# Quizbank/calcPhyEMqAll/c13

calcPhyEMqAll/c13 ID153478379917

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.

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

### c13 A0

1) 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

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

a) 7.890E-01 A
b) 8.679E-01 A
c) 9.547E-01 A
d) 1.050E+00 A
e) 1.155E+00 A

3) 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) 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
5)
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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.29 T and ${\displaystyle \omega =}$4.720E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.658 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 6.420E+04 V
b) 7.062E+04 V
c) 7.768E+04 V
d) 8.545E+04 V
e) 9.400E+04 V

8) A long solenoid has a radius of 0.716 m and 96 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

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

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

a) 2.154E-05 V/m
b) 2.369E-05 V/m
c) 2.606E-05 V/m
d) 2.867E-05 V/m
e) 3.154E-05 V/m

#### c13 A1

1) 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

2) 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

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 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

5) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$1.8 T and ${\displaystyle \omega =}$1.530E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.519 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.422E+03 V
b) 8.164E+03 V
c) 8.981E+03 V
d) 9.879E+03 V
e) 1.087E+04 V

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

a) 7.890E-01 A
b) 8.679E-01 A
c) 9.547E-01 A
d) 1.050E+00 A
e) 1.155E+00 A

7) 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

8) 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

9) 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

#### c13 A2

1) 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

2) 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

3) 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

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

5) 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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.75 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

8) 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
9)
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

### c13 B0

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 0.752 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

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

a) 6.598E+03 V
b) 7.258E+03 V
c) 7.984E+03 V
d) 8.782E+03 V
e) 9.660E+03 V
5)
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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.31 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

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

a) 1.479E-04 V/m
b) 1.627E-04 V/m
c) 1.789E-04 V/m
d) 1.968E-04 V/m
e) 2.165E-04 V/m

9) 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 B1

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

a) 2.154E-05 V/m
b) 2.369E-05 V/m
c) 2.606E-05 V/m
d) 2.867E-05 V/m
e) 3.154E-05 V/m

2) 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

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

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

4) 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
5)
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

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$1.97 T and ${\displaystyle \omega =}$5.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.244 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.485E+04 V
b) 1.634E+04 V
c) 1.797E+04 V
d) 1.977E+04 V
e) 2.175E+04 V

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

a) 1.240E-01 A
b) 1.364E-01 A
c) 1.500E-01 A
d) 1.650E-01 A
e) 1.815E-01 A

8) A 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

9) 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

#### c13 B2

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 cylinder of height 3.82 cm and radius 5.6 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.89 cm from point O and moves at a speed of 4.25 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.280E+01 cm3/s
b) 8.008E+01 cm3/s
c) 8.808E+01 cm3/s
d) 9.689E+01 cm3/s
e) 1.066E+02 cm3/s

3) 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

4) 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

5) 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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.7 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

8) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 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=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 6.581E-01 A
b) 7.239E-01 A
c) 7.963E-01 A
d) 8.759E-01 A
e) 9.635E-01 A

9) 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

### c13 C0

1) 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

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) 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

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
5)
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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

8) 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

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

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

#### c13 C1

1) 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

2) 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

3) Calculate the motional emf induced along a 32.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 5.280E-05 Tesla magnetic field.

a) 1.093E+04 V
b) 1.202E+04 V
c) 1.322E+04 V
d) 1.454E+04 V
e) 1.600E+04 V

4) 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

5) 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

6) 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
7)
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

8) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.34 T and ${\displaystyle \omega =}$2.670E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.646 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.905E+04 V
b) 2.096E+04 V
c) 2.305E+04 V
d) 2.536E+04 V
e) 2.790E+04 V

9) 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 C2

1) 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

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) 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 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

5) Calculate the motional emf induced along a 32.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 5.280E-05 Tesla magnetic field.

a) 1.093E+04 V
b) 1.202E+04 V
c) 1.322E+04 V
d) 1.454E+04 V
e) 1.600E+04 V

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

7) 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

8) 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
9)
A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 3.093E+01 cm3/s
b) 3.403E+01 cm3/s
c) 3.743E+01 cm3/s
d) 4.117E+01 cm3/s
e) 4.529E+01 cm3/s

### c13 D0

1) 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

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) 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

4) 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
5)
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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.79 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

8) 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

9) 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 D1

1)
A cylinder of height 2.91 cm and radius 8.33 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.7 cm from point O and moves at a speed of 9.14 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 2.061E+02 cm3/s
b) 2.267E+02 cm3/s
c) 2.494E+02 cm3/s
d) 2.743E+02 cm3/s
e) 3.018E+02 cm3/s

2) 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

3) 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

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}=}$3.54 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

5) 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

6) 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

7) 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

8) 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

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

a) 8.802E+03 V
b) 9.682E+03 V
c) 1.065E+04 V
d) 1.172E+04 V
e) 1.289E+04 V

#### c13 D2

1) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 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=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 6.581E-01 A
b) 7.239E-01 A
c) 7.963E-01 A
d) 8.759E-01 A
e) 9.635E-01 A

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

a) 1.473E-04 V/m
b) 1.621E-04 V/m
c) 1.783E-04 V/m
d) 1.961E-04 V/m
e) 2.157E-04 V/m

5) A 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

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

7) 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

8) 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

9) 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 E0

1) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 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=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 6.581E-01 A
b) 7.239E-01 A
c) 7.963E-01 A
d) 8.759E-01 A
e) 9.635E-01 A

2) 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

3) 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

4) 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
5)
A cylinder of height 2.94 cm and radius 5.05 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.37 cm from point O and moves at a speed of 7.29 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.153E+02 cm3/s
b) 1.268E+02 cm3/s
c) 1.395E+02 cm3/s
d) 1.535E+02 cm3/s
e) 1.688E+02 cm3/s

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

a) 1.086E+04 V
b) 1.195E+04 V
c) 1.314E+04 V
d) 1.446E+04 V
e) 1.590E+04 V

7) 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

8) 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

9) 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 E1

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 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) 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

4) 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
5)
A cylinder of height 1.3 cm and radius 6.01 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.61 cm from point O and moves at a speed of 2.11 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.372E+01 cm3/s
b) 1.509E+01 cm3/s
c) 1.660E+01 cm3/s
d) 1.826E+01 cm3/s
e) 2.009E+01 cm3/s

6) A 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

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

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

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

a) 7.890E-01 A
b) 8.679E-01 A
c) 9.547E-01 A
d) 1.050E+00 A
e) 1.155E+00 A

9) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

#### c13 E2

1) A recangular coil with an area of 0.45 m2 and 18 turns is placed in a uniform magnetic field of 2.68 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.730E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 87 s?

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

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) 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 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

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

a) 4.817E-01 A
b) 5.298E-01 A
c) 5.828E-01 A
d) 6.411E-01 A
e) 7.052E-01 A

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

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

7) 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

8) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.31 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

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

a) 2.571E-05 V/m
b) 2.828E-05 V/m
c) 3.111E-05 V/m
d) 3.422E-05 V/m
e) 3.764E-05 V/m

### c13 F0

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 0.861 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= 2.760E+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) 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
5)
A cylinder of height 3.82 cm and radius 5.6 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.89 cm from point O and moves at a speed of 4.25 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.280E+01 cm3/s
b) 8.008E+01 cm3/s
c) 8.808E+01 cm3/s
d) 9.689E+01 cm3/s
e) 1.066E+02 cm3/s

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.11 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

8) 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

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

a) 1.256E-05 V/m
b) 1.382E-05 V/m
c) 1.520E-05 V/m
d) 1.672E-05 V/m
e) 1.839E-05 V/m

#### c13 F1

1)
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

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) 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

4) A long solenoid has a radius of 0.583 m and 38 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$24 s−1.What is the induced electric fied at a distance 2.09 m from the axis at time t=0.0388 s ?

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

5) 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

6) 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

7) A square coil has sides that are L= 0.259 m long and is tightly wound with N=628 turns of wire. The resistance of the coil is R=6.51 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0372 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

8) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.25 T and ${\displaystyle \omega =}$8.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.227 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 2.657E+04 V
b) 2.923E+04 V
c) 3.215E+04 V
d) 3.537E+04 V
e) 3.890E+04 V

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

a) 1.256E-05 V/m
b) 1.382E-05 V/m
c) 1.520E-05 V/m
d) 1.672E-05 V/m
e) 1.839E-05 V/m

#### c13 F2

1) 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

2) 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

3) 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
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

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

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

6) 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

7) 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

8) A long solenoid has a radius of 0.732 m and 55 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$25 s−1.What is the induced electric fied at a distance 0.203 m from the axis at time t=0.0448 s ?

a) 5.150E-04 V/m
b) 5.665E-04 V/m
c) 6.232E-04 V/m
d) 6.855E-04 V/m
e) 7.540E-04 V/m

9) 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 G0

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

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

3) 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

4) 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
5)
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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.7 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

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

a) 1.479E-04 V/m
b) 1.627E-04 V/m
c) 1.789E-04 V/m
d) 1.968E-04 V/m
e) 2.165E-04 V/m

9) 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 G1

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 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) 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 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

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

a) 6.527E-04 V/m
b) 7.180E-04 V/m
c) 7.898E-04 V/m
d) 8.688E-04 V/m
e) 9.556E-04 V/m

6) 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
7)
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

8) 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

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

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

#### c13 G2

1)
A cylinder of height 2.91 cm and radius 8.33 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.7 cm from point O and moves at a speed of 9.14 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 2.061E+02 cm3/s
b) 2.267E+02 cm3/s
c) 2.494E+02 cm3/s
d) 2.743E+02 cm3/s
e) 3.018E+02 cm3/s

2) 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

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) 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

5) 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

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

7) A long solenoid has a radius of 0.624 m and 84 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 1.78 m from the axis at time t=0.0579 s ?

a) 3.597E-04 V/m
b) 3.956E-04 V/m
c) 4.352E-04 V/m
d) 4.787E-04 V/m
e) 5.266E-04 V/m

8) 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

9) 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 H0

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) 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) 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 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
5)
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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

8) 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

9) 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 H1

1)
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

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}=}$3.11 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

3) 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

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

a) 8.953E-01 A
b) 9.848E-01 A
c) 1.083E+00 A
d) 1.192E+00 A
e) 1.311E+00 A

5) 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

6) 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

7) 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

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

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

9) 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 H2

1) 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

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}=}$3.29 T and ${\displaystyle \omega =}$4.720E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.658 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 6.420E+04 V
b) 7.062E+04 V
c) 7.768E+04 V
d) 8.545E+04 V
e) 9.400E+04 V

3) 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

4) 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

5) 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
6)
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

7) 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

8) 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

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

a) 1.126E-04 V
b) 1.238E-04 V
c) 1.362E-04 V
d) 1.498E-04 V
e) 1.648E-04 V

### c13 I0

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

a) 7.801E+03 V
b) 8.581E+03 V
c) 9.439E+03 V
d) 1.038E+04 V
e) 1.142E+04 V
5)
A 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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.54 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

8) 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

9) 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 I1

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 cylinder of height 1.34 cm and radius 2.47 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 1.23 cm from point O and moves at a speed of 6.23 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) 1.414E+01 cm3/s
b) 1.556E+01 cm3/s
c) 1.711E+01 cm3/s
d) 1.882E+01 cm3/s
e) 2.070E+01 cm3/s

3) 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

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

5) 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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.75 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

8) 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

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

a) 1.567E+00 A
b) 1.724E+00 A
c) 1.897E+00 A
d) 2.086E+00 A
e) 2.295E+00 A

#### c13 I2

1)
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

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) 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

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

a) 6.527E-04 V/m
b) 7.180E-04 V/m
c) 7.898E-04 V/m
d) 8.688E-04 V/m
e) 9.556E-04 V/m

6) 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

7) 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

8) 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

9) 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

### c13 J0

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 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) 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

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

a) 6.598E+03 V
b) 7.258E+03 V
c) 7.984E+03 V
d) 8.782E+03 V
e) 9.660E+03 V
5)
A cylinder of height 2.25 cm and radius 6.77 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.27 cm from point O and moves at a speed of 4.07 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 5.834E+01 cm3/s
b) 6.418E+01 cm3/s
c) 7.059E+01 cm3/s
d) 7.765E+01 cm3/s
e) 8.542E+01 cm3/s

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

8) 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

9) 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

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

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

3) 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

4) 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
5)
A cylinder of height 2.12 cm and radius 2.28 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.52 cm from point O and moves at a speed of 8.21 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 2.976E+01 cm3/s
b) 3.274E+01 cm3/s
c) 3.601E+01 cm3/s
d) 3.961E+01 cm3/s
e) 4.358E+01 cm3/s

6) The 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

7) 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

8) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 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=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 6.581E-01 A
b) 7.239E-01 A
c) 7.963E-01 A
d) 8.759E-01 A
e) 9.635E-01 A

9) 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 J2

1) 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

2) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 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=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 6.581E-01 A
b) 7.239E-01 A
c) 7.963E-01 A
d) 8.759E-01 A
e) 9.635E-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) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.29 T and ${\displaystyle \omega =}$4.720E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.658 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 6.420E+04 V
b) 7.062E+04 V
c) 7.768E+04 V
d) 8.545E+04 V
e) 9.400E+04 V

5) 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

6) 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

7) 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

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

a) 9.140E+03 V
b) 1.005E+04 V
c) 1.106E+04 V
d) 1.217E+04 V
e) 1.338E+04 V
9)
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

### c13 K0

1) 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

2) 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

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

a) 1.126E-04 V
b) 1.238E-04 V
c) 1.362E-04 V
d) 1.498E-04 V
e) 1.648E-04 V

4) 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
5)
A cylinder of height 2.42 cm and radius 6.94 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 2.59 cm from point O and moves at a speed of 4.87 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) 9.962E+01 cm3/s
b) 1.096E+02 cm3/s
c) 1.205E+02 cm3/s
d) 1.326E+02 cm3/s
e) 1.459E+02 cm3/s

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.31 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

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

a) 1.479E-04 V/m
b) 1.627E-04 V/m
c) 1.789E-04 V/m
d) 1.968E-04 V/m
e) 2.165E-04 V/m

9) 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

#### c13 K1

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

a) 2.154E-05 V/m
b) 2.369E-05 V/m
c) 2.606E-05 V/m
d) 2.867E-05 V/m
e) 3.154E-05 V/m

2) 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

3) 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

4) A long solenoid has a radius of 0.716 m and 96 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

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

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

a) 9.140E+03 V
b) 1.005E+04 V
c) 1.106E+04 V
d) 1.217E+04 V
e) 1.338E+04 V
6)
A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 3.093E+01 cm3/s
b) 3.403E+01 cm3/s
c) 3.743E+01 cm3/s
d) 4.117E+01 cm3/s
e) 4.529E+01 cm3/s

7) A 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

8) 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

9) 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

#### c13 K2

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 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

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}=}$3.84 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

4) 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
5)
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

6) 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

7) 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

8) 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

9) 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

### c13 L0

1) 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

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

a) 9.140E+03 V
b) 1.005E+04 V
c) 1.106E+04 V
d) 1.217E+04 V
e) 1.338E+04 V
5)
A cylinder of height 2.94 cm and radius 5.05 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.37 cm from point O and moves at a speed of 7.29 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.153E+02 cm3/s
b) 1.268E+02 cm3/s
c) 1.395E+02 cm3/s
d) 1.535E+02 cm3/s
e) 1.688E+02 cm3/s

6) A 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.58 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

8) 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

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

a) 2.154E-05 V/m
b) 2.369E-05 V/m
c) 2.606E-05 V/m
d) 2.867E-05 V/m
e) 3.154E-05 V/m

#### c13 L1

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 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 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 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

5) A long solenoid has a radius of 0.716 m and 96 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

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

6) A 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

7) 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

8) 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

9) 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

#### c13 L2

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}=}$3.31 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

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 24.6 km conductor moving at an orbital speed of 7.89 km/s perpendicular to Earth's 5.180E-05 Tesla magnetic field.

a) 9.140E+03 V
b) 1.005E+04 V
c) 1.106E+04 V
d) 1.217E+04 V
e) 1.338E+04 V

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

a) 1.479E-04 V/m
b) 1.627E-04 V/m
c) 1.789E-04 V/m
d) 1.968E-04 V/m
e) 2.165E-04 V/m

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

a) 1.086E+04 V
b) 1.195E+04 V
c) 1.314E+04 V
d) 1.446E+04 V
e) 1.590E+04 V

6) 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

7) 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

8) 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
9)
A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 3.093E+01 cm3/s
b) 3.403E+01 cm3/s
c) 3.743E+01 cm3/s
d) 4.117E+01 cm3/s
e) 4.529E+01 cm3/s

### c13 M0

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 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

3) 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

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

a) 9.140E+03 V
b) 1.005E+04 V
c) 1.106E+04 V
d) 1.217E+04 V
e) 1.338E+04 V
5)
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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

8) 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

9) 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

#### c13 M1

1) 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
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 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 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

5) 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

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

7) 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

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

a) 1.126E-04 V
b) 1.238E-04 V
c) 1.362E-04 V
d) 1.498E-04 V
e) 1.648E-04 V

9) 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

#### c13 M2

1) 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

2) A recangular coil with an area of 0.23 m2 and 20 turns is placed in a uniform magnetic field of 1.66 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 1.380E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 4 s?

a) 2.317E+03 V
b) 2.549E+03 V
c) 2.804E+03 V
d) 3.084E+03 V
e) 3.393E+03 V

3) A 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

4) 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

5) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.7 T and ${\displaystyle \omega =}$8.100E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.827 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.416E+05 V
b) 1.557E+05 V
c) 1.713E+05 V
d) 1.884E+05 V
e) 2.073E+05 V

6) 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
7)
A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.892E+01 cm3/s
b) 2.081E+01 cm3/s
c) 2.289E+01 cm3/s
d) 2.518E+01 cm3/s
e) 2.770E+01 cm3/s

8) 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

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

a) 1.126E-04 V
b) 1.238E-04 V
c) 1.362E-04 V
d) 1.498E-04 V
e) 1.648E-04 V

### c13 N0

1) 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

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) 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) 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
5)
A cylinder of height 3.82 cm and radius 5.6 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.89 cm from point O and moves at a speed of 4.25 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.280E+01 cm3/s
b) 8.008E+01 cm3/s
c) 8.808E+01 cm3/s
d) 9.689E+01 cm3/s
e) 1.066E+02 cm3/s

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.29 T and ${\displaystyle \omega =}$4.720E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.658 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 6.420E+04 V
b) 7.062E+04 V
c) 7.768E+04 V
d) 8.545E+04 V
e) 9.400E+04 V

8) A long solenoid has a radius of 0.716 m and 96 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

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

9) 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 N1

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= 0.888 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) 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

4) 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

5) 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
6)
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

7) 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

8) A long solenoid has a radius of 0.624 m and 84 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 1.78 m from the axis at time t=0.0579 s ?

a) 3.597E-04 V/m
b) 3.956E-04 V/m
c) 4.352E-04 V/m
d) 4.787E-04 V/m
e) 5.266E-04 V/m

9) 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

#### c13 N2

1) 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

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}=}$3.71 T and ${\displaystyle \omega =}$6.600E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.31 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 4.769E+04 V
b) 5.246E+04 V
c) 5.771E+04 V
d) 6.348E+04 V
e) 6.983E+04 V

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) 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

5) A long solenoid has a radius of 0.716 m and 96 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

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

6) 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

7) 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

8) 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
9)
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 O0

1) 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

2) 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

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) 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
5)
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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.75 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

8) A long solenoid has a radius of 0.624 m and 84 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 1.78 m from the axis at time t=0.0579 s ?

a) 3.597E-04 V/m
b) 3.956E-04 V/m
c) 4.352E-04 V/m
d) 4.787E-04 V/m
e) 5.266E-04 V/m

9) 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

#### c13 O1

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 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

3) 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

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
5)
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

6) 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

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

a) 4.769E+04 V
b) 5.246E+04 V
c) 5.771E+04 V
d) 6.348E+04 V
e) 6.983E+04 V

8) 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

9) 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

#### c13 O2

1)
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

2) 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

3) 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

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

a) 1.479E-04 V/m
b) 1.627E-04 V/m
c) 1.789E-04 V/m
d) 1.968E-04 V/m
e) 2.165E-04 V/m

5) 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

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

7) 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

8) 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

9) 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

### c13 P0

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

a) 7.801E+03 V
b) 8.581E+03 V
c) 9.439E+03 V
d) 1.038E+04 V
e) 1.142E+04 V
5)
A 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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.75 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

8) 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

9) 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 P1

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) 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 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

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

a) 7.801E+03 V
b) 8.581E+03 V
c) 9.439E+03 V
d) 1.038E+04 V
e) 1.142E+04 V
5)
A 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

6) 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

7) 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

8) A long solenoid has a radius of 0.624 m and 84 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 1.78 m from the axis at time t=0.0579 s ?

a) 3.597E-04 V/m
b) 3.956E-04 V/m
c) 4.352E-04 V/m
d) 4.787E-04 V/m
e) 5.266E-04 V/m

9) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.54 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

#### c13 P2

1) 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

2) A recangular coil with an area of 0.45 m2 and 18 turns is placed in a uniform magnetic field of 2.68 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.730E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 87 s?

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

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

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

5) 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

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.25 T and ${\displaystyle \omega =}$8.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.227 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 2.657E+04 V
b) 2.923E+04 V
c) 3.215E+04 V
d) 3.537E+04 V
e) 3.890E+04 V

8) 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

9) 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

### c13 Q0

1) 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

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

a) 9.140E+03 V
b) 1.005E+04 V
c) 1.106E+04 V
d) 1.217E+04 V
e) 1.338E+04 V
5)
A cylinder of height 2.12 cm and radius 2.28 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.52 cm from point O and moves at a speed of 8.21 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 2.976E+01 cm3/s
b) 3.274E+01 cm3/s
c) 3.601E+01 cm3/s
d) 3.961E+01 cm3/s
e) 4.358E+01 cm3/s

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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

8) 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

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

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

#### c13 Q1

1) 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

2) 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

3) 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

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}=}$3.54 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

5) 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
6)
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

7) 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

8) 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

9) 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

#### c13 Q2

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

a) 3.688E+03 V
b) 4.057E+03 V
c) 4.463E+03 V
d) 4.909E+03 V
e) 5.400E+03 V

2) 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

3) A recangular coil with an area of 0.45 m2 and 18 turns is placed in a uniform magnetic field of 2.68 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.730E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 87 s?

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

4) 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

5) 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

6) 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

7) 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

8) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$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
9)
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

### c13 R0

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 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= 2.980E+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

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
5)
A cylinder of height 1.34 cm and radius 2.47 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 1.23 cm from point O and moves at a speed of 6.23 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) 1.414E+01 cm3/s
b) 1.556E+01 cm3/s
c) 1.711E+01 cm3/s
d) 1.882E+01 cm3/s
e) 2.070E+01 cm3/s

6) 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

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.7 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

8) 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

9) 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

#### c13 R1

1) Calculate the motional emf induced along a 32.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 5.280E-05 Tesla magnetic field.

a) 1.093E+04 V
b) 1.202E+04 V
c) 1.322E+04 V
d) 1.454E+04 V
e) 1.600E+04 V

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 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

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}=}$3.29 T and ${\displaystyle \omega =}$4.720E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.658 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 6.420E+04 V
b) 7.062E+04 V
c) 7.768E+04 V
d) 8.545E+04 V
e) 9.400E+04 V

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

a) 2.154E-05 V/m
b) 2.369E-05 V/m
c) 2.606E-05 V/m
d) 2.867E-05 V/m
e) 3.154E-05 V/m

6) 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

7) 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
8)
A cylinder of height 3.82 cm and radius 5.6 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.89 cm from point O and moves at a speed of 4.25 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.280E+01 cm3/s
b) 8.008E+01 cm3/s
c) 8.808E+01 cm3/s
d) 9.689E+01 cm3/s
e) 1.066E+02 cm3/s

9) 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

#### c13 R2

1) 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

2) 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
3)
A cylinder of height 3.82 cm and radius 5.6 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.89 cm from point O and moves at a speed of 4.25 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.280E+01 cm3/s
b) 8.008E+01 cm3/s
c) 8.808E+01 cm3/s
d) 9.689E+01 cm3/s
e) 1.066E+02 cm3/s

4) 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

5) 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 ${\displaystyle \alpha =}$