# Quizbank/Electricity and Magnetism (calculus based)/c13

calcPhyEMq/c13 ID153287923206 (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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### c13 A0

1) 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

2) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 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=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.685E+00 A
b) 2.953E+00 A
c) 3.248E+00 A
d) 3.573E+00 A
e) 3.931E+00 A

3) 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

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

#### c13 A1

1) 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

2) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 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=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 5.743E-01 A
b) 6.318E-01 A
c) 6.950E-01 A
d) 7.645E-01 A
e) 8.409E-01 A

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

a) 7.402E-01 A
b) 8.142E-01 A
c) 8.956E-01 A
d) 9.852E-01 A
e) 1.084E+00 A

4) A long solenoid has a radius of 0.591 m and 41 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 0.234 m from the axis at time t=0.0208 s ?

a) 6.618E-05 V/m
b) 7.280E-05 V/m
c) 8.008E-05 V/m
d) 8.809E-05 V/m
e) 9.689E-05 V/m

#### c13 A2

1) A long solenoid has a radius of 0.845 m and 78 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 =}$20 s−1.What is the induced electric fied at a distance 0.214 m from the axis at time t=0.0655 s ?

a) 1.160E-04 V/m
b) 1.276E-04 V/m
c) 1.403E-04 V/m
d) 1.544E-04 V/m
e) 1.698E-04 V/m

2) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 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=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 5.743E-01 A
b) 6.318E-01 A
c) 6.950E-01 A
d) 7.645E-01 A
e) 8.409E-01 A

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.708 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.16)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$6.34 s. What is the current in the coil if the impedance of the coil is 89.8 Ω?

a) 2.313E-01 A
b) 2.544E-01 A
c) 2.798E-01 A
d) 3.078E-01 A
e) 3.386E-01 A

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

### c13 B0

1) A long solenoid has a radius of 0.845 m and 65 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 =}$30 s−1.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

a) 3.371E-04 V/m
b) 3.709E-04 V/m
c) 4.079E-04 V/m
d) 4.487E-04 V/m
e) 4.936E-04 V/m

2) A recangular coil with an area of 0.432 m2 and 16 turns is placed in a uniform magnetic field of 3.7 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 5.020E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 55 s?

a) 1.055E+05 V
b) 1.161E+05 V
c) 1.277E+05 V
d) 1.405E+05 V
e) 1.545E+05 V

3) 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

4) A long solenoid has a radius of 0.613 m and 75 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 =}$22 s−1.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

a) 1.370E-04 V/m
b) 1.507E-04 V/m
c) 1.657E-04 V/m
d) 1.823E-04 V/m
e) 2.005E-04 V/m

#### c13 B1

1) 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

2) A long solenoid has a radius of 0.845 m and 65 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 =}$30 s−1.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

a) 3.371E-04 V/m
b) 3.709E-04 V/m
c) 4.079E-04 V/m
d) 4.487E-04 V/m
e) 4.936E-04 V/m

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

a) 1.456E-04 V/m
b) 1.601E-04 V/m
c) 1.762E-04 V/m
d) 1.938E-04 V/m
e) 2.132E-04 V/m

4) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 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=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.685E+00 A
b) 2.953E+00 A
c) 3.248E+00 A
d) 3.573E+00 A
e) 3.931E+00 A

#### c13 B2

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

a) 3.792E+04 V
b) 4.172E+04 V
c) 4.589E+04 V
d) 5.048E+04 V
e) 5.552E+04 V

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

a) 3.660E+00 A
b) 4.027E+00 A
c) 4.429E+00 A
d) 4.872E+00 A
e) 5.359E+00 A

3) A long solenoid has a radius of 0.845 m and 65 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 =}$30 s−1.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

a) 3.371E-04 V/m
b) 3.709E-04 V/m
c) 4.079E-04 V/m
d) 4.487E-04 V/m
e) 4.936E-04 V/m

4) 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

### c13 C0

1) 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

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

a) 1.090E+04 V
b) 1.199E+04 V
c) 1.319E+04 V
d) 1.451E+04 V
e) 1.596E+04 V
3)
A cylinder of height 1.68 cm and radius 2.74 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 1.78 cm from point O and moves at a speed of 3.44 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) 8.324E+00 cm3/s
b) 9.157E+00 cm3/s
c) 1.007E+01 cm3/s
d) 1.108E+01 cm3/s
e) 1.219E+01 cm3/s

4) 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

#### c13 C1

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

a) 7.402E-01 A
b) 8.142E-01 A
c) 8.956E-01 A
d) 9.852E-01 A
e) 1.084E+00 A

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

a) 1.090E+04 V
b) 1.199E+04 V
c) 1.319E+04 V
d) 1.451E+04 V
e) 1.596E+04 V
3)
A cylinder of height 2.15 cm and radius 7.03 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 3.83 cm from point O and moves at a speed of 5.7 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) 6.534E+01 cm3/s
b) 7.188E+01 cm3/s
c) 7.907E+01 cm3/s
d) 8.697E+01 cm3/s
e) 9.567E+01 cm3/s

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

#### c13 C2

1)
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

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) 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

4) A long solenoid has a radius of 0.845 m and 78 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 =}$20 s−1.What is the induced electric fied at a distance 0.214 m from the axis at time t=0.0655 s ?

a) 1.160E-04 V/m
b) 1.276E-04 V/m
c) 1.403E-04 V/m
d) 1.544E-04 V/m
e) 1.698E-04 V/m

### c13 D0

1) A long solenoid has a radius of 0.887 m and 45 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 =}$25 s−1.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

a) 4.896E-05 V/m
b) 5.385E-05 V/m
c) 5.924E-05 V/m
d) 6.516E-05 V/m
e) 7.168E-05 V/m

2) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 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) 1.215E-04 V
b) 1.337E-04 V
c) 1.470E-04 V
d) 1.617E-04 V
e) 1.779E-04 V

3) Calculate the motional emf induced along a 24.9 km conductor moving at an orbital speed of 7.82 km/s perpendicular to Earth's 5.040E-05 Tesla magnetic field.

a) 8.111E+03 V
b) 8.922E+03 V
c) 9.814E+03 V
d) 1.080E+04 V
e) 1.187E+04 V

4) A recangular coil with an area of 0.219 m2 and 14 turns is placed in a uniform magnetic field of 3.71 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 7.540E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 15 s?

a) 2.959E+04 V
b) 3.255E+04 V
c) 3.581E+04 V
d) 3.939E+04 V
e) 4.332E+04 V

#### c13 D1

1) 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

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

a) 2.065E-04 V/m
b) 2.271E-04 V/m
c) 2.499E-04 V/m
d) 2.748E-04 V/m
e) 3.023E-04 V/m

3) Calculate the motional emf induced along a 24.9 km conductor moving at an orbital speed of 7.82 km/s perpendicular to Earth's 5.040E-05 Tesla magnetic field.

a) 8.111E+03 V
b) 8.922E+03 V
c) 9.814E+03 V
d) 1.080E+04 V
e) 1.187E+04 V

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

#### c13 D2

1) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 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) 1.215E-04 V
b) 1.337E-04 V
c) 1.470E-04 V
d) 1.617E-04 V
e) 1.779E-04 V

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 recangular coil with an area of 0.479 m2 and 11 turns is placed in a uniform magnetic field of 1.34 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 4.200E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 38 s?

a) 2.148E+04 V
b) 2.363E+04 V
c) 2.599E+04 V
d) 2.859E+04 V
e) 3.145E+04 V

4) 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

### c13 E0

1) 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

2) 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

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}=}$3.75 T and ${\displaystyle \omega =}$1.740E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.417 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) 1.168E+04 V
b) 1.284E+04 V
c) 1.413E+04 V
d) 1.554E+04 V
e) 1.710E+04 V
4)
A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.479E+00 cm3/s
b) 8.227E+00 cm3/s
c) 9.049E+00 cm3/s
d) 9.954E+00 cm3/s
e) 1.095E+01 cm3/s

#### c13 E1

1) 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

2) 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

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}=}$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
4)
A cylinder of height 1.69 cm and radius 4.56 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 2.33 cm from point O and moves at a speed of 4.9 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) 3.054E+01 cm3/s
b) 3.359E+01 cm3/s
c) 3.695E+01 cm3/s
d) 4.065E+01 cm3/s
e) 4.471E+01 cm3/s

#### c13 E2

1) 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
2)
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

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}=}$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

4) A long solenoid has a radius of 0.777 m and 67 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 =}$20 s−1.What is the induced electric fied at a distance 2.39 m from the axis at time t=0.0399 s ?

a) 3.924E-04 V/m
b) 4.317E-04 V/m
c) 4.748E-04 V/m
d) 5.223E-04 V/m
e) 5.745E-04 V/m

### c13 F0

1) 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

2) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 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=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.737E+00 A
b) 1.910E+00 A
c) 2.101E+00 A
d) 2.311E+00 A
e) 2.543E+00 A

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}=}$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

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

a) 1.090E+04 V
b) 1.199E+04 V
c) 1.319E+04 V
d) 1.451E+04 V
e) 1.596E+04 V

#### c13 F1

1) 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

2) 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

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}=}$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

4) 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

#### c13 F2

1) 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

2) A square coil has sides that are L= 0.245 m long and is tightly wound with N=925 turns of wire. The resistance of the coil is R=8.0 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=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.545E-01 A
b) 3.899E-01 A
c) 4.289E-01 A
d) 4.718E-01 A
e) 5.190E-01 A

3) Calculate the motional emf induced along a 27.5 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.520E-05 Tesla magnetic field.

a) 8.074E+03 V
b) 8.882E+03 V
c) 9.770E+03 V
d) 1.075E+04 V
e) 1.182E+04 V

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}=}$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

### c13 G0

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}=}$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

2) 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

3) 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

4) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 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) 2.081E-04 V
b) 2.289E-04 V
c) 2.518E-04 V
d) 2.770E-04 V
e) 3.047E-04 V

#### c13 G1

1) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 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=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 4.414E+00 A
b) 4.855E+00 A
c) 5.341E+00 A
d) 5.875E+00 A
e) 6.462E+00 A

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (3.01)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.53 s. What is the current in the coil if the impedance of the coil is 27.4 Ω?

a) 6.149E-01 A
b) 6.763E-01 A
c) 7.440E-01 A
d) 8.184E-01 A
e) 9.002E-01 A

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

a) 1.463E-04 V
b) 1.609E-04 V
c) 1.770E-04 V
d) 1.947E-04 V
e) 2.142E-04 V

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}=}$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

#### c13 G2

1) 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

2) 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

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}=}$3.31 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

4) 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

### c13 H0

1) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.45 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) 1.066E-04 V
b) 1.173E-04 V
c) 1.290E-04 V
d) 1.419E-04 V
e) 1.561E-04 V

2) A recangular coil with an area of 0.315 m2 and 20 turns is placed in a uniform magnetic field of 3.45 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 9.480E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 26 s?

a) 1.342E+04 V
b) 1.476E+04 V
c) 1.624E+04 V
d) 1.786E+04 V
e) 1.965E+04 V

3) 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

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

#### c13 H1

1) 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

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

a) 3.792E+04 V
b) 4.172E+04 V
c) 4.589E+04 V
d) 5.048E+04 V
e) 5.552E+04 V

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) 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

#### c13 H2

1) 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

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) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 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) 1.215E-04 V
b) 1.337E-04 V
c) 1.470E-04 V
d) 1.617E-04 V
e) 1.779E-04 V

4) A long solenoid has a radius of 0.887 m and 45 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 =}$25 s−1.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

a) 4.896E-05 V/m
b) 5.385E-05 V/m
c) 5.924E-05 V/m
d) 6.516E-05 V/m
e) 7.168E-05 V/m

### c13 I0

1) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 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=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 5.743E-01 A
b) 6.318E-01 A
c) 6.950E-01 A
d) 7.645E-01 A
e) 8.409E-01 A

2) Calculate the motional emf induced along a 24.4 km conductor moving at an orbital speed of 7.79 km/s perpendicular to Earth's 4.790E-05 Tesla magnetic field.

a) 6.840E+03 V
b) 7.524E+03 V
c) 8.277E+03 V
d) 9.105E+03 V
e) 1.002E+04 V
3)
A cylinder of height 2.58 cm and radius 9.47 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 3.62 cm from point O and moves at a speed of 4.7 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) 1.128E+02 cm3/s
b) 1.241E+02 cm3/s
c) 1.365E+02 cm3/s
d) 1.502E+02 cm3/s
e) 1.652E+02 cm3/s

4) 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

#### c13 I1

1) A square coil has sides that are L= 0.458 m long and is tightly wound with N=742 turns of wire. The resistance of the coil is R=6.81 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=0.0559 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.056E+00 A
b) 1.161E+00 A
c) 1.278E+00 A
d) 1.405E+00 A
e) 1.546E+00 A

2) Calculate the motional emf induced along a 24.9 km conductor moving at an orbital speed of 7.82 km/s perpendicular to Earth's 5.040E-05 Tesla magnetic field.

a) 8.111E+03 V
b) 8.922E+03 V
c) 9.814E+03 V
d) 1.080E+04 V
e) 1.187E+04 V
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 long solenoid has a radius of 0.613 m and 75 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 =}$22 s−1.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

a) 1.370E-04 V/m
b) 1.507E-04 V/m
c) 1.657E-04 V/m
d) 1.823E-04 V/m
e) 2.005E-04 V/m

#### c13 I2

1) A square coil has sides that are L= 0.465 m long and is tightly wound with N=954 turns of wire. The resistance of the coil is R=6.06 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=0.0367 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.136E+00 A
b) 1.249E+00 A
c) 1.374E+00 A
d) 1.512E+00 A
e) 1.663E+00 A

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

a) 1.536E+04 V
b) 1.690E+04 V
c) 1.859E+04 V
d) 2.045E+04 V
e) 2.249E+04 V

3) 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
4)
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

### c13 J0

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}=}$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

2) 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

3) 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

4) 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

#### c13 J1

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}=}$1.71 T and ${\displaystyle \omega =}$4.780E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.294 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) 1.510E+04 V
b) 1.661E+04 V
c) 1.827E+04 V
d) 2.010E+04 V
e) 2.211E+04 V

2) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns 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) 1.602E-04 V
b) 1.762E-04 V
c) 1.939E-04 V
d) 2.132E-04 V
e) 2.346E-04 V

3) 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

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

#### c13 J2

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}=}$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

2) 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

3) 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

4) 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

### c13 K0

1)
A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.479E+00 cm3/s
b) 8.227E+00 cm3/s
c) 9.049E+00 cm3/s
d) 9.954E+00 cm3/s
e) 1.095E+01 cm3/s

2) Calculate the motional emf induced along a 11.9 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.870E-05 Tesla magnetic field.

a) 3.736E+03 V
b) 4.109E+03 V
c) 4.520E+03 V
d) 4.972E+03 V
e) 5.470E+03 V

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}=}$3.75 T and ${\displaystyle \omega =}$1.740E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.417 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) 1.168E+04 V
b) 1.284E+04 V
c) 1.413E+04 V
d) 1.554E+04 V
e) 1.710E+04 V

4) A long solenoid has a radius of 0.436 m and 87 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 =}$27 s−1.What is the induced electric fied at a distance 0.153 m from the axis at time t=0.02 s ?

a) 4.785E-04 V/m
b) 5.264E-04 V/m
c) 5.790E-04 V/m
d) 6.369E-04 V/m
e) 7.006E-04 V/m

#### c13 K1

1) A long solenoid has a radius of 0.887 m and 45 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 =}$25 s−1.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

a) 4.896E-05 V/m
b) 5.385E-05 V/m
c) 5.924E-05 V/m
d) 6.516E-05 V/m
e) 7.168E-05 V/m

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}=}$1.89 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
3)
A cylinder of height 2.15 cm and radius 7.03 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 3.83 cm from point O and moves at a speed of 5.7 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) 6.534E+01 cm3/s
b) 7.188E+01 cm3/s
c) 7.907E+01 cm3/s
d) 8.697E+01 cm3/s
e) 9.567E+01 cm3/s

4) 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

#### c13 K2

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}=}$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
2)
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

3) 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

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

### c13 L0

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 time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.549 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.97)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.0 s. What is the current in the coil if the impedance of the coil is 46.7 Ω?

a) 2.032E-01 A
b) 2.235E-01 A
c) 2.458E-01 A
d) 2.704E-01 A
e) 2.975E-01 A

3) 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

4) 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

#### c13 L1

1) 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

2) 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

3) 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

4) A long solenoid has a radius of 0.613 m and 75 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 =}$22 s−1.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

a) 1.370E-04 V/m
b) 1.507E-04 V/m
c) 1.657E-04 V/m
d) 1.823E-04 V/m
e) 2.005E-04 V/m

#### c13 L2

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.348 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.3)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.57 s. What is the current in the coil if the impedance of the coil is 68.6 Ω?

a) 5.720E-02 A
b) 6.292E-02 A
c) 6.921E-02 A
d) 7.613E-02 A
e) 8.375E-02 A

2) A recangular coil with an area of 0.897 m2 and 8 turns is placed in a uniform magnetic field of 2.83 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 8.740E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 3 s?

a) 4.695E+04 V
b) 5.165E+04 V
c) 5.681E+04 V
d) 6.249E+04 V
e) 6.874E+04 V

3) 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

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

a) 1.456E-04 V/m
b) 1.601E-04 V/m
c) 1.762E-04 V/m
d) 1.938E-04 V/m
e) 2.132E-04 V/m

### c13 M0

1) 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

2) 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

3) 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

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}=}$3.79 T and ${\displaystyle \omega =}$7.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.668 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) 7.910E+04 V
b) 8.701E+04 V
c) 9.571E+04 V
d) 1.053E+05 V
e) 1.158E+05 V

#### c13 M1

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}=}$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

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) 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

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

#### c13 M2

1) A recangular coil with an area of 0.315 m2 and 20 turns is placed in a uniform magnetic field of 3.45 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 9.480E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 26 s?

a) 1.342E+04 V
b) 1.476E+04 V
c) 1.624E+04 V
d) 1.786E+04 V
e) 1.965E+04 V

2) A long solenoid has a radius of 0.806 m and 41 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 2.67 m from the axis at time t=0.0701 s ?

a) 6.040E-05 V/m
b) 6.644E-05 V/m
c) 7.309E-05 V/m
d) 8.039E-05 V/m
e) 8.843E-05 V/m

3) 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

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

### c13 N0

1) 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

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

a) 1.616E-04 V/m
b) 1.778E-04 V/m
c) 1.955E-04 V/m
d) 2.151E-04 V/m
e) 2.366E-04 V/m

3) 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

4) A long solenoid has a radius of 0.447 m and 85 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 =}$23 s−1.What is the induced electric fied at a distance 0.212 m from the axis at time t=0.0819 s ?

a) 1.893E-04 V/m
b) 2.082E-04 V/m
c) 2.290E-04 V/m
d) 2.519E-04 V/m
e) 2.771E-04 V/m

#### c13 N1

1) 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

2) 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

3) 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

4) A long solenoid has a radius of 0.591 m and 41 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 0.234 m from the axis at time t=0.0208 s ?

a) 6.618E-05 V/m
b) 7.280E-05 V/m
c) 8.008E-05 V/m
d) 8.809E-05 V/m
e) 9.689E-05 V/m

#### c13 N2

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 current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 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) 1.215E-04 V
b) 1.337E-04 V
c) 1.470E-04 V
d) 1.617E-04 V
e) 1.779E-04 V

3) 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

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

a) 6.182E-04 V/m
b) 6.801E-04 V/m
c) 7.481E-04 V/m
d) 8.229E-04 V/m
e) 9.052E-04 V/m

### c13 O0

1)
A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.479E+00 cm3/s
b) 8.227E+00 cm3/s
c) 9.049E+00 cm3/s
d) 9.954E+00 cm3/s
e) 1.095E+01 cm3/s

2) 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

3) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 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=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.685E+00 A
b) 2.953E+00 A
c) 3.248E+00 A
d) 3.573E+00 A
e) 3.931E+00 A

4) Calculate the motional emf induced along a 11.9 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.870E-05 Tesla magnetic field.

a) 3.736E+03 V
b) 4.109E+03 V
c) 4.520E+03 V
d) 4.972E+03 V
e) 5.470E+03 V

#### c13 O1

1)
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

2) 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

3) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 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=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 4.414E+00 A
b) 4.855E+00 A
c) 5.341E+00 A
d) 5.875E+00 A
e) 6.462E+00 A

4) 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

#### c13 O2

1) 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
2)
A cylinder of height 1.69 cm and radius 4.56 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 2.33 cm from point O and moves at a speed of 4.9 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) 3.054E+01 cm3/s
b) 3.359E+01 cm3/s
c) 3.695E+01 cm3/s
d) 4.065E+01 cm3/s
e) 4.471E+01 cm3/s

3) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 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=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 5.743E-01 A
b) 6.318E-01 A
c) 6.950E-01 A
d) 7.645E-01 A
e) 8.409E-01 A

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

### c13 P0

1) 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
2)
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

3) 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

4) A long solenoid has a radius of 0.613 m and 75 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 =}$22 s−1.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

a) 1.370E-04 V/m
b) 1.507E-04 V/m
c) 1.657E-04 V/m
d) 1.823E-04 V/m
e) 2.005E-04 V/m

#### c13 P1

1) A long solenoid has a radius of 0.591 m and 41 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 0.234 m from the axis at time t=0.0208 s ?

a) 6.618E-05 V/m
b) 7.280E-05 V/m
c) 8.008E-05 V/m
d) 8.809E-05 V/m
e) 9.689E-05 V/m

2) 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
3)
A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.479E+00 cm3/s
b) 8.227E+00 cm3/s
c) 9.049E+00 cm3/s
d) 9.954E+00 cm3/s
e) 1.095E+01 cm3/s

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

#### c13 P2

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

a) 1.536E+04 V
b) 1.690E+04 V
c) 1.859E+04 V
d) 2.045E+04 V
e) 2.249E+04 V
2)
A cylinder of height 1.68 cm and radius 2.74 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 1.78 cm from point O and moves at a speed of 3.44 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) 8.324E+00 cm3/s
b) 9.157E+00 cm3/s
c) 1.007E+01 cm3/s
d) 1.108E+01 cm3/s
e) 1.219E+01 cm3/s

3) 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

4) 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

### c13 Q0

1) A recangular coil with an area of 0.446 m2 and 13 turns is placed in a uniform magnetic field of 3.17 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 5.060E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 54 s?

a) 1.957E+03 V
b) 2.153E+03 V
c) 2.368E+03 V
d) 2.605E+03 V
e) 2.865E+03 V

2) 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

3) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 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=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.737E+00 A
b) 1.910E+00 A
c) 2.101E+00 A
d) 2.311E+00 A
e) 2.543E+00 A

4) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 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) 2.081E-04 V
b) 2.289E-04 V
c) 2.518E-04 V
d) 2.770E-04 V
e) 3.047E-04 V

#### c13 Q1

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.348 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.3)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.57 s. What is the current in the coil if the impedance of the coil is 68.6 Ω?

a) 5.720E-02 A
b) 6.292E-02 A
c) 6.921E-02 A
d) 7.613E-02 A
e) 8.375E-02 A

2) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns 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) 1.602E-04 V
b) 1.762E-04 V
c) 1.939E-04 V
d) 2.132E-04 V
e) 2.346E-04 V

3) 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

4) A recangular coil with an area of 0.157 m2 and 17 turns is placed in a uniform magnetic field of 3.64 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 5.890E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 9 s?

a) 4.464E+04 V
b) 4.911E+04 V
c) 5.402E+04 V
d) 5.942E+04 V
e) 6.536E+04 V

#### c13 Q2

1) 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

2) 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

3) 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

4) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 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) 2.081E-04 V
b) 2.289E-04 V
c) 2.518E-04 V
d) 2.770E-04 V
e) 3.047E-04 V

### c13 R0

1) A long solenoid has a radius of 0.887 m and 45 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 =}$25 s−1.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

a) 4.896E-05 V/m
b) 5.385E-05 V/m
c) 5.924E-05 V/m
d) 6.516E-05 V/m
e) 7.168E-05 V/m

2) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 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=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.737E+00 A
b) 1.910E+00 A
c) 2.101E+00 A
d) 2.311E+00 A
e) 2.543E+00 A

3) 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
4)
A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.479E+00 cm3/s
b) 8.227E+00 cm3/s
c) 9.049E+00 cm3/s
d) 9.954E+00 cm3/s
e) 1.095E+01 cm3/s

#### c13 R1

1) 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

2) 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
3)
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

4) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 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=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 4.414E+00 A
b) 4.855E+00 A
c) 5.341E+00 A
d) 5.875E+00 A
e) 6.462E+00 A

#### c13 R2

1) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 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=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 5.743E-01 A
b) 6.318E-01 A
c) 6.950E-01 A
d) 7.645E-01 A
e) 8.409E-01 A
2)
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

3) A long solenoid has a radius of 0.436 m and 87 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 =}$27 s−1.What is the induced electric fied at a distance 0.153 m from the axis at time t=0.02 s ?

a) 4.785E-04 V/m
b) 5.264E-04 V/m
c) 5.790E-04 V/m
d) 6.369E-04 V/m
e) 7.006E-04 V/m

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

### c13 S0

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) 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

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}=}$3.11 T and ${\displaystyle \omega =}$1.150E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.171 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) 2.887E+03 V
b) 3.176E+03 V
c) 3.493E+03 V
d) 3.843E+03 V
e) 4.227E+03 V

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

#### c13 S1

1) 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

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}=}$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

3) 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

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

#### c13 S2

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) 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

3) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.45 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) 1.066E-04 V
b) 1.173E-04 V
c) 1.290E-04 V
d) 1.419E-04 V
e) 1.561E-04 V

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}=}$3.11 T and ${\displaystyle \omega =}$1.150E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.171 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) 2.887E+03 V
b) 3.176E+03 V
c) 3.493E+03 V
d) 3.843E+03 V
e) 4.227E+03 V

### c13 T0

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (3.01)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.53 s. What is the current in the coil if the impedance of the coil is 27.4 Ω?

a) 6.149E-01 A
b) 6.763E-01 A
c) 7.440E-01 A
d) 8.184E-01 A
e) 9.002E-01 A

2) 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

3) A recangular coil with an area of 0.219 m2 and 14 turns is placed in a uniform magnetic field of 3.71 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 7.540E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 15 s?

a) 2.959E+04 V
b) 3.255E+04 V
c) 3.581E+04 V
d) 3.939E+04 V
e) 4.332E+04 V

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}=}$3.79 T and ${\displaystyle \omega =}$7.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.668 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) 7.910E+04 V
b) 8.701E+04 V
c) 9.571E+04 V
d) 1.053E+05 V
e) 1.158E+05 V

#### c13 T1

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (3.01)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.53 s. What is the current in the coil if the impedance of the coil is 27.4 Ω?

a) 6.149E-01 A
b) 6.763E-01 A
c) 7.440E-01 A
d) 8.184E-01 A
e) 9.002E-01 A

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}=}$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

3) 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

4) A recangular coil with an area of 0.897 m2 and 8 turns is placed in a uniform magnetic field of 2.83 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 8.740E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 3 s?

a) 4.695E+04 V
b) 5.165E+04 V
c) 5.681E+04 V
d) 6.249E+04 V
e) 6.874E+04 V

#### c13 T2

1) 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

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

a) 3.792E+04 V
b) 4.172E+04 V
c) 4.589E+04 V
d) 5.048E+04 V
e) 5.552E+04 V

4) 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

### c13 U0

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

a) 1.463E-04 V
b) 1.609E-04 V
c) 1.770E-04 V
d) 1.947E-04 V
e) 2.142E-04 V

2) Calculate the motional emf induced along a 27.5 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.520E-05 Tesla magnetic field.

a) 8.074E+03 V
b) 8.882E+03 V
c) 9.770E+03 V
d) 1.075E+04 V
e) 1.182E+04 V

3) A long solenoid has a radius of 0.806 m and 41 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 2.67 m from the axis at time t=0.0701 s ?

a) 6.040E-05 V/m
b) 6.644E-05 V/m
c) 7.309E-05 V/m
d) 8.039E-05 V/m
e) 8.843E-05 V/m

4) 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

#### c13 U1

1) 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

2) 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

3) 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

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

#### c13 U2

1) 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

2) 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

3) 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

4) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns 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) 1.602E-04 V
b) 1.762E-04 V
c) 1.939E-04 V
d) 2.132E-04 V
e) 2.346E-04 V

### c13 V0

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}=}$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

2) Calculate the motional emf induced along a 11.9 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.870E-05 Tesla magnetic field.

a) 3.736E+03 V
b) 4.109E+03 V
c) 4.520E+03 V
d) 4.972E+03 V
e) 5.470E+03 V
3)
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

4) 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

#### c13 V1

1) 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

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}=}$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
3)
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

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

#### c13 V2

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}=}$3.11 T and ${\displaystyle \omega =}$1.150E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.171 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) 2.887E+03 V
b) 3.176E+03 V
c) 3.493E+03 V
d) 3.843E+03 V
e) 4.227E+03 V

2) 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
3)
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

4) Calculate the motional emf induced along a 24.4 km conductor moving at an orbital speed of 7.79 km/s perpendicular to Earth's 4.790E-05 Tesla magnetic field.

a) 6.840E+03 V
b) 7.524E+03 V
c) 8.277E+03 V
d) 9.105E+03 V
e) 1.002E+04 V

### c13 W0

1)
A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.892E+01 cm3/s
b) 2.081E+01 cm3/s
c) 2.289E+01 cm3/s
d) 2.518E+01 cm3/s
e) 2.770E+01 cm3/s

2) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 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=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.685E+00 A
b) 2.953E+00 A
c) 3.248E+00 A
d) 3.573E+00 A
e) 3.931E+00 A

3) A long solenoid has a radius of 0.887 m and 45 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 =}$25 s−1.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

a) 4.896E-05 V/m
b) 5.385E-05 V/m
c) 5.924E-05 V/m
d) 6.516E-05 V/m
e) 7.168E-05 V/m

4) 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

#### c13 W1

1) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 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=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.661E+00 A
b) 4.028E+00 A
c) 4.430E+00 A
d) 4.873E+00 A
e) 5.361E+00 A

2) 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
3)
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

4) 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

#### c13 W2

1) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns 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) 1.602E-04 V
b) 1.762E-04 V
c) 1.939E-04 V
d) 2.132E-04 V
e) 2.346E-04 V
2)
A cylinder of height 2.58 cm and radius 9.47 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 3.62 cm from point O and moves at a speed of 4.7 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) 1.128E+02 cm3/s
b) 1.241E+02 cm3/s
c) 1.365E+02 cm3/s
d) 1.502E+02 cm3/s
e) 1.652E+02 cm3/s

3) 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

4) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 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=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.685E+00 A
b) 2.953E+00 A
c) 3.248E+00 A
d) 3.573E+00 A
e) 3.931E+00 A

### c13 X0

1) Calculate the motional emf induced along a 24.4 km conductor moving at an orbital speed of 7.79 km/s perpendicular to Earth's 4.790E-05 Tesla magnetic field.

a) 6.840E+03 V
b) 7.524E+03 V
c) 8.277E+03 V
d) 9.105E+03 V
e) 1.002E+04 V
2)
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

3) A recangular coil with an area of 0.219 m2 and 14 turns is placed in a uniform magnetic field of 3.71 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 7.540E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 15 s?

a) 2.959E+04 V
b) 3.255E+04 V
c) 3.581E+04 V
d) 3.939E+04 V
e) 4.332E+04 V

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

#### c13 X1

1) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 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=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.661E+00 A
b) 4.028E+00 A
c) 4.430E+00 A
d) 4.873E+00 A
e) 5.361E+00 A

2) 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

3) Calculate the motional emf induced along a 25.2 km conductor moving at an orbital speed of 7.72 km/s perpendicular to Earth's 4.900E-05 Tesla magnetic field.

a) 7.162E+03 V
b) 7.878E+03 V
c) 8.666E+03 V
d) 9.533E+03 V
e) 1.049E+04 V
4)
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

#### c13 X2

1) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 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=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.737E+00 A
b) 1.910E+00 A
c) 2.101E+00 A
d) 2.311E+00 A
e) 2.543E+00 A
2)
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

3) 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

4) A recangular coil with an area of 0.219 m2 and 14 turns is placed in a uniform magnetic field of 3.71 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 7.540E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 15 s?

a) 2.959E+04 V
b) 3.255E+04 V
c) 3.581E+04 V
d) 3.939E+04 V
e) 4.332E+04 V

### c13 Y0

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 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) 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

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

a) 6.182E-04 V/m
b) 6.801E-04 V/m
c) 7.481E-04 V/m
d) 8.229E-04 V/m
e) 9.052E-04 V/m

#### c13 Y1

1) A recangular coil with an area of 0.897 m2 and 8 turns is placed in a uniform magnetic field of 2.83 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 8.740E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 3 s?

a) 4.695E+04 V
b) 5.165E+04 V
c) 5.681E+04 V
d) 6.249E+04 V
e) 6.874E+04 V

2) 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

3) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 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=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.685E+00 A
b) 2.953E+00 A
c) 3.248E+00 A
d) 3.573E+00 A
e) 3.931E+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

#### c13 Y2

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 square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 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=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.661E+00 A
b) 4.028E+00 A
c) 4.430E+00 A
d) 4.873E+00 A
e) 5.361E+00 A

3) 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

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

a) 7.734E+04 V
b) 8.507E+04 V
c) 9.358E+04 V
d) 1.029E+05 V
e) 1.132E+05 V

### c13 Z0

1) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 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) 2.081E-04 V
b) 2.289E-04 V
c) 2.518E-04 V
d) 2.770E-04 V
e) 3.047E-04 V

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (3.01)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.53 s. What is the current in the coil if the impedance of the coil is 27.4 Ω?

a) 6.149E-01 A
b) 6.763E-01 A
c) 7.440E-01 A
d) 8.184E-01 A
e) 9.002E-01 A
3)
A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.892E+01 cm3/s
b) 2.081E+01 cm3/s
c) 2.289E+01 cm3/s
d) 2.518E+01 cm3/s
e) 2.770E+01 cm3/s

4) A recangular coil with an area of 0.219 m2 and 14 turns is placed in a uniform magnetic field of 3.71 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 7.540E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 15 s?

a) 2.959E+04 V
b) 3.255E+04 V
c) 3.581E+04 V
d) 3.939E+04 V
e) 4.332E+04 V

#### c13 Z1

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

a) 7.402E-01 A
b) 8.142E-01 A
c) 8.956E-01 A
d) 9.852E-01 A
e) 1.084E+00 A

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

a) 1.463E-04 V
b) 1.609E-04 V
c) 1.770E-04 V
d) 1.947E-04 V
e) 2.142E-04 V

3) 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
4)
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

#### c13 Z2

1) The current through the windings of a solenoid with n= 2.840E+03 turns per meter is changing at a rate dI/dt=19 A/s. The solenoid is 65 cm long and has a cross-sectional diameter of 2.18 cm. A small coil consisting of N=25turns 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) 2.206E-04 V
b) 2.426E-04 V
c) 2.669E-04 V
d) 2.936E-04 V
e) 3.230E-04 V

2) 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

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

a) 4.465E+04 V
b) 4.912E+04 V
c) 5.403E+04 V
d) 5.943E+04 V
e) 6.538E+04 V
4)
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

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### Key: A0

1) 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

2) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 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=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 2.685E+00 A
-b) 2.953E+00 A
+c) 3.248E+00 A
-d) 3.573E+00 A
-e) 3.931E+00 A

3) 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

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

Click these links for the keys:

#### Key: A1

1) 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

2) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 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=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

+a) 5.743E-01 A
-b) 6.318E-01 A
-c) 6.950E-01 A
-d) 7.645E-01 A
-e) 8.409E-01 A

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

-a) 7.402E-01 A
-b) 8.142E-01 A
-c) 8.956E-01 A
+d) 9.852E-01 A
-e) 1.084E+00 A

4) A long solenoid has a radius of 0.591 m and 41 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 0.234 m from the axis at time t=0.0208 s ?

-a) 6.618E-05 V/m
-b) 7.280E-05 V/m
-c) 8.008E-05 V/m
-d) 8.809E-05 V/m
+e) 9.689E-05 V/m

Click these links for the keys:

#### Key: A2

1) A long solenoid has a radius of 0.845 m and 78 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 =}$20 s−1.What is the induced electric fied at a distance 0.214 m from the axis at time t=0.0655 s ?

-a) 1.160E-04 V/m
-b) 1.276E-04 V/m
-c) 1.403E-04 V/m
-d) 1.544E-04 V/m
+e) 1.698E-04 V/m

2) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 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=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

+a) 5.743E-01 A
-b) 6.318E-01 A
-c) 6.950E-01 A
-d) 7.645E-01 A
-e) 8.409E-01 A

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.708 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.16)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$6.34 s. What is the current in the coil if the impedance of the coil is 89.8 Ω?

-a) 2.313E-01 A
-b) 2.544E-01 A
-c) 2.798E-01 A
-d) 3.078E-01 A
+e) 3.386E-01 A

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

Click these links for the keys:

### Key: B0

1) A long solenoid has a radius of 0.845 m and 65 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 =}$30 s−1.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

-a) 3.371E-04 V/m
+b) 3.709E-04 V/m
-c) 4.079E-04 V/m
-d) 4.487E-04 V/m
-e) 4.936E-04 V/m

2) A recangular coil with an area of 0.432 m2 and 16 turns is placed in a uniform magnetic field of 3.7 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 5.020E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 55 s?

-a) 1.055E+05 V
+b) 1.161E+05 V
-c) 1.277E+05 V
-d) 1.405E+05 V
-e) 1.545E+05 V

3) 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

4) A long solenoid has a radius of 0.613 m and 75 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 =}$22 s−1.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

-a) 1.370E-04 V/m
-b) 1.507E-04 V/m
-c) 1.657E-04 V/m
+d) 1.823E-04 V/m
-e) 2.005E-04 V/m

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#### Key: B1

1) 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

2) A long solenoid has a radius of 0.845 m and 65 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 =}$30 s−1.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

-a) 3.371E-04 V/m
+b) 3.709E-04 V/m
-c) 4.079E-04 V/m
-d) 4.487E-04 V/m
-e) 4.936E-04 V/m

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

-a) 1.456E-04 V/m
-b) 1.601E-04 V/m
-c) 1.762E-04 V/m
+d) 1.938E-04 V/m
-e) 2.132E-04 V/m

4) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 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=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 2.685E+00 A
-b) 2.953E+00 A
+c) 3.248E+00 A
-d) 3.573E+00 A
-e) 3.931E+00 A

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#### Key: B2

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

-a) 3.792E+04 V
-b) 4.172E+04 V
-c) 4.589E+04 V
+d) 5.048E+04 V
-e) 5.552E+04 V

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

-a) 3.660E+00 A
-b) 4.027E+00 A
-c) 4.429E+00 A
+d) 4.872E+00 A
-e) 5.359E+00 A

3) A long solenoid has a radius of 0.845 m and 65 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 =}$30 s−1.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

-a) 3.371E-04 V/m
+b) 3.709E-04 V/m
-c) 4.079E-04 V/m
-d) 4.487E-04 V/m
-e) 4.936E-04 V/m

4) 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

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### Key: C0

1) 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

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

-a) 1.090E+04 V
+b) 1.199E+04 V
-c) 1.319E+04 V
-d) 1.451E+04 V
-e) 1.596E+04 V
3)
A cylinder of height 1.68 cm and radius 2.74 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 1.78 cm from point O and moves at a speed of 3.44 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) 8.324E+00 cm3/s
-b) 9.157E+00 cm3/s
-c) 1.007E+01 cm3/s
-d) 1.108E+01 cm3/s
+e) 1.219E+01 cm3/s

4) 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

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#### Key: C1

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

-a) 7.402E-01 A
-b) 8.142E-01 A
-c) 8.956E-01 A
+d) 9.852E-01 A
-e) 1.084E+00 A

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

-a) 1.090E+04 V
+b) 1.199E+04 V
-c) 1.319E+04 V
-d) 1.451E+04 V
-e) 1.596E+04 V
3)
A cylinder of height 2.15 cm and radius 7.03 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 3.83 cm from point O and moves at a speed of 5.7 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) 6.534E+01 cm3/s
-b) 7.188E+01 cm3/s
+c) 7.907E+01 cm3/s
-d) 8.697E+01 cm3/s
-e) 9.567E+01 cm3/s

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

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#### Key: C2

1)
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

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) 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

4) A long solenoid has a radius of 0.845 m and 78 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 =}$20 s−1.What is the induced electric fied at a distance 0.214 m from the axis at time t=0.0655 s ?

-a) 1.160E-04 V/m
-b) 1.276E-04 V/m
-c) 1.403E-04 V/m
-d) 1.544E-04 V/m
+e) 1.698E-04 V/m

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### Key: D0

1) A long solenoid has a radius of 0.887 m and 45 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 =}$25 s−1.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

-a) 4.896E-05 V/m
-b) 5.385E-05 V/m
+c) 5.924E-05 V/m
-d) 6.516E-05 V/m
-e) 7.168E-05 V/m

2) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 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) 1.215E-04 V
-b) 1.337E-04 V
-c) 1.470E-04 V
-d) 1.617E-04 V
+e) 1.779E-04 V

3) Calculate the motional emf induced along a 24.9 km conductor moving at an orbital speed of 7.82 km/s perpendicular to Earth's 5.040E-05 Tesla magnetic field.

-a) 8.111E+03 V
-b) 8.922E+03 V
+c) 9.814E+03 V
-d) 1.080E+04 V
-e) 1.187E+04 V

4) A recangular coil with an area of 0.219 m2 and 14 turns is placed in a uniform magnetic field of 3.71 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 7.540E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 15 s?

-a) 2.959E+04 V
-b) 3.255E+04 V
-c) 3.581E+04 V
+d) 3.939E+04 V
-e) 4.332E+04 V

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#### Key: D1

1) 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

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

+a) 2.065E-04 V/m
-b) 2.271E-04 V/m
-c) 2.499E-04 V/m
-d) 2.748E-04 V/m
-e) 3.023E-04 V/m

3) Calculate the motional emf induced along a 24.9 km conductor moving at an orbital speed of 7.82 km/s perpendicular to Earth's 5.040E-05 Tesla magnetic field.

-a) 8.111E+03 V
-b) 8.922E+03 V
+c) 9.814E+03 V
-d) 1.080E+04 V
-e) 1.187E+04 V

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

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#### Key: D2

1) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 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) 1.215E-04 V
-b) 1.337E-04 V
-c) 1.470E-04 V
-d) 1.617E-04 V
+e) 1.779E-04 V

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 recangular coil with an area of 0.479 m2 and 11 turns is placed in a uniform magnetic field of 1.34 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 4.200E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 38 s?

+a) 2.148E+04 V
-b) 2.363E+04 V
-c) 2.599E+04 V
-d) 2.859E+04 V
-e) 3.145E+04 V

4) 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

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### Key: E0

1) 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

2) 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

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}=}$3.75 T and ${\displaystyle \omega =}$1.740E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.417 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) 1.168E+04 V
-b) 1.284E+04 V
-c) 1.413E+04 V
-d) 1.554E+04 V
+e) 1.710E+04 V
4)
A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
-a) 7.479E+00 cm3/s
-b) 8.227E+00 cm3/s
-c) 9.049E+00 cm3/s
-d) 9.954E+00 cm3/s
+e) 1.095E+01 cm3/s

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#### Key: E1

1) 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

2) 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

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}=}$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
4)
A cylinder of height 1.69 cm and radius 4.56 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 2.33 cm from point O and moves at a speed of 4.9 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) 3.054E+01 cm3/s
-b) 3.359E+01 cm3/s
+c) 3.695E+01 cm3/s
-d) 4.065E+01 cm3/s
-e) 4.471E+01 cm3/s

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#### Key: E2

1) 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
2)
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

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}=}$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

4) A long solenoid has a radius of 0.777 m and 67 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 =}$20 s−1.What is the induced electric fied at a distance 2.39 m from the axis at time t=0.0399 s ?

-a) 3.924E-04 V/m
-b) 4.317E-04 V/m
-c) 4.748E-04 V/m
-d) 5.223E-04 V/m
+e) 5.745E-04 V/m

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### Key: F0

1) 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

2) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 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=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 1.737E+00 A
+b) 1.910E+00 A
-c) 2.101E+00 A
-d) 2.311E+00 A
-e) 2.543E+00 A

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}=}$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

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

-a) 1.090E+04 V
+b) 1.199E+04 V
-c) 1.319E+04 V
-d) 1.451E+04 V
-e) 1.596E+04 V

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#### Key: F1

1) 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

2) 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

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}=}$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

4) 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

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#### Key: F2

1) 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

2) A square coil has sides that are L= 0.245 m long and is tightly wound with N=925 turns of wire. The resistance of the coil is R=8.0 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=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 3.545E-01 A
-b) 3.899E-01 A
+c) 4.289E-01 A
-d) 4.718E-01 A
-e) 5.190E-01 A

3) Calculate the motional emf induced along a 27.5 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.520E-05 Tesla magnetic field.

-a) 8.074E+03 V
-b) 8.882E+03 V
+c) 9.770E+03 V
-d) 1.075E+04 V
-e) 1.182E+04 V

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}=}$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

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### Key: G0

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}=}$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

2) 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

3) 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

4) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 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) 2.081E-04 V
-b) 2.289E-04 V
-c) 2.518E-04 V
+d) 2.770E-04 V
-e) 3.047E-04 V

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#### Key: G1

1) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 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=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 4.414E+00 A
-b) 4.855E+00 A
-c) 5.341E+00 A
-d) 5.875E+00 A
+e) 6.462E+00 A

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (3.01)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.53 s. What is the current in the coil if the impedance of the coil is 27.4 Ω?

-a) 6.149E-01 A
-b) 6.763E-01 A
-c) 7.440E-01 A
+d) 8.184E-01 A
-e) 9.002E-01 A

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

-a) 1.463E-04 V
-b) 1.609E-04 V
-c) 1.770E-04 V
-d) 1.947E-04 V
+e) 2.142E-04 V

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}=}$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

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#### Key: G2

1) 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

2) 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

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}=}$3.31 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

4) 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

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### Key: H0

1) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.45 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) 1.066E-04 V
-b) 1.173E-04 V
+c) 1.290E-04 V
-d) 1.419E-04 V
-e) 1.561E-04 V

2) A recangular coil with an area of 0.315 m2 and 20 turns is placed in a uniform magnetic field of 3.45 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 9.480E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 26 s?

+a) 1.342E+04 V
-b) 1.476E+04 V
-c) 1.624E+04 V
-d) 1.786E+04 V
-e) 1.965E+04 V

3) 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

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

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#### Key: H1

1) 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

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

-a) 3.792E+04 V
-b) 4.172E+04 V
-c) 4.589E+04 V
+d) 5.048E+04 V
-e) 5.552E+04 V

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) 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

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#### Key: H2

1) 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

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) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 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) 1.215E-04 V
-b) 1.337E-04 V
-c) 1.470E-04 V
-d) 1.617E-04 V
+e) 1.779E-04 V

4) A long solenoid has a radius of 0.887 m and 45 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 =}$25 s−1.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

-a) 4.896E-05 V/m
-b) 5.385E-05 V/m
+c) 5.924E-05 V/m
-d) 6.516E-05 V/m
-e) 7.168E-05 V/m

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### Key: I0

1) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 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=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

+a) 5.743E-01 A
-b) 6.318E-01 A
-c) 6.950E-01 A
-d) 7.645E-01 A
-e) 8.409E-01 A

2) Calculate the motional emf induced along a 24.4 km conductor moving at an orbital speed of 7.79 km/s perpendicular to Earth's 4.790E-05 Tesla magnetic field.

-a) 6.840E+03 V
-b) 7.524E+03 V
-c) 8.277E+03 V
+d) 9.105E+03 V
-e) 1.002E+04 V
3)
A cylinder of height 2.58 cm and radius 9.47 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 3.62 cm from point O and moves at a speed of 4.7 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) 1.128E+02 cm3/s
-b) 1.241E+02 cm3/s
-c) 1.365E+02 cm3/s
+d) 1.502E+02 cm3/s
-e) 1.652E+02 cm3/s

4) 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

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#### Key: I1

1) A square coil has sides that are L= 0.458 m long and is tightly wound with N=742 turns of wire. The resistance of the coil is R=6.81 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=0.0559 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 1.056E+00 A
-b) 1.161E+00 A
+c) 1.278E+00 A
-d) 1.405E+00 A
-e) 1.546E+00 A

2) Calculate the motional emf induced along a 24.9 km conductor moving at an orbital speed of 7.82 km/s perpendicular to Earth's 5.040E-05 Tesla magnetic field.

-a) 8.111E+03 V
-b) 8.922E+03 V
+c) 9.814E+03 V
-d) 1.080E+04 V
-e) 1.187E+04 V
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 long solenoid has a radius of 0.613 m and 75 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 =}$22 s−1.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

-a) 1.370E-04 V/m
-b) 1.507E-04 V/m
-c) 1.657E-04 V/m
+d) 1.823E-04 V/m
-e) 2.005E-04 V/m

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#### Key: I2

1) A square coil has sides that are L= 0.465 m long and is tightly wound with N=954 turns of wire. The resistance of the coil is R=6.06 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=0.0367 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 1.136E+00 A
+b) 1.249E+00 A
-c) 1.374E+00 A
-d) 1.512E+00 A
-e) 1.663E+00 A

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

-a) 1.536E+04 V
+b) 1.690E+04 V
-c) 1.859E+04 V
-d) 2.045E+04 V
-e) 2.249E+04 V

3) 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
4)
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

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### Key: J0

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}=}$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

2) 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

3) 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

4) 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

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#### Key: J1

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}=}$1.71 T and ${\displaystyle \omega =}$4.780E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.294 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) 1.510E+04 V
-b) 1.661E+04 V
-c) 1.827E+04 V
-d) 2.010E+04 V
-e) 2.211E+04 V

2) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns 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) 1.602E-04 V
-b) 1.762E-04 V
+c) 1.939E-04 V
-d) 2.132E-04 V
-e) 2.346E-04 V

3) 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

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

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#### Key: J2

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}=}$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

2) 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

3) 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

4) 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

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### Key: K0

1)
A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
-a) 7.479E+00 cm3/s
-b) 8.227E+00 cm3/s
-c) 9.049E+00 cm3/s
-d) 9.954E+00 cm3/s
+e) 1.095E+01 cm3/s

2) Calculate the motional emf induced along a 11.9 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.870E-05 Tesla magnetic field.

-a) 3.736E+03 V
-b) 4.109E+03 V
+c) 4.520E+03 V
-d) 4.972E+03 V
-e) 5.470E+03 V

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}=}$3.75 T and ${\displaystyle \omega =}$1.740E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.417 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) 1.168E+04 V
-b) 1.284E+04 V
-c) 1.413E+04 V
-d) 1.554E+04 V
+e) 1.710E+04 V

4) A long solenoid has a radius of 0.436 m and 87 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 =}$27 s−1.What is the induced electric fied at a distance 0.153 m from the axis at time t=0.02 s ?

-a) 4.785E-04 V/m
+b) 5.264E-04 V/m
-c) 5.790E-04 V/m
-d) 6.369E-04 V/m
-e) 7.006E-04 V/m

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#### Key: K1

1) A long solenoid has a radius of 0.887 m and 45 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 =}$25 s−1.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

-a) 4.896E-05 V/m
-b) 5.385E-05 V/m
+c) 5.924E-05 V/m
-d) 6.516E-05 V/m
-e) 7.168E-05 V/m

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}=}$1.89 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
3)
A cylinder of height 2.15 cm and radius 7.03 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 3.83 cm from point O and moves at a speed of 5.7 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) 6.534E+01 cm3/s
-b) 7.188E+01 cm3/s
+c) 7.907E+01 cm3/s
-d) 8.697E+01 cm3/s
-e) 9.567E+01 cm3/s

4) 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

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#### Key: K2

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}=}$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
2)
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

3) 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

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

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### Key: L0

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 time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.549 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.97)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.0 s. What is the current in the coil if the impedance of the coil is 46.7 Ω?

-a) 2.032E-01 A
-b) 2.235E-01 A
-c) 2.458E-01 A
-d) 2.704E-01 A
+e) 2.975E-01 A

3) 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

4) 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

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#### Key: L1

1) 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

2) 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

3) 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

4) A long solenoid has a radius of 0.613 m and 75 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 =}$22 s−1.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

-a) 1.370E-04 V/m
-b) 1.507E-04 V/m
-c) 1.657E-04 V/m
+d) 1.823E-04 V/m
-e) 2.005E-04 V/m

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#### Key: L2

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.348 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.3)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.57 s. What is the current in the coil if the impedance of the coil is 68.6 Ω?

-a) 5.720E-02 A
-b) 6.292E-02 A
-c) 6.921E-02 A
+d) 7.613E-02 A
-e) 8.375E-02 A

2) A recangular coil with an area of 0.897 m2 and 8 turns is placed in a uniform magnetic field of 2.83 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 8.740E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 3 s?

+a) 4.695E+04 V
-b) 5.165E+04 V
-c) 5.681E+04 V
-d) 6.249E+04 V
-e) 6.874E+04 V

3) 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

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

-a) 1.456E-04 V/m
-b) 1.601E-04 V/m
-c) 1.762E-04 V/m
+d) 1.938E-04 V/m
-e) 2.132E-04 V/m

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### Key: M0

1) 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

2) 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

3) 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

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}=}$3.79 T and ${\displaystyle \omega =}$7.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.668 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) 7.910E+04 V
-b) 8.701E+04 V
-c) 9.571E+04 V
-d) 1.053E+05 V
+e) 1.158E+05 V

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#### Key: M1

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}=}$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

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) 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

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

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#### Key: M2

1) A recangular coil with an area of 0.315 m2 and 20 turns is placed in a uniform magnetic field of 3.45 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 9.480E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 26 s?

+a) 1.342E+04 V
-b) 1.476E+04 V
-c) 1.624E+04 V
-d) 1.786E+04 V
-e) 1.965E+04 V

2) A long solenoid has a radius of 0.806 m and 41 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 2.67 m from the axis at time t=0.0701 s ?

+a) 6.040E-05 V/m
-b) 6.644E-05 V/m
-c) 7.309E-05 V/m
-d) 8.039E-05 V/m
-e) 8.843E-05 V/m

3) 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

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

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### Key: N0

1) 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

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

-a) 1.616E-04 V/m
-b) 1.778E-04 V/m
-c) 1.955E-04 V/m
-d) 2.151E-04 V/m
+e) 2.366E-04 V/m

3) 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

4) A long solenoid has a radius of 0.447 m and 85 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 =}$23 s−1.What is the induced electric fied at a distance 0.212 m from the axis at time t=0.0819 s ?

-a) 1.893E-04 V/m
-b) 2.082E-04 V/m
-c) 2.290E-04 V/m
-d) 2.519E-04 V/m
+e) 2.771E-04 V/m

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#### Key: N1

1) 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

2) 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

3) 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

4) A long solenoid has a radius of 0.591 m and 41 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 0.234 m from the axis at time t=0.0208 s ?

-a) 6.618E-05 V/m
-b) 7.280E-05 V/m
-c) 8.008E-05 V/m
-d) 8.809E-05 V/m
+e) 9.689E-05 V/m

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#### Key: N2

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 current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 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) 1.215E-04 V
-b) 1.337E-04 V
-c) 1.470E-04 V
-d) 1.617E-04 V
+e) 1.779E-04 V

3) 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

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

+a) 6.182E-04 V/m
-b) 6.801E-04 V/m
-c) 7.481E-04 V/m
-d) 8.229E-04 V/m
-e) 9.052E-04 V/m

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### Key: O0

1)
A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
-a) 7.479E+00 cm3/s
-b) 8.227E+00 cm3/s
-c) 9.049E+00 cm3/s
-d) 9.954E+00 cm3/s
+e) 1.095E+01 cm3/s

2) 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

3) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 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=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 2.685E+00 A
-b) 2.953E+00 A
+c) 3.248E+00 A
-d) 3.573E+00 A
-e) 3.931E+00 A

4) Calculate the motional emf induced along a 11.9 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.870E-05 Tesla magnetic field.

-a) 3.736E+03 V
-b) 4.109E+03 V
+c) 4.520E+03 V
-d) 4.972E+03 V
-e) 5.470E+03 V

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#### Key: O1

1)
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

2) 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

3) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 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=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

-a) 4.414E+00 A
-b) 4.855E+00 A
-c) 5.341E+00 A
-d) 5.875E+00 A
+e) 6.462E+00 A

4) 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

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#### Key: O2

1) 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
2)
A cylinder of height 1.69 cm and radius 4.56 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 2.33 cm from point O and moves at a speed of 4.9 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) 3.054E+01 cm3/s
-b) 3.359E+01 cm3/s
+c) 3.695E+01 cm3/s
-d) 4.065E+01 cm3/s
-e) 4.471E+01 cm3/s

3) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 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=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

+a) 5.743E-01 A
-b) 6.318E-01 A
-c) 6.950E-01 A
-d) 7.645E-01 A
-e) 8.409E-01 A

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

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### Key: P0

1) 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
2)
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

3) 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

4) A long solenoid has a radius of 0.613 m and 75 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 =}$22 s−1.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

-a) 1.370E-04 V/m
-b) 1.507E-04 V/m
-c) 1.657E-04 V/m
+d) 1.823E-04 V/m
-e) 2.005E-04 V/m

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#### Key: P1

1) A long solenoid has a radius of 0.591 m and 41 turns per meter; its current decreases with time according to