.176E-01 s
e) -4.593E-01 s

4) An alpha-particle (q=3.2x10−19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.23 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

5) Two loops of wire carry the same current of 43 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.516 m while the other has a radius of 1.22 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 0.565 m from the first (smaller) loopif the disance between the loops is 1.78 m?

a) 1.798E-02 T
b) 1.978E-02 T
c) 2.176E-02 T
d) 2.394E-02 T
e) 2.633E-02 T

6) 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 ${\displaystyle a=}$ 0.432 m and ${\displaystyle B_{max}=\,}$ 0.402 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.275 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.277E+05 A
b) 3.604E+05 A
c) 3.965E+05 A
d) 4.361E+05 A
e) 4.797E+05 A

7) What is the radiation force on an object that is 6.70E+11 m away from the sun and has cross-sectional area of 0.095 m2? The average power output of the Sun is 3.80E+26 W.

a) 3.528E-08 N
b) 3.881E-08 N
c) 4.269E-08 N
d) 4.696E-08 N
e) 5.166E-08 N

8) 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?

9) 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

10) 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

### T2(11-16) M0

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

a) 5.554E+05 m/s
b) 6.110E+05 m/s
c) 6.720E+05 m/s
d) 7.393E+05 m/s
e) 8.132E+05 m/s
2)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ 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
3)
Three wires sit at the corners of a square of length 0.784 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 (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 7.487E-05 T
b) Bx= 8.236E-05 T
c) Bx= 9.060E-05 T
d) Bx= 9.966E-05 T
e) Bx= 1.096E-04 T

4) A long solenoid has a radius of 0.583 m and 38 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 =}$24 s−1.What is the induced electric fied at a distance 2.09 m from the axis at time t=0.0388 s ?

a) 1.655E-04 V/m
b) 1.821E-04 V/m
c) 2.003E-04 V/m
d) 2.203E-04 V/m
e) 2.424E-04 V/m

5) The current through the windings of a solenoid with n= 1.850E+03 turns per meter is changing at a rate dI/dt=17 A/s. The solenoid is 98 cm long and has a cross-sectional diameter of 3.38 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.72 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.587E-04 V
b) 1.745E-04 V
c) 1.920E-04 V
d) 2.112E-04 V
e) 2.323E-04 V

6) In an LC circuit, the self-inductance is 0.0156 H and the capacitance is 6.950E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 4.830E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.886E-04 s
b) 4.275E-04 s
c) 4.702E-04 s
d) 5.172E-04 s
e) 5.689E-04 s
7)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =6.45 s if ε = 7.01 V , R = 7.04 Ω, and L = 8.75 H?
a) 9.902E-01 V
b) 1.188E+00 V
c) 1.426E+00 V
d) 1.711E+00 V
e) 2.053E+00 V

8) The output of an ac generator connected to an RLC series combination has a frequency of 750 Hz and an amplitude of 0.88 V;. If R =4 Ω, L= 5.60E-03H , and C=9.70E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) The output of an ac generator connected to an RLC series combination has a frequency of 5.70E+04 Hz and an amplitude of 5 V. If R =9 Ω, L= 6.10E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

a) 9.443E-04 Watts
b) 1.039E-03 Watts
c) 1.143E-03 Watts
d) 1.257E-03 Watts
e) 1.383E-03 Watts

10) 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

#### T2(11-16) M1

1)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =3.96 s if ε = 4.92 V , R = 5.02 Ω, and L = 5.0 H?
a) 9.618E-01 V
b) 1.154E+00 V
c) 1.385E+00 V
d) 1.662E+00 V
e) 1.994E+00 V

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

a) 2.204E-04 V
b) 2.425E-04 V
c) 2.667E-04 V
d) 2.934E-04 V
e) 3.227E-04 V

3) What is the radiation force on an object that is 4.70E+11 m away from the sun and has cross-sectional area of 0.015 m2? The average power output of the Sun is 3.80E+26 W.

a) 1.029E-08 N
b) 1.132E-08 N
c) 1.245E-08 N
d) 1.370E-08 N
e) 1.507E-08 N
4)
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=2.85 kA, I2=1.8 kA, and I3=4.89 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 3.530E-03 T-m
b) 3.883E-03 T-m
c) 4.271E-03 T-m
d) 4.698E-03 T-m
e) 5.168E-03 T-m

5) 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

6) An electron beam (m=9.1 x 10−31kg, q=1.6 x 10−19C) enters a crossed-field velocity selector with magnetic and electric fields of 6.97 mT and 2.240E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 2.656E+05 m/s
b) 2.922E+05 m/s
c) 3.214E+05 m/s
d) 3.535E+05 m/s
e) 3.889E+05 m/s

7) 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?

8)
Three wires sit at the corners of a square of length 0.78 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 (2.13 A, 1.35 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 6.282E-05 T
b) Bx= 6.910E-05 T
c) Bx= 7.601E-05 T
d) Bx= 8.361E-05 T
e) Bx= 9.198E-05 T

9) In an LC circuit, the self-inductance is 0.0116 H and the capacitance is 7.040E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.140E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.489E-04 s
b) 4.938E-04 s
c) 5.432E-04 s
d) 5.975E-04 s
e) 6.572E-04 s

10) The output of an ac generator connected to an RLC series combination has a frequency of 2.30E+04 Hz and an amplitude of 7 V. If R =3 Ω, L= 4.10E-03H , and C=8.70E-06 F, what is the rms power transferred to the resistor?

a) 8.369E-03 Watts
b) 9.206E-03 Watts
c) 1.013E-02 Watts
d) 1.114E-02 Watts
e) 1.225E-02 Watts

#### T2(11-16) M2

1) 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

2) 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
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=2.51 kA, I2=2.33 kA, and I3=5.35 kA, take the ${\displaystyle \beta }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 3.795E-03 T-m
b) 4.175E-03 T-m
c) 4.592E-03 T-m
d) 5.051E-03 T-m
e) 5.556E-03 T-m
4)
Three wires sit at the corners of a square of length 0.533 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 (2.17 A, 2.25 A, 2.22 A), respectively. What is the x-component of the magnetic field at point P?
a) Bx= 1.037E-04 T
b) Bx= 1.141E-04 T
c) Bx= 1.255E-04 T
d) Bx= 1.381E-04 T
e) Bx= 1.519E-04 T

5) 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 5.04 mT and 7.820E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 1.060E+06 m/s
b) 1.166E+06 m/s
c) 1.282E+06 m/s
d) 1.411E+06 m/s
e) 1.552E+06 m/s

6) The output of an ac generator connected to an RLC series combination has a frequency of 970 Hz and an amplitude of 0.11 V;. If R =9 Ω, L= 8.50E-03H , and C=7.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

7) The current through the windings of a solenoid with n= 1.820E+03 turns per meter is changing at a rate dI/dt=7 A/s. The solenoid is 78 cm long and has a cross-sectional diameter of 3.26 cm. A small coil consisting of N=35turns wraped in a circle of diameter 1.68 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.242E-04 V
b) 1.366E-04 V
c) 1.503E-04 V
d) 1.653E-04 V
e) 1.819E-04 V
8)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =3.8 s if ε = 3.36 V , R = 5.2 Ω, and L = 3.37 H?
a) 5.369E-01 V
b) 6.443E-01 V
c) 7.732E-01 V
d) 9.278E-01 V
e) 1.113E+00 V

9) What is the radiation force on an object that is 6.70E+11 m away from the sun and has cross-sectional area of 0.095 m2? The average power output of the Sun is 3.80E+26 W.

a) 3.528E-08 N
b) 3.881E-08 N
c) 4.269E-08 N
d) 4.696E-08 N
e) 5.166E-08 N

10) 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

### T2(11-16) N0

1) An alpha-particle (q=3.2x10−19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 1.21 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(2.75 i + 9.06 j  + 3.5 k) x 104 m/s?

a) 2.899E-14 N
b) 3.189E-14 N
c) 3.508E-14 N
d) 3.859E-14 N
e) 4.245E-14 N
2)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.35 kA, I2=0.809 kA, and I3=2.34 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 4.031E-03 T-m
b) 4.434E-03 T-m
c) 4.877E-03 T-m
d) 5.365E-03 T-m
e) 5.901E-03 T-m

3) 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 ${\displaystyle a=}$ 0.259 m and ${\displaystyle B_{max}=\,}$ 0.575 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.191 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.492E+05 A
b) 3.841E+05 A
c) 4.225E+05 A
d) 4.648E+05 A
e) 5.113E+05 A

4) 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

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.477 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.67)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$8.01 s. What is the current in the coil if the impedance of the coil is 75.6 Ω?

a) 2.215E-01 A
b) 2.437E-01 A
c) 2.681E-01 A
d) 2.949E-01 A
e) 3.244E-01 A
6)
A long solenoid has a length 0.634 meters, radius 3.04 cm, and 522 turns. It surrounds coil of radius 9.17 meters and 9turns. If the current in the solenoid is changing at a rate of 283 A/s, what is the emf induced in the surounding coil?
a) 1.986E-02 V
b) 2.185E-02 V
c) 2.404E-02 V
d) 2.644E-02 V
e) 2.908E-02 V
7)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =5.9 s if ε = 7.85 V , R = 6.89 Ω, and L = 7.36 H?
a) 6.567E-01 V
b) 7.880E-01 V
c) 9.456E-01 V
d) 1.135E+00 V
e) 1.362E+00 V

8) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=6 V. The resistance, inductance, and capacitance are R =0.27 Ω, L= 4.20E-03H , and C=3.70E-06 F, respectively.

a) Q = 7.135E+01
b) Q = 8.205E+01
c) Q = 9.435E+01
d) Q = 1.085E+02
e) Q = 1.248E+02

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 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

#### T2(11-16) N1

1)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.47 s if ε = 7.04 V , R = 7.69 Ω, and L = 5.78 H?
a) 4.249E-01 V
b) 5.099E-01 V
c) 6.118E-01 V
d) 7.342E-01 V
e) 8.810E-01 V

2) The output of an ac generator connected to an RLC series combination has a frequency of 300 Hz and an amplitude of 0.76 V;. If R =5 Ω, L= 6.10E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

3) An alpha-particle (q=3.2x10−19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 9.76 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(6.97 i + 8.52 j  + 9.46 k) x 104 m/s?

a) 2.199E-13 N
b) 2.419E-13 N
c) 2.661E-13 N
d) 2.927E-13 N
e) 3.220E-13 N
4)
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=2.33 kA, I2=0.741 kA, and I3=2.21 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 3.261E-03 T-m
b) 3.587E-03 T-m
c) 3.945E-03 T-m
d) 4.340E-03 T-m
e) 4.774E-03 T-m

5) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=6 V. The resistance, inductance, and capacitance are R =0.27 Ω, L= 4.20E-03H , and C=3.70E-06 F, respectively.

a) Q = 7.135E+01
b) Q = 8.205E+01
c) Q = 9.435E+01
d) Q = 1.085E+02
e) Q = 1.248E+02

6) 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 ${\displaystyle a=}$ 0.432 m and ${\displaystyle B_{max}=\,}$ 0.402 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.275 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.277E+05 A
b) 3.604E+05 A
c) 3.965E+05 A
d) 4.361E+05 A
e) 4.797E+05 A
7)
A long solenoid has a length 0.896 meters, radius 4.28 cm, and 550 turns. It surrounds coil of radius 6.65 meters and 9turns. If the current in the solenoid is changing at a rate of 204 A/s, what is the emf induced in the surounding coil?
a) 2.328E-02 V
b) 2.560E-02 V
c) 2.817E-02 V
d) 3.098E-02 V
e) 3.408E-02 V
8)
A parallel plate capacitor with a capicatnce C=8.30E-06 F whose plates have an area A=7.00E+03 m2 and separation d=7.50E-03 m is connected via a swith to a 51 Ω resistor and a battery of voltage V0=81 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=1.20E-03?
a) 5.728E+01 V
b) 6.301E+01 V
c) 6.931E+01 V
d) 7.624E+01 V
e) 8.387E+01 V

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.861 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (5.39)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$4.2 s. What is the current in the coil if the impedance of the coil is 19.8 Ω?

a) 1.751E+00 A
b) 1.926E+00 A
c) 2.119E+00 A
d) 2.331E+00 A
e) 2.564E+00 A

10) A recangular coil with an area of 0.291 m2 and 6 turns is placed in a uniform magnetic field of 2.63 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 7.130E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 35 s?

a) 1.490E+04 V
b) 1.639E+04 V
c) 1.803E+04 V
d) 1.983E+04 V
e) 2.181E+04 V

#### T2(11-16) N2

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 ${\displaystyle a=}$ 0.353 m and ${\displaystyle B_{max}=\,}$ 0.697 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) 5.479E+05 A
b) 6.027E+05 A
c) 6.630E+05 A
d) 7.293E+05 A
e) 8.022E+05 A
2)
The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled ${\displaystyle \beta }$ and ${\displaystyle \omega }$. If I1=2.35 kA, I2=0.809 kA, and I3=2.34 kA, take the ${\displaystyle \omega }$ path and evalulate the line integral,
${\displaystyle \oint {\vec {B}}\cdot d{\vec {\ell }}}$:
a) 4.031E-03 T-m
b) 4.434E-03 T-m
c) 4.877E-03 T-m
d) 5.365E-03 T-m
e) 5.901E-03 T-m

3) The output of an ac generator connected to an RLC series combination has a frequency of 410 Hz and an amplitude of 0.82 V;. If R =7 Ω, L= 9.70E-03H , and C=9.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

4) An alpha-particle (q=3.2x10−19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 9.76 T. What is the x-component of the force on the alpha-particle if it is moving with a velocity
(6.97 i + 8.52 j  + 9.46 k) x 104 m/s?

a) 2.199E-13 N
b) 2.419E-13 N
c) 2.661E-13 N
d) 2.927E-13 N
e) 3.220E-13 N
5)
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

6) A recangular coil with an area of 0.45 m2 and 18 turns is placed in a uniform magnetic field of 2.68 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 3.730E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 87 s?

a) 4.861E+04 V
b) 5.347E+04 V
c) 5.882E+04 V
d) 6.470E+04 V
e) 7.117E+04 V

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.21 Ω, L= 5.40E-03H , and C=3.20E-06 F, respectively.

a) Q = 1.286E+02
b) Q = 1.479E+02
c) Q = 1.701E+02
d) Q = 1.956E+02
e) Q = 2.250E+02
8)
A parallel plate capacitor with a capicatnce C=5.60E-06 F whose plates have an area A=3.50E+03 m2 and separation d=5.60E-03 m is connected via a swith to a 94 Ω resistor and a battery of voltage V0=21 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) 1.258E+01 V
b) 1.384E+01 V
c) 1.522E+01 V
d) 1.674E+01 V
e) 1.842E+01 V
9)
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

10) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.78 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.22)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.74 s. What is the current in the coil if the impedance of the coil is 32.1 Ω?

a) 1.742E+00 A
b) 1.916E+00 A
c) 2.108E+00 A
d) 2.319E+00 A
e) 2.551E+00 A

### T2(11-16) O0

1) A 57 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 0.447 T. What current is required to maintain this balance?

a) 2.225E-01 A
b) 2.448E-01 A
c) 2.692E-01 A
d) 2.962E-01 A
e) 3.258E-01 A

2) A solenoid has 4.900E+04 turns wound around a cylinder of diameter 1.74 cm and length 19 m. The current through the coils is 0.432 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−4.18 cm to z=+1.77 cm

a) 6.884E-05 T-m
b) 7.573E-05 T-m
c) 8.330E-05 T-m
d) 9.163E-05 T-m
e) 1.008E-04 T-m

3) 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 ${\displaystyle a=}$ 0.248 m and ${\displaystyle B_{max}=\,}$ 0.459 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.152 m that is centered on the axis with its plane perpendicular to the axis?

a) 2.228E+05 A
b) 2.451E+05 A
c) 2.696E+05 A
d) 2.966E+05 A
e) 3.262E+05 A

4) Calculate the motional emf induced along a 24.7 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.410E-05 Tesla magnetic field.

a) 7.801E+03 V
b) 8.581E+03 V
c) 9.439E+03 V
d) 1.038E+04 V
e) 1.142E+04 V

5) 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}=}$3.7 T and ${\displaystyle \omega =}$8.100E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.827 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) 1.416E+05 V
b) 1.557E+05 V
c) 1.713E+05 V
d) 1.884E+05 V
e) 2.073E+05 V
6)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.55 s if ε = 5.97 V , R = 7.74 Ω, and L = 2.62 H?
a) 3.682E-01 V
b) 4.418E-01 V
c) 5.301E-01 V
d) 6.362E-01 V
e) 7.634E-01 V

7) 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

8) 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

9) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=2 V. The resistance, inductance, and capacitance are R =0.28 Ω, L= 4.70E-03H , and C=2.50E-06 F, respectively.

a) Q = 1.171E+02
b) Q = 1.347E+02
c) Q = 1.549E+02
d) Q = 1.781E+02
e) Q = 2.048E+02

10) 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

#### T2(11-16) O1

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 ${\displaystyle a=}$ 0.52 m and ${\displaystyle B_{max}=\,}$ 0.657 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.295 m that is centered on the axis with its plane perpendicular to the axis?

a) 7.876E+05 A
b) 8.664E+05 A
c) 9.530E+05 A
d) 1.048E+06 A
e) 1.153E+06 A

2) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.27 Ω, L= 4.30E-03H , and C=2.20E-06 F, respectively.

a) Q = 1.238E+02
b) Q = 1.424E+02
c) Q = 1.637E+02
d) Q = 1.883E+02
e) Q = 2.165E+02

3) 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}=}$3.54 T and ${\displaystyle \omega =}$1.860E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.642 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) 2.415E+04 V
b) 2.656E+04 V
c) 2.922E+04 V
d) 3.214E+04 V
e) 3.535E+04 V

4) 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

5) 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

6) A solenoid has 5.640E+04 turns wound around a cylinder of diameter 1.35 cm and length 16 m. The current through the coils is 0.912 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.11 cm to z=+2.76 cm

a) 1.068E-04 T-m
b) 1.175E-04 T-m
c) 1.292E-04 T-m
d) 1.421E-04 T-m
e) 1.563E-04 T-m

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

a) 4.535E-01 H
b) 4.988E-01 H
c) 5.487E-01 H
d) 6.035E-01 H
e) 6.639E-01 H

8) Calculate the motional emf induced along a 21.3 km conductor moving at an orbital speed of 7.75 km/s perpendicular to Earth's 5.320E-05 Tesla magnetic field.

a) 6.598E+03 V
b) 7.258E+03 V
c) 7.984E+03 V
d) 8.782E+03 V
e) 9.660E+03 V
9)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =6.01 s if ε = 5.75 V , R = 5.73 Ω, and L = 7.46 H?
a) 9.936E-01 V
b) 1.192E+00 V
c) 1.431E+00 V
d) 1.717E+00 V
e) 2.060E+00 V

10) 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

#### T2(11-16) O2

1) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.3 V. The resistance, inductance, and capacitance are R =2 Ω, L= 8.10E-03H , and C=9.40E-04 F, respectively. What is the amplitude of the current?

a) 1.364E-01 A
b) 1.500E-01 A
c) 1.650E-01 A
d) 1.815E-01 A
e) 1.997E-01 A

2) A solenoid has 3.950E+04 turns wound around a cylinder of diameter 1.64 cm and length 16 m. The current through the coils is 0.441 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−2.05 cm to z=+3.97 cm

a) 6.807E-05 T-m
b) 7.487E-05 T-m
c) 8.236E-05 T-m
d) 9.060E-05 T-m
e) 9.966E-05 T-m

3) 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 ${\displaystyle a=}$ 0.645 m and ${\displaystyle B_{max}=\,}$ 0.469 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.26 m that is centered on the axis with its plane perpendicular to the axis?

a) 2.949E+05 A
b) 3.244E+05 A
c) 3.568E+05 A
d) 3.925E+05 A
e) 4.317E+05 A

4) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=4 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 4.80E-03H , and C=2.60E-06 F, respectively.

a) Q = 1.300E+02
b) Q = 1.495E+02
c) Q = 1.719E+02
d) Q = 1.976E+02
e) Q = 2.273E+02

5) What is the radiation force on an object that is 6.70E+11 m away from the sun and has cross-sectional area of 0.095 m2? The average power output of the Sun is 3.80E+26 W.

a) 3.528E-08 N
b) 3.881E-08 N
c) 4.269E-08 N
d) 4.696E-08 N
e) 5.166E-08 N

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}=}$1.97 T and ${\displaystyle \omega =}$5.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.244 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.485E+04 V
b) 1.634E+04 V
c) 1.797E+04 V
d) 1.977E+04 V
e) 2.175E+04 V
7)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =6.01 s if ε = 5.75 V , R = 5.73 Ω, and L = 7.46 H?
a) 9.936E-01 V
b) 1.192E+00 V
c) 1.431E+00 V
d) 1.717E+00 V
e) 2.060E+00 V

8) A 57 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 0.447 T. What current is required to maintain this balance?

a) 2.225E-01 A
b) 2.448E-01 A
c) 2.692E-01 A
d) 2.962E-01 A
e) 3.258E-01 A

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

a) 1.022E+00 H
b) 1.124E+00 H
c) 1.237E+00 H
d) 1.360E+00 H
e) 1.496E+00 H

10) 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

### T2(11-16) P0

1)
The silver ribbon shown are a=3.74 cm, b=2.68 cm, and c= 0.415 cm. The current carries a current of 228 A and it lies in a uniform magnetic field of 1.49 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 8.660E-06 V
b) 9.526E-06 V
c) 1.048E-05 V
d) 1.153E-05 V
e) 1.268E-05 V

2) A solenoid has 9.160E+04 turns wound around a cylinder of diameter 1.64 cm and length 16 m. The current through the coils is 0.873 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.74 cm to z=+4.75 cm

a) 3.369E-04 T-m
b) 3.706E-04 T-m
c) 4.076E-04 T-m
d) 4.484E-04 T-m
e) 4.932E-04 T-m

3) 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

4) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 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=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.157E+00 A
b) 1.273E+00 A
c) 1.400E+00 A
d) 1.540E+00 A
e) 1.694E+00 A

5) 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
6)
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 2.69% of its maximum value if ε = 4.79 V , R = 4.18 Ω, and L = 2.7 H?
a) -8.773E-01 s
b) -9.651E-01 s
c) -1.062E+00 s
d) -1.168E+00 s
e) -1.284E+00 s
7)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =0.741 s if ε = 7.36 V , R = 5.33 Ω, and L = 1.27 H?
a) 7.635E-01 V
b) 9.162E-01 V
c) 1.099E+00 V
d) 1.319E+00 V
e) 1.583E+00 V

8) The output of an ac generator connected to an RLC series combination has a frequency of 160 Hz and an amplitude of 0.47 V;. If R =8 Ω, L= 1.30E-03H , and C=6.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.17 Ω, L= 4.40E-03H , and C=3.40E-06 F, respectively.

a) Q = 1.391E+02
b) Q = 1.600E+02
c) Q = 1.840E+02
d) Q = 2.116E+02
e) Q = 2.434E+02

10) A 58 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?

a) 1.418E+02 km
b) 1.560E+02 km
c) 1.716E+02 km
d) 1.887E+02 km
e) 2.076E+02 km

#### T2(11-16) P1

1) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=6 V. The resistance, inductance, and capacitance are R =0.3 Ω, L= 5.90E-03H , and C=3.80E-06 F, respectively.

a) Q = 7.510E+01
b) Q = 8.636E+01
c) Q = 9.932E+01
d) Q = 1.142E+02
e) Q = 1.313E+02

2) 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
3)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.47 s if ε = 7.04 V , R = 7.69 Ω, and L = 5.78 H?
a) 4.249E-01 V
b) 5.099E-01 V
c) 6.118E-01 V
d) 7.342E-01 V
e) 8.810E-01 V
4)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.65% of its maximum value if ε = 3.62 V , R = 4.07 Ω, and L = 7.19 H?
a) -2.476E+00 s
b) -2.724E+00 s
c) -2.996E+00 s
d) -3.296E+00 s
e) -3.625E+00 s
5)
The silver ribbon shown are a=4.14 cm, b=3.69 cm, and c= 1.13 cm. The current carries a current of 291 A and it lies in a uniform magnetic field of 3.32 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 6.795E-06 V
b) 7.475E-06 V
c) 8.222E-06 V
d) 9.045E-06 V
e) 9.949E-06 V

6) 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?

7) A square coil has sides that are L= 0.259 m long and is tightly wound with N=628 turns of wire. The resistance of the coil is R=6.51 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=0.0372 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.809E-01 A
b) 1.989E-01 A
c) 2.188E-01 A
d) 2.407E-01 A
e) 2.648E-01 A

8) A 55 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 93 kW?

a) 1.270E+02 km
b) 1.397E+02 km
c) 1.537E+02 km
d) 1.690E+02 km
e) 1.859E+02 km

9) Two loops of wire carry the same current of 66 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.485 m while the other has a radius of 1.27 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 0.507 m from the first (smaller) loopif the disance between the loops is 1.76 m?

a) 2.733E-02 T
b) 3.007E-02 T
c) 3.307E-02 T
d) 3.638E-02 T
e) 4.002E-02 T

10) A solenoid has 4.730E+04 turns wound around a cylinder of diameter 1.46 cm and length 15 m. The current through the coils is 0.754 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−3.4 cm to z=+1.14 cm

a) 1.121E-04 T-m
b) 1.233E-04 T-m
c) 1.356E-04 T-m
d) 1.492E-04 T-m
e) 1.641E-04 T-m

#### T2(11-16) P2

1)
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 2.63% of its maximum value if ε = 8.7 V , R = 8.35 Ω, and L = 1.44 H?
a) -3.137E-01 s
b) -3.451E-01 s
c) -3.796E-01 s
d) -4.176E-01 s
e) -4.593E-01 s

2) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=2 V. The resistance, inductance, and capacitance are R =0.28 Ω, L= 4.70E-03H , and C=2.50E-06 F, respectively.

a) Q = 1.171E+02
b) Q = 1.347E+02
c) Q = 1.549E+02
d) Q = 1.781E+02
e) Q = 2.048E+02
3)
The silver ribbon shown are a=4.14 cm, b=3.69 cm, and c= 1.13 cm. The current carries a current of 291 A and it lies in a uniform magnetic field of 3.32 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 6.795E-06 V
b) 7.475E-06 V
c) 8.222E-06 V
d) 9.045E-06 V
e) 9.949E-06 V

4) Two loops of wire carry the same current of 18 kA, and flow in the same direction. They share a common axis and orientation. One loop has a radius of 0.848 m while the other has a radius of 1.42 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 0.625 m from the first (smaller) loopif the disance between the loops is 1.55 m?

a) 7.952E-03 T
b) 8.747E-03 T
c) 9.622E-03 T
d) 1.058E-02 T
e) 1.164E-02 T

5) A long solenoid has a radius of 0.786 m and 60 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 =}$21 s−1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?

a) 1.605E-04 V/m
b) 1.766E-04 V/m
c) 1.942E-04 V/m
d) 2.136E-04 V/m
e) 2.350E-04 V/m
6)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.53 s if ε = 6.14 V , R = 4.22 Ω, and L = 1.91 H?
a) 1.007E+00 V
b) 1.208E+00 V
c) 1.450E+00 V
d) 1.739E+00 V
e) 2.087E+00 V

7) The output of an ac generator connected to an RLC series combination has a frequency of 750 Hz and an amplitude of 0.88 V;. If R =4 Ω, L= 5.60E-03H , and C=9.70E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

8) 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

9) A 42 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 94 kW?

a) 1.768E+02 km
b) 1.945E+02 km
c) 2.139E+02 km
d) 2.353E+02 km
e) 2.589E+02 km

10) A solenoid has 5.980E+04 turns wound around a cylinder of diameter 1.8 cm and length 17 m. The current through the coils is 0.933 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−3.68 cm to z=+1.29 cm

a) 1.863E-04 T-m
b) 2.050E-04 T-m
c) 2.255E-04 T-m
d) 2.480E-04 T-m
e) 2.728E-04 T-m

### T2(11-16) Q0

1) 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 6.97 mT and 2.240E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 2.656E+05 m/s
b) 2.922E+05 m/s
c) 3.214E+05 m/s
d) 3.535E+05 m/s
e) 3.889E+05 m/s

2) A solenoid has 8.890E+04 turns wound around a cylinder of diameter 1.32 cm and length 15 m. The current through the coils is 0.297 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.41 cm to z=+2.56 cm

a) 7.257E-05 T-m
b) 7.983E-05 T-m
c) 8.781E-05 T-m
d) 9.660E-05 T-m
e) 1.063E-04 T-m
3)
Three wires sit at the corners of a square of length 0.819 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 (2.01 A, 1.09 A, 1.56 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 4.688E-05 T
b) By= 5.156E-05 T
c) By= 5.672E-05 T
d) By= 6.239E-05 T
e) By= 6.863E-05 T

4) The current through the windings of a solenoid with n= 2.760E+03 turns per meter is changing at a rate dI/dt=8 A/s. The solenoid is 74 cm long and has a cross-sectional diameter of 2.57 cm. A small coil consisting of N=32turns wraped in a circle of diameter 1.49 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.407E-04 V
b) 1.548E-04 V
c) 1.703E-04 V
d) 1.873E-04 V
e) 2.061E-04 V

5) A long solenoid has a radius of 0.716 m and 96 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 =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

a) 1.426E-03 V/m
b) 1.568E-03 V/m
c) 1.725E-03 V/m
d) 1.897E-03 V/m
e) 2.087E-03 V/m

6) A washer has an inner diameter of 2.16 cm and an outer diamter of 4.82 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.22mm}$, and ${\displaystyle n=2.8}$. What is the volume of the washer?

a) 1.342E+00 cm3
b) 1.477E+00 cm3
c) 1.624E+00 cm3
d) 1.787E+00 cm3
e) 1.965E+00 cm3
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 1.53% of its maximum value if ε = 6.08 V , R = 1.88 Ω, and L = 4.67 H?
a) -5.192E+00 s
b) -5.711E+00 s
c) -6.282E+00 s
d) -6.910E+00 s
e) -7.601E+00 s

8) 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

9) A step-down transformer steps 7 kV down to 190 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 190 V side ?)

a) 1.675E+02 A
b) 1.842E+02 A
c) 2.026E+02 A
d) 2.229E+02 A
e) 2.452E+02 A

10) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.051 m2? The average power output of the Sun is 3.80E+26 W.

a) 4.555E-07 N/m2
b) 5.010E-07 N/m2
c) 5.511E-07 N/m2
d) 6.063E-07 N/m2
e) 6.669E-07 N/m2

#### T2(11-16) Q1

1)
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 2.69% of its maximum value if ε = 4.79 V , R = 4.18 Ω, and L = 2.7 H?
a) -8.773E-01 s
b) -9.651E-01 s
c) -1.062E+00 s
d) -1.168E+00 s
e) -1.284E+00 s

2) A solenoid has 9.880E+04 turns wound around a cylinder of diameter 1.5 cm and length 15 m. The current through the coils is 0.981 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.56 cm to z=+3.22 cm

a) 2.916E-04 T-m
b) 3.208E-04 T-m
c) 3.528E-04 T-m
d) 3.881E-04 T-m
e) 4.269E-04 T-m

3) The current through the windings of a solenoid with n= 2.210E+03 turns per meter is changing at a rate dI/dt=18 A/s. The solenoid is 65 cm long and has a cross-sectional diameter of 2.2 cm. A small coil consisting of N=36turns wraped in a circle of diameter 1.29 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 2.352E-04 V
b) 2.587E-04 V
c) 2.846E-04 V
d) 3.131E-04 V
e) 3.444E-04 V

4) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.92mm}$, and ${\displaystyle n=2.68}$. What is the volume of the washer?

a) 1.118E+00 cm3
b) 1.229E+00 cm3
c) 1.352E+00 cm3
d) 1.487E+00 cm3
e) 1.636E+00 cm3

5) 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 4.15 mT and 4.440E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 1.070E+06 m/s
b) 1.177E+06 m/s
c) 1.295E+06 m/s
d) 1.424E+06 m/s
e) 1.566E+06 m/s

6) An ac generator produces an emf of amplitude 76 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a 14 mF inductor?

a) 3.606E+00 A
b) 3.967E+00 A
c) 4.364E+00 A
d) 4.800E+00 A
e) 5.280E+00 A

7) 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

8) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.025 m2? The average power output of the Sun is 3.80E+26 W.

a) 5.511E-07 N/m2
b) 6.063E-07 N/m2
c) 6.669E-07 N/m2
d) 7.336E-07 N/m2
e) 8.069E-07 N/m2

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)
Three wires sit at the corners of a square of length 0.819 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 (2.01 A, 1.09 A, 1.56 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 4.688E-05 T
b) By= 5.156E-05 T
c) By= 5.672E-05 T
d) By= 6.239E-05 T
e) By= 6.863E-05 T

#### T2(11-16) Q2

1) A long solenoid has a radius of 0.394 m and 13 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 1.8 m from the axis at time t=0.0757 s ?

a) 2.132E-05 V/m
b) 2.345E-05 V/m
c) 2.579E-05 V/m
d) 2.837E-05 V/m
e) 3.121E-05 V/m

2) A step-down transformer steps 18 kV down to 260 V. The high-voltage input is provided by a 290 Ω power line that carries 3 A of currentWhat is the output current (at the 260 V side ?)

a) 1.888E+02 A
b) 2.077E+02 A
c) 2.285E+02 A
d) 2.513E+02 A
e) 2.764E+02 A

3) An ac generator produces an emf of amplitude 60 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a 85 mF inductor?

a) 7.856E-01 A
b) 8.642E-01 A
c) 9.506E-01 A
d) 1.046E+00 A
e) 1.150E+00 A
4)
Three wires sit at the corners of a square of length 0.547 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 (1.78 A, 1.34 A, 1.64 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.118E-05 T
b) By= 6.730E-05 T
c) By= 7.403E-05 T
d) By= 8.144E-05 T
e) By= 8.958E-05 T

5) 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 5.85 mT and 3.760E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?

a) 4.829E+05 m/s
b) 5.312E+05 m/s
c) 5.843E+05 m/s
d) 6.427E+05 m/s
e) 7.070E+05 m/s

6) A washer has an inner diameter of 2.6 cm and an outer diamter of 4.17 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.38mm}$, and ${\displaystyle n=2.62}$. What is the volume of the washer?

a) 7.196E-01 cm3
b) 7.916E-01 cm3
c) 8.707E-01 cm3
d) 9.578E-01 cm3
e) 1.054E+00 cm3

7) The current through the windings of a solenoid with n= 2.760E+03 turns per meter is changing at a rate dI/dt=8 A/s. The solenoid is 74 cm long and has a cross-sectional diameter of 2.57 cm. A small coil consisting of N=32turns wraped in a circle of diameter 1.49 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.407E-04 V
b) 1.548E-04 V
c) 1.703E-04 V
d) 1.873E-04 V
e) 2.061E-04 V

8) A solenoid has 9.160E+04 turns wound around a cylinder of diameter 1.64 cm and length 16 m. The current through the coils is 0.873 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.74 cm to z=+4.75 cm

a) 3.369E-04 T-m
b) 3.706E-04 T-m
c) 4.076E-04 T-m
d) 4.484E-04 T-m
e) 4.932E-04 T-m

9) What is the radiation pressure on an object that is 2.20E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.

a) 3.131E-06 N/m2
b) 3.445E-06 N/m2
c) 3.789E-06 N/m2
d) 4.168E-06 N/m2
e) 4.585E-06 N/m2
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 1.53% of its maximum value if ε = 6.08 V , R = 1.88 Ω, and L = 4.67 H?
a) -5.192E+00 s
b) -5.711E+00 s
c) -6.282E+00 s
d) -6.910E+00 s
e) -7.601E+00 s

### T2(11-16) R0

1) 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

2) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.9 mm from the center of a wire of radius 4 mm if the current is 1A?

a) 1.784E-05 T
b) 1.963E-05 T
c) 2.159E-05 T
d) 2.375E-05 T
e) 2.613E-05 T

3) Two parallel wires each carry a 3.8 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.74 cm, 1.47 cm), while the other is located at (5.26 cm, 5.87 cm). What is the force per unit length between the wires?

a) 5.926E-11 N/m
b) 6.518E-11 N/m
c) 7.170E-11 N/m
d) 7.887E-11 N/m
e) 8.676E-11 N/m

4) 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

5) 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
6)
A long solenoid has a length 0.923 meters, radius 4.08 cm, and 579 turns. It surrounds coil of radius 6.86 meters and 14turns. If the current in the solenoid is changing at a rate of 139 A/s, what is the emf induced in the surounding coil?
a) 1.894E-02 V
b) 2.083E-02 V
c) 2.291E-02 V
d) 2.520E-02 V
e) 2.772E-02 V
7)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =5.9 s if ε = 7.85 V , R = 6.89 Ω, and L = 7.36 H?
a) 6.567E-01 V
b) 7.880E-01 V
c) 9.456E-01 V
d) 1.135E+00 V
e) 1.362E+00 V

8) 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

9) The output of an ac generator connected to an RLC series combination has a frequency of 220 Hz and an amplitude of 0.71 V;. If R =7 Ω, L= 8.20E-03H , and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

10)
A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=980.0 m2 and separation d=6.20E-03 m is connected via a swith to a 8 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 magnitude of the electric field at time t=2.40E-05?
a) 5.154E+03 V/m
b) 5.669E+03 V/m
c) 6.236E+03 V/m
d) 6.860E+03 V/m
e) 7.545E+03 V/m

#### T2(11-16) R1

1) 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

2) A recangular coil with an area of 0.23 m2 and 20 turns is placed in a uniform magnetic field of 1.66 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 1.380E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 4 s?

a) 2.317E+03 V
b) 2.549E+03 V
c) 2.804E+03 V
d) 3.084E+03 V
e) 3.393E+03 V
3)
A parallel plate capacitor with a capicatnce C=1.20E-06 F whose plates have an area A=1.00E+03 m2 and separation d=7.70E-03 m is connected via a swith to a 32 Ω resistor and a battery of voltage V0=38 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=1.40E-04?
a) 3.972E+03 V/m
b) 4.369E+03 V/m
c) 4.806E+03 V/m
d) 5.287E+03 V/m
e) 5.816E+03 V/m

4) 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?

5) 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

6) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.208E-05 T
b) 1.329E-05 T
c) 1.462E-05 T
d) 1.608E-05 T
e) 1.769E-05 T

7) A charged particle in a magnetic field of 4.970E-04 T is moving perpendicular to the magnetic field with a speed of 2.950E+05 m/s. What is the period of orbit if orbital radius is 0.344 m?

a) 7.327E-06 s
b) 8.060E-06 s
c) 8.865E-06 s
d) 9.752E-06 s
e) 1.073E-05 s
8)
A long solenoid has a length 0.567 meters, radius 3.35 cm, and 555 turns. It surrounds coil of radius 5.73 meters and 9turns. If the current in the solenoid is changing at a rate of 281 A/s, what is the emf induced in the surounding coil?
a) 3.446E-02 V
b) 3.790E-02 V
c) 4.169E-02 V
d) 4.586E-02 V
e) 5.045E-02 V
9)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.55 s if ε = 5.97 V , R = 7.74 Ω, and L = 2.62 H?
a) 3.682E-01 V
b) 4.418E-01 V
c) 5.301E-01 V
d) 6.362E-01 V
e) 7.634E-01 V

10) 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

#### T2(11-16) R2

1) The output of an ac generator connected to an RLC series combination has a frequency of 970 Hz and an amplitude of 0.11 V;. If R =9 Ω, L= 8.50E-03H , and C=7.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

2) An ac generator produces an emf of amplitude 32 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 14 mF capacitor?

a) 3.378E-01 A
b) 3.716E-01 A
c) 4.087E-01 A
d) 4.496E-01 A
e) 4.945E-01 A

3) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.59 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 2.072E-05 T
b) 2.279E-05 T
c) 2.507E-05 T
d) 2.758E-05 T
e) 3.034E-05 T

4) A recangular coil with an area of 0.182 m2 and 5 turns is placed in a uniform magnetic field of 2.74 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 2.390E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 79 s?

a) 1.656E+03 V
b) 1.821E+03 V
c) 2.003E+03 V
d) 2.204E+03 V
e) 2.424E+03 V

5) A long solenoid has a radius of 0.45 m and 35 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 =}$28 s−1.What is the induced electric fied at a distance 2.35 m from the axis at time t=0.0709 s ?

a) 5.475E-06 V/m
b) 6.023E-06 V/m
c) 6.625E-06 V/m
d) 7.288E-06 V/m
e) 8.017E-06 V/m

6) Two parallel wires each carry a 1.65 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.59 cm, 1.81 cm), while the other is located at (5.78 cm, 4.43 cm). What is the force per unit length between the wires?

a) 1.422E-11 N/m
b) 1.564E-11 N/m
c) 1.720E-11 N/m
d) 1.892E-11 N/m
e) 2.081E-11 N/m
7)
A parallel plate capacitor with a capicatnce C=2.60E-06 F whose plates have an area A=2.60E+03 m2 and separation d=9.00E-03 m is connected via a swith to a 63 Ω resistor and a battery of voltage V0=86 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=8.00E-04?
a) 7.125E+03 V/m
b) 7.837E+03 V/m
c) 8.621E+03 V/m
d) 9.483E+03 V/m
e) 1.043E+04 V/m

8) A charged particle in a magnetic field of 3.820E-04 T is moving perpendicular to the magnetic field with a speed of 3.890E+05 m/s. What is the period of orbit if orbital radius is 0.718 m?

a) 8.713E-06 s
b) 9.584E-06 s
c) 1.054E-05 s
d) 1.160E-05 s
e) 1.276E-05 s
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)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =5.9 s if ε = 7.85 V , R = 6.89 Ω, and L = 7.36 H?
a) 6.567E-01 V
b) 7.880E-01 V
c) 9.456E-01 V
d) 1.135E+00 V
e) 1.362E+00 V

### T2(11-16) S0

1) 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

2) 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 ${\displaystyle a=}$ 0.432 m and ${\displaystyle B_{max}=\,}$ 0.402 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.275 m that is centered on the axis with its plane perpendicular to the axis?

a) 3.277E+05 A
b) 3.604E+05 A
c) 3.965E+05 A
d) 4.361E+05 A
e) 4.797E+05 A

3) Two parallel wires each carry a 1.65 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.59 cm, 1.81 cm), while the other is located at (5.78 cm, 4.43 cm). What is the force per unit length between the wires?

a) 1.422E-11 N/m
b) 1.564E-11 N/m
c) 1.720E-11 N/m
d) 1.892E-11 N/m
e) 2.081E-11 N/m

4) 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

5) 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}=}$1.89 T and ${\displaystyle \omega =}$1.710E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.476 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) 7.262E+03 V
b) 7.988E+03 V
c) 8.787E+03 V
d) 9.666E+03 V
e) 1.063E+04 V
6)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =6.01 s if ε = 5.75 V , R = 5.73 Ω, and L = 7.46 H?
a) 9.936E-01 V
b) 1.192E+00 V
c) 1.431E+00 V
d) 1.717E+00 V
e) 2.060E+00 V

7) 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

8) 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

9) An ac generator produces an emf of amplitude 58 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 66 mF capacitor?

a) 3.976E+00 A
b) 4.373E+00 A
c) 4.810E+00 A
d) 5.291E+00 A
e) 5.821E+00 A

10) 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

#### T2(11-16) S1

1) Two parallel wires each carry a 3.51 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.14 cm, 1.43 cm), while the other is located at (4.14 cm, 5.23 cm). What is the force per unit length between the wires?

a) 6.484E-11 N/m
b) 7.133E-11 N/m
c) 7.846E-11 N/m
d) 8.631E-11 N/m
e) 9.494E-11 N/m

2) 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 ${\displaystyle a=}$ 0.248 m and ${\displaystyle B_{max}=\,}$ 0.459 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.152 m that is centered on the axis with its plane perpendicular to the axis?

a) 2.228E+05 A
b) 2.451E+05 A
c) 2.696E+05 A
d) 2.966E+05 A
e) 3.262E+05 A

3) 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

4) 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

5) 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

6) In an LC circuit, the self-inductance is 0.0307 H and the capacitance is 5.330E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 1.840E-05 C. How long does it take for the capacitor to become completely discharged?

a) 5.251E-04 s
b) 5.776E-04 s
c) 6.354E-04 s
d) 6.989E-04 s
e) 7.688E-04 s

7) A 46 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 78 kW?

a) 1.563E+02 km
b) 1.719E+02 km
c) 1.891E+02 km
d) 2.080E+02 km
e) 2.288E+02 km

8) 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

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}=}$3.29 T and ${\displaystyle \omega =}$4.720E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.658 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) 6.420E+04 V
b) 7.062E+04 V
c) 7.768E+04 V
d) 8.545E+04 V
e) 9.400E+04 V
10)
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

#### T2(11-16) S2

1) In an LC circuit, the self-inductance is 0.0216 H and the capacitance is 6.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 1.240E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.846E-04 s
b) 5.330E-04 s
c) 5.863E-04 s
d) 6.449E-04 s
e) 7.094E-04 s

2) 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}=}$1.8 T and ${\displaystyle \omega =}$1.530E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.519 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) 7.422E+03 V
b) 8.164E+03 V
c) 8.981E+03 V
d) 9.879E+03 V
e) 1.087E+04 V

3) 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 ${\displaystyle a=}$ 0.248 m and ${\displaystyle B_{max}=\,}$ 0.459 T, then how much current (in the z-direction) flows through a circle of radius ${\displaystyle r=}$ 0.152 m that is centered on the axis with its plane perpendicular to the axis?

a) 2.228E+05 A
b) 2.451E+05 A
c) 2.696E+05 A
d) 2.966E+05 A
e) 3.262E+05 A

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) 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

6) 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

7) Two parallel wires each carry a 7.48 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (3.13 cm, 0.955 cm), while the other is located at (5.37 cm, 5.48 cm). What is the force per unit length between the wires?

a) 2.015E-10 N/m
b) 2.216E-10 N/m
c) 2.438E-10 N/m
d) 2.682E-10 N/m
e) 2.950E-10 N/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 73 kW?

a) 1.003E+02 km
b) 1.103E+02 km
c) 1.213E+02 km
d) 1.335E+02 km
e) 1.468E+02 km

9) A circular current loop of radius 1.88 cm carries a current of 3.41 mA. What is the magnitude of the torque if the dipole is oriented at 62 ° to a uniform magnetic fied of 0.415 T?

a) 1.387E-06 N m
b) 1.526E-06 N m
c) 1.679E-06 N m
d) 1.847E-06 N m
e) 2.031E-06 N m
10)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.47 s if ε = 7.04 V , R = 7.69 Ω, and L = 5.78 H?
a) 4.249E-01 V
b) 5.099E-01 V
c) 6.118E-01 V
d) 7.342E-01 V
e) 8.810E-01 V

### T2(11-16) T0

1)
The silver ribbon shown are a=3.84 cm, b=3.45 cm, and c= 1.38 cm. The current carries a current of 92 A and it lies in a uniform magnetic field of 1.35 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 7.153E-07 V
b) 7.869E-07 V
c) 8.655E-07 V
d) 9.521E-07 V
e) 1.047E-06 V

2) 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

3) 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

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.59)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.58 s. What is the current in the coil if the impedance of the coil is 13.3 Ω?

a) 4.141E-01 A
b) 4.555E-01 A
c) 5.011E-01 A
d) 5.512E-01 A
e) 6.063E-01 A

5) 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}=}$3.75 T and ${\displaystyle \omega =}$9.800E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.22 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) 4.198E+04 V
b) 4.618E+04 V
c) 5.080E+04 V
d) 5.588E+04 V
e) 6.147E+04 V

6) In an LC circuit, the self-inductance is 0.0216 H and the capacitance is 6.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 1.240E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.846E-04 s
b) 5.330E-04 s
c) 5.863E-04 s
d) 6.449E-04 s
e) 7.094E-04 s

7) A washer has an inner diameter of 2.2 cm and an outer diamter of 4.11 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.23mm}$, and ${\displaystyle n=2.74}$. What is the volume of the washer?

a) 7.110E-01 cm3
b) 7.821E-01 cm3
c) 8.603E-01 cm3
d) 9.463E-01 cm3
e) 1.041E+00 cm3

8) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.25 V. The resistance, inductance, and capacitance are R =3 Ω, L= 2.20E-03H , and C=6.30E-04 F, respectively. What is the amplitude of the current?

a) 7.576E-02 A
b) 8.333E-02 A
c) 9.167E-02 A
d) 1.008E-01 A
e) 1.109E-01 A

9) 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
10)
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

#### T2(11-16) T1

1) 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

2) Two parallel wires each carry a 3.8 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.74 cm, 1.47 cm), while the other is located at (5.26 cm, 5.87 cm). What is the force per unit length between the wires?

a) 5.926E-11 N/m
b) 6.518E-11 N/m
c) 7.170E-11 N/m
d) 7.887E-11 N/m
e) 8.676E-11 N/m

3) In an LC circuit, the self-inductance is 0.0156 H and the capacitance is 6.950E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 4.830E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.886E-04 s
b) 4.275E-04 s
c) 4.702E-04 s
d) 5.172E-04 s
e) 5.689E-04 s

4) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 2.04 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.115E-05 T
b) 1.226E-05 T
c) 1.349E-05 T
d) 1.484E-05 T
e) 1.632E-05 T

5) A step-down transformer steps 15 kV down to 240 V. The high-voltage input is provided by a 200 Ω power line that carries 4 A of currentWhat is the output current (at the 240 V side ?)

a) 1.708E+02 A
b) 1.878E+02 A
c) 2.066E+02 A
d) 2.273E+02 A
e) 2.500E+02 A

6) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.16 V. The resistance, inductance, and capacitance are R =8 Ω, L= 5.40E-03H , and C=5.40E-04 F, respectively. What is the amplitude of the current?

a) 2.000E-02 A
b) 2.200E-02 A
c) 2.420E-02 A
d) 2.662E-02 A
e) 2.928E-02 A
7)
The silver ribbon shown are a=3.96 cm, b=3.35 cm, and c= 1.07 cm. The current carries a current of 295 A and it lies in a uniform magnetic field of 3.4 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 9.015E-06 V
b) 9.916E-06 V
c) 1.091E-05 V
d) 1.200E-05 V
e) 1.320E-05 V

8) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.594 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.89)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.6 s. What is the current in the coil if the impedance of the coil is 6.65 Ω?

a) 2.088E+00 A
b) 2.297E+00 A
c) 2.527E+00 A
d) 2.779E+00 A
e) 3.057E+00 A

9) A washer has an inner diameter of 2.6 cm and an outer diamter of 4.17 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.38mm}$, and ${\displaystyle n=2.62}$. What is the volume of the washer?

a) 7.196E-01 cm3
b) 7.916E-01 cm3
c) 8.707E-01 cm3
d) 9.578E-01 cm3
e) 1.054E+00 cm3
10)
A parallel plate capacitor with a capicatnce C=9.60E-06 F whose plates have an area A=5.40E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 29 Ω resistor and a battery of voltage V0=50 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=8.30E-04?
a) 3.923E+01 V
b) 4.315E+01 V
c) 4.746E+01 V
d) 5.221E+01 V
e) 5.743E+01 V

#### T2(11-16) T2

1) A step-down transformer steps 15 kV down to 240 V. The high-voltage input is provided by a 120 Ω power line that carries 3 A of currentWhat is the output current (at the 240 V side ?)

a) 1.550E+02 A
b) 1.705E+02 A
c) 1.875E+02 A
d) 2.063E+02 A
e) 2.269E+02 A
2)
The silver ribbon shown are a=4.65 cm, b=3.43 cm, and c= 1.15 cm. The current carries a current of 279 A and it lies in a uniform magnetic field of 3.48 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 6.100E-06 V
b) 6.710E-06 V
c) 7.381E-06 V
d) 8.120E-06 V
e) 8.931E-06 V

3) Two parallel wires each carry a 7.75 mA current and are oriented in the z direction. The first wire is located in the x-y plane at (4.62 cm, 1.31 cm), while the other is located at (4.63 cm, 5.53 cm). What is the force per unit length between the wires?

a) 2.588E-10 N/m
b) 2.847E-10 N/m
c) 3.131E-10 N/m
d) 3.444E-10 N/m
e) 3.789E-10 N/m
4)
A parallel plate capacitor with a capicatnce C=9.60E-06 F whose plates have an area A=5.40E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 29 Ω resistor and a battery of voltage V0=50 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=8.30E-04?
a) 3.923E+01 V
b) 4.315E+01 V
c) 4.746E+01 V
d) 5.221E+01 V
e) 5.743E+01 V

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.8 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.6)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$8.91 s. What is the current in the coil if the impedance of the coil is 61.7 Ω?

a) 5.369E-01 A
b) 5.906E-01 A
c) 6.496E-01 A
d) 7.146E-01 A
e) 7.860E-01 A

6) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.83 V. The resistance, inductance, and capacitance are R =9 Ω, L= 8.50E-03H , and C=7.20E-04 F, respectively. What is the amplitude of the current?

a) 8.384E-02 A
b) 9.222E-02 A
c) 1.014E-01 A
d) 1.116E-01 A
e) 1.227E-01 A

7) Under most conditions the current is distributed uniformly over the cross section of the wire. What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?

a) 1.208E-05 T
b) 1.329E-05 T
c) 1.462E-05 T
d) 1.608E-05 T
e) 1.769E-05 T

8) 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}=}$3.58 T and ${\displaystyle \omega =}$4.310E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.879 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.043E+04 V
b) 7.747E+04 V
c) 8.522E+04 V
d) 9.374E+04 V
e) 1.031E+05 V

9) In an LC circuit, the self-inductance is 0.0689 H and the capacitance is 2.110E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.220E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.950E-04 s
b) 5.445E-04 s
c) 5.989E-04 s
d) 6.588E-04 s
e) 7.247E-04 s

10) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.92mm}$, and ${\displaystyle n=2.68}$. What is the volume of the washer?

a) 1.118E+00 cm3
b) 1.229E+00 cm3
c) 1.352E+00 cm3
d) 1.487E+00 cm3
e) 1.636E+00 cm3

### T2(11-16) U0

1)
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

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 23 turns per centimeter and the current applied to the solenoid is 534 mA, the net magnetic field is measured to be 1.48 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.917E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.708E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.579E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.054E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.159E+03
3)
Three wires sit at the corners of a square of length 0.823 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.718E-05 T
b) By= 7.390E-05 T
c) By= 8.129E-05 T
d) By= 8.942E-05 T
e) By= 9.836E-05 T

4) The current through the windings of a solenoid with n= 2.400E+03 turns per meter is changing at a rate dI/dt=3 A/s. The solenoid is 93 cm long and has a cross-sectional diameter of 2.13 cm. A small coil consisting of N=30turns wraped in a circle of diameter 1.35 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 3.885E-05 V
b) 4.274E-05 V
c) 4.701E-05 V
d) 5.171E-05 V
e) 5.688E-05 V

5) Calculate the motional emf induced along a 37.9 km conductor moving at an orbital speed of 7.84 km/s perpendicular to Earth's 5.410E-05 Tesla magnetic field.

a) 1.208E+04 V
b) 1.329E+04 V
c) 1.461E+04 V
d) 1.608E+04 V
e) 1.768E+04 V

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)
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 2.78% of its maximum value if ε = 1.39 V , R = 2.88 Ω, and L = 4.06 H?
a) -2.296E+00 s
b) -2.525E+00 s
c) -2.778E+00 s
d) -3.056E+00 s
e) -3.361E+00 s

8) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=6 V. The resistance, inductance, and capacitance are R =0.27 Ω, L= 4.20E-03H , and C=3.70E-06 F, respectively.

a) Q = 7.135E+01
b) Q = 8.205E+01
c) Q = 9.435E+01
d) Q = 1.085E+02
e) Q = 1.248E+02

9) 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

10) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.051 m2? The average power output of the Sun is 3.80E+26 W.

a) 4.555E-07 N/m2
b) 5.010E-07 N/m2
c) 5.511E-07 N/m2
d) 6.063E-07 N/m2
e) 6.669E-07 N/m2

#### T2(11-16) U1

1) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 24 turns per centimeter and the current applied to the solenoid is 595 mA, the net magnetic field is measured to be 1.46 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 6.716E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 7.387E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.126E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.939E+02
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.833E+02

2) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 4.70E-03H , and C=3.30E-06 F, respectively.

a) Q = 1.313E+02
b) Q = 1.510E+02
c) Q = 1.736E+02
d) Q = 1.996E+02
e) Q = 2.296E+02

3) What is the radiation pressure on an object that is 8.10E+11 m away from the sun and has cross-sectional area of 0.057 m2? The average power output of the Sun is 3.80E+26 W.

a) 3.075E-07 N/m2
b) 3.382E-07 N/m2
c) 3.720E-07 N/m2
d) 4.092E-07 N/m2
e) 4.502E-07 N/m2
4)
Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 4.028E-05 T
b) By= 4.431E-05 T
c) By= 4.874E-05 T
d) By= 5.361E-05 T
e) By= 5.897E-05 T

5) In an LC circuit, the self-inductance is 0.0156 H and the capacitance is 6.950E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 4.830E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.886E-04 s
b) 4.275E-04 s
c) 4.702E-04 s
d) 5.172E-04 s
e) 5.689E-04 s
6)
The silver ribbon shown are a=4.72 cm, b=4.17 cm, and c= 1.53 cm. The current carries a current of 235 A and it lies in a uniform magnetic field of 1.35 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 1.648E-06 V
b) 1.813E-06 V
c) 1.994E-06 V
d) 2.194E-06 V
e) 2.413E-06 V
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 1.82% of its maximum value if ε = 8.65 V , R = 3.02 Ω, and L = 1.75 H?
a) -9.593E-01 s
b) -1.055E+00 s
c) -1.161E+00 s
d) -1.277E+00 s
e) -1.405E+00 s

8) The current through the windings of a solenoid with n= 2.460E+03 turns per meter is changing at a rate dI/dt=7 A/s. The solenoid is 87 cm long and has a cross-sectional diameter of 3.32 cm. A small coil consisting of N=38turns wraped in a circle of diameter 1.29 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 7.340E-05 V
b) 8.075E-05 V
c) 8.882E-05 V
d) 9.770E-05 V
e) 1.075E-04 V

9) 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

10) 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

#### T2(11-16) U2

1) The current through the windings of a solenoid with n= 2.100E+03 turns per meter is changing at a rate dI/dt=7 A/s. The solenoid is 91 cm long and has a cross-sectional diameter of 3.24 cm. A small coil consisting of N=22turns wraped in a circle of diameter 1.22 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 3.245E-05 V
b) 3.569E-05 V
c) 3.926E-05 V
d) 4.319E-05 V
e) 4.751E-05 V

2) 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

3) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=2 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 4.20E-03H , and C=2.70E-06 F, respectively.

a) Q = 1.372E+02
b) Q = 1.578E+02
c) Q = 1.814E+02
d) Q = 2.086E+02
e) Q = 2.399E+02

4) The output of an ac generator connected to an RLC series combination has a frequency of 2.70E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 9.10E-03H , and C=9.60E-06 F, what is the rms power transferred to the resistor?

a) 2.188E-03 Watts
b) 2.407E-03 Watts
c) 2.647E-03 Watts
d) 2.912E-03 Watts
e) 3.203E-03 Watts

5) 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

6) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 24 turns per centimeter and the current applied to the solenoid is 242 mA, the net magnetic field is measured to be 1.38 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.718E+03
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.890E+03
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.079E+03
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.287E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 2.515E+03
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 2.54% of its maximum value if ε = 2.46 V , R = 2.8 Ω, and L = 5.67 H?
a) -2.540E+00 s
b) -2.794E+00 s
c) -3.073E+00 s
d) -3.381E+00 s
e) -3.719E+00 s

8) What is the radiation pressure on an object that is 2.20E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.

a) 3.131E-06 N/m2
b) 3.445E-06 N/m2
c) 3.789E-06 N/m2
d) 4.168E-06 N/m2
e) 4.585E-06 N/m2
9)
The silver ribbon shown are a=3.96 cm, b=3.35 cm, and c= 1.07 cm. The current carries a current of 295 A and it lies in a uniform magnetic field of 3.4 T. Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
a) 9.015E-06 V
b) 9.916E-06 V
c) 1.091E-05 V
d) 1.200E-05 V
e) 1.320E-05 V
10)
Three wires sit at the corners of a square of length 0.699 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.87 A, 2.18 A, 1.34 A), respectively. What is the y-component of the magnetic field at point P?
a) By= 6.999E-05 T
b) By= 7.699E-05 T
c) By= 8.469E-05 T
d) By= 9.316E-05 T
e) By= 1.025E-04 T

### T2(11-16) V0

1) 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

2) A solenoid has 4.730E+04 turns wound around a cylinder of diameter 1.46 cm and length 15 m. The current through the coils is 0.754 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−3.4 cm to z=+1.14 cm

a) 1.121E-04 T-m
b) 1.233E-04 T-m
c) 1.356E-04 T-m
d) 1.492E-04 T-m
e) 1.641E-04 T-m

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 22 turns per centimeter and the current applied to the solenoid is 568 mA, the net magnetic field is measured to be 1.29 T. What is the magnetic susceptibility for this case?

a) ${\displaystyle \chi {\text{ (chi) }}=}$ 8.205E+02
b) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.026E+02
c) ${\displaystyle \chi {\text{ (chi) }}=}$ 9.928E+02
d) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.092E+03
e) ${\displaystyle \chi {\text{ (chi) }}=}$ 1.201E+03

4) 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

5) A square coil has sides that are L= 0.894 m long and is tightly wound with N=255 turns of wire. The resistance of the coil is R=8.83 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=0.0682 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.301E+00 A
b) 1.431E+00 A
c) 1.574E+00 A
d) 1.732E+00 A
e) 1.905E+00 A

6) 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
7)
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

8) The output of an ac generator connected to an RLC series combination has a frequency of 810 Hz and an amplitude of 0.64 V;. If R =6 Ω, L= 8.70E-03H , and C=8.20E-04 F, what is the impedance?

a) 4.444E+01 Ω
b) 4.889E+01 Ω
c) 5.378E+01 Ω
d) 5.916E+01 Ω
e) 6.507E+01 Ω

9) An ac generator produces an emf of amplitude 49 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

a) 8.956E-01 A
b) 9.852E-01 A
c) 1.084E+00 A
d) 1.192E+00 A
e) 1.311E+00 A
10)
A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=7.30E+03 m2 and separation d=7.00E-03 m is connected via a swith to a 75 Ω resistor and a battery of voltage V0=78 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=1.90E-03?
a) 6.624E-02 A
b) 7.287E-02 A
c) 8.016E-02 A
d) 8.817E-02 A
e) 9.699E-02 A

#### T2(11-16) V1

1) A long solenoid has a radius of 0.394 m and 13 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 1.8 m from the axis at time t=0.0757 s ?

a) 2.132E-05 V/m
b) 2.345E-05 V/m
c) 2.579E-05 V/m
d) 2.837E-05 V/m
e) 3.121E-05 V/m

2) A solenoid has 9.880E+04 turns wound around a cylinder of diameter 1.5 cm and length 15 m. The current through the coils is 0.981 A. Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral ${\displaystyle \int {\vec {B}}\cdot {\vec {\ell }}}$ alongthe axis from z=−1.56 cm to z=+3.22 cm

a) 2.916E-04 T-m
b) 3.208E-04 T-m
c) 3.528E-04 T-m
d) 3.881E-04 T-m
e) 4.269E-04 T-m

3) A cyclotron used to accelerate alpha particlesm=6.64 x 10−27kg, q=3.2&#