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

calcPhyEMq/c13 ID153287923206 (Study guide)

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

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

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

**Links:** Quizbank/Instructions Study guide file:Quizbank153287923206.pdf

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

### c13 A0[edit | edit source]

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

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

2) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to , where 5.58 s. What is the current in the coil if the impedance of the coil is 13.3 Ω?

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

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

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

#### c13 A1[edit | edit source]

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

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

2) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to , where 7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

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

4) A long solenoid has a radius of 0.591 m and 41 turns per meter; its current decreases with time according to , where 1 A and 30 s^{−1}.What is the induced electric fied at a distance 0.234 m from the axis at time t=0.0208 s ?

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

#### c13 A2[edit | edit source]

1) A long solenoid has a radius of 0.845 m and 78 turns per meter; its current decreases with time according to , where 3 A and 20 s^{−1}.What is the induced electric fied at a distance 0.214 m from the axis at time t=0.0655 s ?

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

2) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.708 m. The magnetic field is spatially uniform but decays in time according to , where 6.34 s. What is the current in the coil if the impedance of the coil is 89.8 Ω?

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

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

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

### c13 B0[edit | edit source]

1) A long solenoid has a radius of 0.845 m and 65 turns per meter; its current decreases with time according to , where 6 A and 30 s^{−1}.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

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

2) A recangular coil with an area of 0.432 m^{2} and 16 turns is placed in a uniform magnetic field of 3.7 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.020E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 55 s?

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

3) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

4) A long solenoid has a radius of 0.613 m and 75 turns per meter; its current decreases with time according to , where 2 A and 22 s^{−1}.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

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

#### c13 B1[edit | edit source]

1) A recangular coil with an area of 0.587 m^{2} and 13 turns is placed in a uniform magnetic field of 1.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.800E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 93 s?

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

2) A long solenoid has a radius of 0.845 m and 65 turns per meter; its current decreases with time according to , where 6 A and 30 s^{−1}.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

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

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

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

4) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

#### c13 B2[edit | edit source]

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

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

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

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

3) A long solenoid has a radius of 0.845 m and 65 turns per meter; its current decreases with time according to , where 6 A and 30 s^{−1}.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

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

4) A long solenoid has a radius of 0.517 m and 23 turns per meter; its current decreases with time according to , where 1 A and 30 s^{−1}.What is the induced electric fied at a distance 0.162 m from the axis at time t=0.0679 s ?

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

### c13 C0[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.798 m. The magnetic field is spatially uniform but decays in time according to , where 4.63 s. What is the current in the coil if the impedance of the coil is 75.7 Ω?

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

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

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

--(

*Answer & Why this question is different.*)

- a) 8.324E+00 cm
^{3}/s - b) 9.157E+00 cm
^{3}/s - c) 1.007E+01 cm
^{3}/s - d) 1.108E+01 cm
^{3}/s - e) 1.219E+01 cm
^{3}/s

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

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

#### c13 C1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to , where 7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

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

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

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

--(

*Answer & Why this question is different.*)

- a) 6.534E+01 cm
^{3}/s - b) 7.188E+01 cm
^{3}/s - c) 7.907E+01 cm
^{3}/s - d) 8.697E+01 cm
^{3}/s - e) 9.567E+01 cm
^{3}/s

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

- a) 1.026E-05 V/m
- b) 1.129E-05 V/m
- c) 1.242E-05 V/m
- d) 1.366E-05 V/m
- e) 1.502E-05 V/m

#### c13 C2[edit | edit source]

1) A cylinder of height 1.48 cm and radius 7.74 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.76 cm from point O and moves at a speed of 3.09 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)--(

*Answer & Why this question is different.*)

- a) 3.312E+01 cm
^{3}/s - b) 3.643E+01 cm
^{3}/s - c) 4.008E+01 cm
^{3}/s - d) 4.408E+01 cm
^{3}/s - e) 4.849E+01 cm
^{3}/s

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

- a) 1.224E+04 V
- b) 1.346E+04 V
- c) 1.481E+04 V
- d) 1.629E+04 V
- e) 1.792E+04 V

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.477 m. The magnetic field is spatially uniform but decays in time according to , where 8.01 s. What is the current in the coil if the impedance of the coil is 75.6 Ω?

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

4) A long solenoid has a radius of 0.845 m and 78 turns per meter; its current decreases with time according to , where 3 A and 20 s^{−1}.What is the induced electric fied at a distance 0.214 m from the axis at time t=0.0655 s ?

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

### c13 D0[edit | edit source]

1) A long solenoid has a radius of 0.887 m and 45 turns per meter; its current decreases with time according to , where 3 A and 25 s^{−1}.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

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

2) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.215E-04 V
- b) 1.337E-04 V
- c) 1.470E-04 V
- d) 1.617E-04 V
- e) 1.779E-04 V

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

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

4) A recangular coil with an area of 0.219 m^{2} and 14 turns is placed in a uniform magnetic field of 3.71 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.540E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 15 s?

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

#### c13 D1[edit | edit source]

1) A recangular coil with an area of 0.178 m^{2} and 17 turns is placed in a uniform magnetic field of 2.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.380E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 45 s?

- a) 1.068E+04 V
- b) 1.175E+04 V
- c) 1.293E+04 V
- d) 1.422E+04 V
- e) 1.564E+04 V

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

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

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

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

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

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

#### c13 D2[edit | edit source]

1) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.215E-04 V
- b) 1.337E-04 V
- c) 1.470E-04 V
- d) 1.617E-04 V
- e) 1.779E-04 V

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

- a) 1.026E-05 V/m
- b) 1.129E-05 V/m
- c) 1.242E-05 V/m
- d) 1.366E-05 V/m
- e) 1.502E-05 V/m

3) A recangular coil with an area of 0.479 m^{2} and 11 turns is placed in a uniform magnetic field of 1.34 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.200E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 38 s?

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

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

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

### c13 E0[edit | edit source]

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

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

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

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.75 T and 1.740E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

--(

*Answer & Why this question is different.*)

- a) 7.479E+00 cm
^{3}/s - b) 8.227E+00 cm
^{3}/s - c) 9.049E+00 cm
^{3}/s - d) 9.954E+00 cm
^{3}/s - e) 1.095E+01 cm
^{3}/s

#### c13 E1[edit | edit source]

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

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

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

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.97 T and 5.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

--(

*Answer & Why this question is different.*)

- a) 3.054E+01 cm
^{3}/s - b) 3.359E+01 cm
^{3}/s - c) 3.695E+01 cm
^{3}/s - d) 4.065E+01 cm
^{3}/s - e) 4.471E+01 cm
^{3}/s

#### c13 E2[edit | edit source]

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

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

--(

*Answer & Why this question is different.*)

- a) 1.372E+01 cm
^{3}/s - b) 1.509E+01 cm
^{3}/s - c) 1.660E+01 cm
^{3}/s - d) 1.826E+01 cm
^{3}/s - e) 2.009E+01 cm
^{3}/s

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 2.18 T and 4.840E+03 s^{−1}. Suppose the electric field is always zero at point , and consider a circle of radius 0.387 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral around the circle.

- a) 1.928E+04 V
- b) 2.120E+04 V
- c) 2.332E+04 V
- d) 2.566E+04 V
- e) 2.822E+04 V

4) A long solenoid has a radius of 0.777 m and 67 turns per meter; its current decreases with time according to , where 6 A and 20 s^{−1}.What is the induced electric fied at a distance 2.39 m from the axis at time t=0.0399 s ?

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

### c13 F0[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.798 m. The magnetic field is spatially uniform but decays in time according to , where 4.63 s. What is the current in the coil if the impedance of the coil is 75.7 Ω?

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

2) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.8 T and 1.530E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

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

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

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

#### c13 F1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.8 m. The magnetic field is spatially uniform but decays in time according to , where 8.91 s. What is the current in the coil if the impedance of the coil is 61.7 Ω?

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

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

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.89 T and 1.710E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 7.262E+03 V
- b) 7.988E+03 V
- c) 8.787E+03 V
- d) 9.666E+03 V
- e) 1.063E+04 V

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

- a) 2.609E+00 A
- b) 2.870E+00 A
- c) 3.157E+00 A
- d) 3.473E+00 A
- e) 3.820E+00 A

#### c13 F2[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.274 m. The magnetic field is spatially uniform but decays in time according to , where 9.59 s. What is the current in the coil if the impedance of the coil is 33.0 Ω?

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

2) A square coil has sides that are L= 0.245 m long and is tightly wound with N=925 turns of wire. The resistance of the coil is R=8.0 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

4) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.97 T and 5.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

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

### c13 G0[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.58 T and 4.310E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

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

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

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.227 m. The magnetic field is spatially uniform but decays in time according to , where 3.92 s. What is the current in the coil if the impedance of the coil is 22.7 Ω?

- a) 1.082E-01 A
- b) 1.190E-01 A
- c) 1.309E-01 A
- d) 1.440E-01 A
- e) 1.584E-01 A

4) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 2.081E-04 V
- b) 2.289E-04 V
- c) 2.518E-04 V
- d) 2.770E-04 V
- e) 3.047E-04 V

#### c13 G1[edit | edit source]

1) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to , where 9.53 s. What is the current in the coil if the impedance of the coil is 27.4 Ω?

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

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

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

4) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.97 T and 5.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

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

#### c13 G2[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.8 m. The magnetic field is spatially uniform but decays in time according to , where 8.91 s. What is the current in the coil if the impedance of the coil is 61.7 Ω?

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

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

- a) 1.242E-04 V
- b) 1.366E-04 V
- c) 1.503E-04 V
- d) 1.653E-04 V
- e) 1.819E-04 V

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.31 T and 8.360E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 7.145E+04 V
- b) 7.860E+04 V
- c) 8.646E+04 V
- d) 9.510E+04 V
- e) 1.046E+05 V

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

- a) 1.791E-01 A
- b) 1.970E-01 A
- c) 2.167E-01 A
- d) 2.384E-01 A
- e) 2.622E-01 A

### c13 H0[edit | edit source]

1) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.45 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.066E-04 V
- b) 1.173E-04 V
- c) 1.290E-04 V
- d) 1.419E-04 V
- e) 1.561E-04 V

2) A recangular coil with an area of 0.315 m^{2} and 20 turns is placed in a uniform magnetic field of 3.45 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 9.480E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 26 s?

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

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

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

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

- a) 1.026E-05 V/m
- b) 1.129E-05 V/m
- c) 1.242E-05 V/m
- d) 1.366E-05 V/m
- e) 1.502E-05 V/m

#### c13 H1[edit | edit source]

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

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

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

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

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

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

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

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

#### c13 H2[edit | edit source]

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

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

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

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

3) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.215E-04 V
- b) 1.337E-04 V
- c) 1.470E-04 V
- d) 1.617E-04 V
- e) 1.779E-04 V

4) A long solenoid has a radius of 0.887 m and 45 turns per meter; its current decreases with time according to , where 3 A and 25 s^{−1}.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

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

### c13 I0[edit | edit source]

1) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

--(

*Answer & Why this question is different.*)

- a) 1.128E+02 cm
^{3}/s - b) 1.241E+02 cm
^{3}/s - c) 1.365E+02 cm
^{3}/s - d) 1.502E+02 cm
^{3}/s - e) 1.652E+02 cm
^{3}/s

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

- a) 6.277E-05 V/m
- b) 6.904E-05 V/m
- c) 7.595E-05 V/m
- d) 8.354E-05 V/m
- e) 9.190E-05 V/m

#### c13 I1[edit | edit source]

1) A square coil has sides that are L= 0.458 m long and is tightly wound with N=742 turns of wire. The resistance of the coil is R=6.81 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0559 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

--(

*Answer & Why this question is different.*)

- a) 3.312E+01 cm
^{3}/s - b) 3.643E+01 cm
^{3}/s - c) 4.008E+01 cm
^{3}/s - d) 4.408E+01 cm
^{3}/s - e) 4.849E+01 cm
^{3}/s

4) A long solenoid has a radius of 0.613 m and 75 turns per meter; its current decreases with time according to , where 2 A and 22 s^{−1}.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

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

#### c13 I2[edit | edit source]

1) A square coil has sides that are L= 0.465 m long and is tightly wound with N=954 turns of wire. The resistance of the coil is R=6.06 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0367 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

3) A long solenoid has a radius of 0.732 m and 55 turns per meter; its current decreases with time according to , where 9 A and 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

--(

*Answer & Why this question is different.*)

- a) 2.061E+02 cm
^{3}/s - b) 2.267E+02 cm
^{3}/s - c) 2.494E+02 cm
^{3}/s - d) 2.743E+02 cm
^{3}/s - e) 3.018E+02 cm
^{3}/s

### c13 J0[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.7 T and 8.100E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

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

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

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.78 m. The magnetic field is spatially uniform but decays in time according to , where 9.74 s. What is the current in the coil if the impedance of the coil is 32.1 Ω?

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

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

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

#### c13 J1[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.71 T and 4.780E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 1.510E+04 V
- b) 1.661E+04 V
- c) 1.827E+04 V
- d) 2.010E+04 V
- e) 2.211E+04 V

2) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns wraped in a circle of diameter 1.44 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.602E-04 V
- b) 1.762E-04 V
- c) 1.939E-04 V
- d) 2.132E-04 V
- e) 2.346E-04 V

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

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

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to , where 5.58 s. What is the current in the coil if the impedance of the coil is 13.3 Ω?

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

#### c13 J2[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.84 T and 4.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 3.333E+04 V
- b) 3.666E+04 V
- c) 4.033E+04 V
- d) 4.436E+04 V
- e) 4.879E+04 V

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.861 m. The magnetic field is spatially uniform but decays in time according to , where 4.2 s. What is the current in the coil if the impedance of the coil is 19.8 Ω?

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

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

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

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

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

### c13 K0[edit | edit source]

1) A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)--(

*Answer & Why this question is different.*)

- a) 7.479E+00 cm
^{3}/s - b) 8.227E+00 cm
^{3}/s - c) 9.049E+00 cm
^{3}/s - d) 9.954E+00 cm
^{3}/s - e) 1.095E+01 cm
^{3}/s

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

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.75 T and 1.740E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 1.168E+04 V
- b) 1.284E+04 V
- c) 1.413E+04 V
- d) 1.554E+04 V
- e) 1.710E+04 V

4) A long solenoid has a radius of 0.436 m and 87 turns per meter; its current decreases with time according to , where 4 A and 27 s^{−1}.What is the induced electric fied at a distance 0.153 m from the axis at time t=0.02 s ?

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

#### c13 K1[edit | edit source]

1) A long solenoid has a radius of 0.887 m and 45 turns per meter; its current decreases with time according to , where 3 A and 25 s^{−1}.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

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

2) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.89 T and 1.710E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

--(

*Answer & Why this question is different.*)

- a) 6.534E+01 cm
^{3}/s - b) 7.188E+01 cm
^{3}/s - c) 7.907E+01 cm
^{3}/s - d) 8.697E+01 cm
^{3}/s - e) 9.567E+01 cm
^{3}/s

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

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

#### c13 K2[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.58 T and 4.310E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

--(

*Answer & Why this question is different.*)

- a) 3.312E+01 cm
^{3}/s - b) 3.643E+01 cm
^{3}/s - c) 4.008E+01 cm
^{3}/s - d) 4.408E+01 cm
^{3}/s - e) 4.849E+01 cm
^{3}/s

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

- a) 6.277E-05 V/m
- b) 6.904E-05 V/m
- c) 7.595E-05 V/m
- d) 8.354E-05 V/m
- e) 9.190E-05 V/m

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

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

### c13 L0[edit | edit source]

1) A long solenoid has a radius of 0.394 m and 13 turns per meter; its current decreases with time according to , where 9 A and 28 s^{−1}.What is the induced electric fied at a distance 1.8 m from the axis at time t=0.0757 s ?

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

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.549 m. The magnetic field is spatially uniform but decays in time according to , where 7.0 s. What is the current in the coil if the impedance of the coil is 46.7 Ω?

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

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

- a) 1.026E-05 V/m
- b) 1.129E-05 V/m
- c) 1.242E-05 V/m
- d) 1.366E-05 V/m
- e) 1.502E-05 V/m

4) A recangular coil with an area of 0.291 m^{2} and 6 turns is placed in a uniform magnetic field of 2.63 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.130E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 35 s?

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

#### c13 L1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.419 m. The magnetic field is spatially uniform but decays in time according to , where 9.15 s. What is the current in the coil if the impedance of the coil is 67.8 Ω?

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

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

- a) 1.598E-04 V/m
- b) 1.758E-04 V/m
- c) 1.934E-04 V/m
- d) 2.127E-04 V/m
- e) 2.340E-04 V/m

3) A recangular coil with an area of 0.182 m^{2} and 5 turns is placed in a uniform magnetic field of 2.74 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 2.390E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 79 s?

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

4) A long solenoid has a radius of 0.613 m and 75 turns per meter; its current decreases with time according to , where 2 A and 22 s^{−1}.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

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

#### c13 L2[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.348 m. The magnetic field is spatially uniform but decays in time according to , where 7.57 s. What is the current in the coil if the impedance of the coil is 68.6 Ω?

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

2) A recangular coil with an area of 0.897 m^{2} and 8 turns is placed in a uniform magnetic field of 2.83 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 8.740E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 3 s?

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

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

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

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

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

### c13 M0[edit | edit source]

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

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

2) A long solenoid has a radius of 0.45 m and 35 turns per meter; its current decreases with time according to , where 1 A and 28 s^{−1}.What is the induced electric fied at a distance 2.35 m from the axis at time t=0.0709 s ?

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

3) A recangular coil with an area of 0.137 m^{2} and 18 turns is placed in a uniform magnetic field of 1.18 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.120E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 47 s?

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

4) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.79 T and 7.280E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 7.910E+04 V
- b) 8.701E+04 V
- c) 9.571E+04 V
- d) 1.053E+05 V
- e) 1.158E+05 V

#### c13 M1[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.54 T and 1.860E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 2.415E+04 V
- b) 2.656E+04 V
- c) 2.922E+04 V
- d) 3.214E+04 V
- e) 3.535E+04 V

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

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

3) A recangular coil with an area of 0.137 m^{2} and 18 turns is placed in a uniform magnetic field of 1.18 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.120E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 47 s?

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

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

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

#### c13 M2[edit | edit source]

1) A recangular coil with an area of 0.315 m^{2} and 20 turns is placed in a uniform magnetic field of 3.45 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 9.480E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 26 s?

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

2) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to , where 2 A and 21 s^{−1}.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?

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

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

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

4) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.84 T and 4.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 3.333E+04 V
- b) 3.666E+04 V
- c) 4.033E+04 V
- d) 4.436E+04 V
- e) 4.879E+04 V

### c13 N0[edit | edit source]

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

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

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

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

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

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

4) A long solenoid has a radius of 0.447 m and 85 turns per meter; its current decreases with time according to , where 7 A and 23 s^{−1}.What is the induced electric fied at a distance 0.212 m from the axis at time t=0.0819 s ?

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

#### c13 N1[edit | edit source]

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

- a) 1.598E-04 V/m
- b) 1.758E-04 V/m
- c) 1.934E-04 V/m
- d) 2.127E-04 V/m
- e) 2.340E-04 V/m

2) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

4) A long solenoid has a radius of 0.591 m and 41 turns per meter; its current decreases with time according to , where 1 A and 30 s^{−1}.What is the induced electric fied at a distance 0.234 m from the axis at time t=0.0208 s ?

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

#### c13 N2[edit | edit source]

1) A long solenoid has a radius of 0.517 m and 23 turns per meter; its current decreases with time according to , where 1 A and 30 s^{−1}.What is the induced electric fied at a distance 0.162 m from the axis at time t=0.0679 s ?

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

2) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.215E-04 V
- b) 1.337E-04 V
- c) 1.470E-04 V
- d) 1.617E-04 V
- e) 1.779E-04 V

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

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

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

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

### c13 O0[edit | edit source]

1) A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)--(

*Answer & Why this question is different.*)

- a) 7.479E+00 cm
^{3}/s - b) 8.227E+00 cm
^{3}/s - c) 9.049E+00 cm
^{3}/s - d) 9.954E+00 cm
^{3}/s - e) 1.095E+01 cm
^{3}/s

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

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

3) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

#### c13 O1[edit | edit source]

1) A cylinder of height 1.48 cm and radius 7.74 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.76 cm from point O and moves at a speed of 3.09 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)--(

*Answer & Why this question is different.*)

- a) 3.312E+01 cm
^{3}/s - b) 3.643E+01 cm
^{3}/s - c) 4.008E+01 cm
^{3}/s - d) 4.408E+01 cm
^{3}/s - e) 4.849E+01 cm
^{3}/s

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

- a) 1.395E+04 V
- b) 1.534E+04 V
- c) 1.688E+04 V
- d) 1.857E+04 V
- e) 2.042E+04 V

3) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

#### c13 O2[edit | edit source]

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

--(

*Answer & Why this question is different.*)

- a) 3.054E+01 cm
^{3}/s - b) 3.359E+01 cm
^{3}/s - c) 3.695E+01 cm
^{3}/s - d) 4.065E+01 cm
^{3}/s - e) 4.471E+01 cm
^{3}/s

3) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

### c13 P0[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.869 m. The magnetic field is spatially uniform but decays in time according to , where 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

--(

*Answer & Why this question is different.*)

- a) 4.057E+01 cm
^{3}/s - b) 4.463E+01 cm
^{3}/s - c) 4.909E+01 cm
^{3}/s - d) 5.400E+01 cm
^{3}/s - e) 5.940E+01 cm
^{3}/s

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

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

^{−1}.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

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

#### c13 P1[edit | edit source]

1) A long solenoid has a radius of 0.591 m and 41 turns per meter; its current decreases with time according to , where 1 A and 30 s^{−1}.What is the induced electric fied at a distance 0.234 m from the axis at time t=0.0208 s ?

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

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.798 m. The magnetic field is spatially uniform but decays in time according to , where 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

--(

*Answer & Why this question is different.*)

- a) 7.479E+00 cm
^{3}/s - b) 8.227E+00 cm
^{3}/s - c) 9.049E+00 cm
^{3}/s - d) 9.954E+00 cm
^{3}/s - e) 1.095E+01 cm
^{3}/s

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

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

#### c13 P2[edit | edit source]

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

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

--(

*Answer & Why this question is different.*)

- a) 8.324E+00 cm
^{3}/s - b) 9.157E+00 cm
^{3}/s - c) 1.007E+01 cm
^{3}/s - d) 1.108E+01 cm
^{3}/s - e) 1.219E+01 cm
^{3}/s

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.861 m. The magnetic field is spatially uniform but decays in time according to , where 4.2 s. What is the current in the coil if the impedance of the coil is 19.8 Ω?

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

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

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

### c13 Q0[edit | edit source]

1) A recangular coil with an area of 0.446 m^{2} and 13 turns is placed in a uniform magnetic field of 3.17 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.060E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 54 s?

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

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.43 m. The magnetic field is spatially uniform but decays in time according to , where 5.61 s. What is the current in the coil if the impedance of the coil is 4.89 Ω?

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

3) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

4) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 2.081E-04 V
- b) 2.289E-04 V
- c) 2.518E-04 V
- d) 2.770E-04 V
- e) 3.047E-04 V

#### c13 Q1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.348 m. The magnetic field is spatially uniform but decays in time according to , where 7.57 s. What is the current in the coil if the impedance of the coil is 68.6 Ω?

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

2) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns wraped in a circle of diameter 1.44 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.602E-04 V
- b) 1.762E-04 V
- c) 1.939E-04 V
- d) 2.132E-04 V
- e) 2.346E-04 V

3) A square coil has sides that are L= 0.894 m long and is tightly wound with N=255 turns of wire. The resistance of the coil is R=8.83 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0682 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

4) A recangular coil with an area of 0.157 m^{2} and 17 turns is placed in a uniform magnetic field of 3.64 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.890E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 9 s?

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

#### c13 Q2[edit | edit source]

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

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

2) A recangular coil with an area of 0.178 m^{2} and 17 turns is placed in a uniform magnetic field of 2.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.380E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 45 s?

- a) 1.068E+04 V
- b) 1.175E+04 V
- c) 1.293E+04 V
- d) 1.422E+04 V
- e) 1.564E+04 V

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.274 m. The magnetic field is spatially uniform but decays in time according to , where 9.59 s. What is the current in the coil if the impedance of the coil is 33.0 Ω?

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

4) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 2.081E-04 V
- b) 2.289E-04 V
- c) 2.518E-04 V
- d) 2.770E-04 V
- e) 3.047E-04 V

### c13 R0[edit | edit source]

1) A long solenoid has a radius of 0.887 m and 45 turns per meter; its current decreases with time according to , where 3 A and 25 s^{−1}.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

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

2) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.78 m. The magnetic field is spatially uniform but decays in time according to , where 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

--(

*Answer & Why this question is different.*)

- a) 7.479E+00 cm
^{3}/s - b) 8.227E+00 cm
^{3}/s - c) 9.049E+00 cm
^{3}/s - d) 9.954E+00 cm
^{3}/s - e) 1.095E+01 cm
^{3}/s

#### c13 R1[edit | edit source]

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

- a) 6.277E-05 V/m
- b) 6.904E-05 V/m
- c) 7.595E-05 V/m
- d) 8.354E-05 V/m
- e) 9.190E-05 V/m

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to , where 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

--(

*Answer & Why this question is different.*)

- a) 2.976E+01 cm
^{3}/s - b) 3.274E+01 cm
^{3}/s - c) 3.601E+01 cm
^{3}/s - d) 3.961E+01 cm
^{3}/s - e) 4.358E+01 cm
^{3}/s

4) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

#### c13 R2[edit | edit source]

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

--(

*Answer & Why this question is different.*)

- a) 3.312E+01 cm
^{3}/s - b) 3.643E+01 cm
^{3}/s - c) 4.008E+01 cm
^{3}/s - d) 4.408E+01 cm
^{3}/s - e) 4.849E+01 cm
^{3}/s

3) A long solenoid has a radius of 0.436 m and 87 turns per meter; its current decreases with time according to , where 4 A and 27 s^{−1}.What is the induced electric fied at a distance 0.153 m from the axis at time t=0.02 s ?

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

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to , where 5.58 s. What is the current in the coil if the impedance of the coil is 13.3 Ω?

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

### c13 S0[edit | edit source]

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

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

2) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.11 T and 1.150E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 2.887E+03 V
- b) 3.176E+03 V
- c) 3.493E+03 V
- d) 3.843E+03 V
- e) 4.227E+03 V

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

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

#### c13 S1[edit | edit source]

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

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

2) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.84 T and 4.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 3.333E+04 V
- b) 3.666E+04 V
- c) 4.033E+04 V
- d) 4.436E+04 V
- e) 4.879E+04 V

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

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

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

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

#### c13 S2[edit | edit source]

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

- a) 3.006E-06 V/m
- b) 3.307E-06 V/m
- c) 3.637E-06 V/m
- d) 4.001E-06 V/m
- e) 4.401E-06 V/m

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

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

3) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.45 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.066E-04 V
- b) 1.173E-04 V
- c) 1.290E-04 V
- d) 1.419E-04 V
- e) 1.561E-04 V

4) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.11 T and 1.150E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 2.887E+03 V
- b) 3.176E+03 V
- c) 3.493E+03 V
- d) 3.843E+03 V
- e) 4.227E+03 V

### c13 T0[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to , where 9.53 s. What is the current in the coil if the impedance of the coil is 27.4 Ω?

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

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

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

3) A recangular coil with an area of 0.219 m^{2} 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 where 3.79 T and 7.280E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 7.910E+04 V
- b) 8.701E+04 V
- c) 9.571E+04 V
- d) 1.053E+05 V
- e) 1.158E+05 V

#### c13 T1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to , where 9.53 s. What is the current in the coil if the impedance of the coil is 27.4 Ω?

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

2) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.84 T and 4.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 3.333E+04 V
- b) 3.666E+04 V
- c) 4.033E+04 V
- d) 4.436E+04 V
- e) 4.879E+04 V

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

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

4) A recangular coil with an area of 0.897 m^{2} and 8 turns is placed in a uniform magnetic field of 2.83 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 8.740E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 3 s?

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

#### c13 T2[edit | edit source]

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

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

2) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.8 T and 1.530E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

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

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

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

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.43 m. The magnetic field is spatially uniform but decays in time according to , where 5.61 s. What is the current in the coil if the impedance of the coil is 4.89 Ω?

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

### c13 U0[edit | edit source]

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

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

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

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

3) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to , where 2 A and 21 s^{−1}.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?

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

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

- a) 6.277E-05 V/m
- b) 6.904E-05 V/m
- c) 7.595E-05 V/m
- d) 8.354E-05 V/m
- e) 9.190E-05 V/m

#### c13 U1[edit | edit source]

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

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

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

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

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

- a) 1.319E-05 V/m
- b) 1.451E-05 V/m
- c) 1.596E-05 V/m
- d) 1.756E-05 V/m
- e) 1.932E-05 V/m

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

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

#### c13 U2[edit | edit source]

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

- a) 2.529E-05 V/m
- b) 2.782E-05 V/m
- c) 3.060E-05 V/m
- d) 3.366E-05 V/m
- e) 3.703E-05 V/m

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

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

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

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

4) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns wraped in a circle of diameter 1.44 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.602E-04 V
- b) 1.762E-04 V
- c) 1.939E-04 V
- d) 2.132E-04 V
- e) 2.346E-04 V

### c13 V0[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.75 T and 9.800E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 4.198E+04 V
- b) 4.618E+04 V
- c) 5.080E+04 V
- d) 5.588E+04 V
- e) 6.147E+04 V

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

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

--(

*Answer & Why this question is different.*)

- a) 4.057E+01 cm
^{3}/s - b) 4.463E+01 cm
^{3}/s - c) 4.909E+01 cm
^{3}/s - d) 5.400E+01 cm
^{3}/s - e) 5.940E+01 cm
^{3}/s

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.8 m. The magnetic field is spatially uniform but decays in time according to , where 8.91 s. What is the current in the coil if the impedance of the coil is 61.7 Ω?

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

#### c13 V1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to , where 5.58 s. What is the current in the coil if the impedance of the coil is 13.3 Ω?

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

2) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.7 T and 8.100E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

--(

*Answer & Why this question is different.*)

- a) 4.057E+01 cm
^{3}/s - b) 4.463E+01 cm
^{3}/s - c) 4.909E+01 cm
^{3}/s - d) 5.400E+01 cm
^{3}/s - e) 5.940E+01 cm
^{3}/s

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

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

#### c13 V2[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.11 T and 1.150E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- a) 2.887E+03 V
- b) 3.176E+03 V
- c) 3.493E+03 V
- d) 3.843E+03 V
- e) 4.227E+03 V

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.78 m. The magnetic field is spatially uniform but decays in time according to , where 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

--(

*Answer & Why this question is different.*)

- a) 1.153E+02 cm
^{3}/s - b) 1.268E+02 cm
^{3}/s - c) 1.395E+02 cm
^{3}/s - d) 1.535E+02 cm
^{3}/s - e) 1.688E+02 cm
^{3}/s

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

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

### c13 W0[edit | edit source]

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

*Answer & Why this question is different.*)

- a) 1.892E+01 cm
^{3}/s - b) 2.081E+01 cm
^{3}/s - c) 2.289E+01 cm
^{3}/s - d) 2.518E+01 cm
^{3}/s - e) 2.770E+01 cm
^{3}/s

2) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A long solenoid has a radius of 0.887 m and 45 turns per meter; its current decreases with time according to , where 3 A and 25 s^{−1}.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

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

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

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

#### c13 W1[edit | edit source]

1) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

--(

*Answer & Why this question is different.*)

- a) 5.308E+01 cm
^{3}/s - b) 5.839E+01 cm
^{3}/s - c) 6.422E+01 cm
^{3}/s - d) 7.065E+01 cm
^{3}/s - e) 7.771E+01 cm
^{3}/s

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

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

#### c13 W2[edit | edit source]

1) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns wraped in a circle of diameter 1.44 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 1.602E-04 V
- b) 1.762E-04 V
- c) 1.939E-04 V
- d) 2.132E-04 V
- e) 2.346E-04 V

--(

*Answer & Why this question is different.*)

- a) 1.128E+02 cm
^{3}/s - b) 1.241E+02 cm
^{3}/s - c) 1.365E+02 cm
^{3}/s - d) 1.502E+02 cm
^{3}/s - e) 1.652E+02 cm
^{3}/s

3) A long solenoid has a radius of 0.645 m and 37 turns per meter; its current decreases with time according to , where 9 A and 23 s^{−1}.What is the induced electric fied at a distance 0.189 m from the axis at time t=0.0698 s ?

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

4) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

### c13 X0[edit | edit source]

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

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

--(

*Answer & Why this question is different.*)

- a) 2.976E+01 cm
^{3}/s - b) 3.274E+01 cm
^{3}/s - c) 3.601E+01 cm
^{3}/s - d) 3.961E+01 cm
^{3}/s - e) 4.358E+01 cm
^{3}/s

3) A recangular coil with an area of 0.219 m^{2} and 14 turns is placed in a uniform magnetic field of 3.71 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.540E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 15 s?

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

4) A square coil has sides that are L= 0.894 m long and is tightly wound with N=255 turns of wire. The resistance of the coil is R=8.83 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0682 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

#### c13 X1[edit | edit source]

1) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

2) A recangular coil with an area of 0.291 m^{2} and 6 turns is placed in a uniform magnetic field of 2.63 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.130E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 35 s?

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

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

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

--(

*Answer & Why this question is different.*)

- a) 1.153E+02 cm
^{3}/s - b) 1.268E+02 cm
^{3}/s - c) 1.395E+02 cm
^{3}/s - d) 1.535E+02 cm
^{3}/s - e) 1.688E+02 cm
^{3}/s

#### c13 X2[edit | edit source]

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

--(

*Answer & Why this question is different.*)

- a) 1.153E+02 cm
^{3}/s - b) 1.268E+02 cm
^{3}/s - c) 1.395E+02 cm
^{3}/s - d) 1.535E+02 cm
^{3}/s - e) 1.688E+02 cm
^{3}/s

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

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

4) A recangular coil with an area of 0.219 m^{2} and 14 turns is placed in a uniform magnetic field of 3.71 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.540E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 15 s?

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

### c13 Y0[edit | edit source]

1) A recangular coil with an area of 0.815 m^{2} and 11 turns is placed in a uniform magnetic field of 3.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.700E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 59 s?

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

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

- a) 1.791E-01 A
- b) 1.970E-01 A
- c) 2.167E-01 A
- d) 2.384E-01 A
- e) 2.622E-01 A

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

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

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

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

#### c13 Y1[edit | edit source]

1) A recangular coil with an area of 0.897 m^{2} and 8 turns is placed in a uniform magnetic field of 2.83 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 8.740E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 3 s?

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

2) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to , where 2 A and 21 s^{−1}.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?

- a) 1.605E-04 V/m
- b) 1.766E-04 V/m
- c) 1.942E-04 V/m
- d) 2.136E-04 V/m
- e) 2.350E-04 V/m

3) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

#### c13 Y2[edit | edit source]

1) A long solenoid has a radius of 0.394 m and 13 turns per meter; its current decreases with time according to , where 9 A and 28 s^{−1}.What is the induced electric fied at a distance 1.8 m from the axis at time t=0.0757 s ?

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

2) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

4) A recangular coil with an area of 0.449 m^{2} and 20 turns is placed in a uniform magnetic field of 3.58 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.990E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 66 s?

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

### c13 Z0[edit | edit source]

1) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 2.081E-04 V
- b) 2.289E-04 V
- c) 2.518E-04 V
- d) 2.770E-04 V
- e) 3.047E-04 V

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to , where 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

--(

*Answer & Why this question is different.*)

- a) 1.892E+01 cm
^{3}/s - b) 2.081E+01 cm
^{3}/s - c) 2.289E+01 cm
^{3}/s - d) 2.518E+01 cm
^{3}/s - e) 2.770E+01 cm
^{3}/s

4) A recangular coil with an area of 0.219 m^{2} and 14 turns is placed in a uniform magnetic field of 3.71 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.540E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 15 s?

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

#### c13 Z1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to , where 7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

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

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

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

3) A recangular coil with an area of 0.182 m^{2} 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

--(

*Answer & Why this question is different.*)

- a) 5.834E+01 cm
^{3}/s - b) 6.418E+01 cm
^{3}/s - c) 7.059E+01 cm
^{3}/s - d) 7.765E+01 cm
^{3}/s - e) 8.542E+01 cm
^{3}/s

#### c13 Z2[edit | edit source]

1) The current through the windings of a solenoid with n= 2.840E+03 turns per meter is changing at a rate dI/dt=19 A/s. The solenoid is 65 cm long and has a cross-sectional diameter of 2.18 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.35 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- a) 2.206E-04 V
- b) 2.426E-04 V
- c) 2.669E-04 V
- d) 2.936E-04 V
- e) 3.230E-04 V

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.43 m. The magnetic field is spatially uniform but decays in time according to , where 5.61 s. What is the current in the coil if the impedance of the coil is 4.89 Ω?

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

3) A recangular coil with an area of 0.412 m^{2} 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

--(

*Answer & Why this question is different.*)

- a) 5.834E+01 cm
^{3}/s - b) 6.418E+01 cm
^{3}/s - c) 7.059E+01 cm
^{3}/s - d) 7.765E+01 cm
^{3}/s - e) 8.542E+01 cm
^{3}/s

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- of 10 blank lines to separate exams from keys
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### Key: A0[edit | edit source]

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

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

2) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to , where 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

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

Click these links for the keys:

#### Key: A1[edit | edit source]

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

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

2) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to , where 7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

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

4) A long solenoid has a radius of 0.591 m and 41 turns per meter; its current decreases with time according to , where 1 A and 30 s^{−1}.What is the induced electric fied at a distance 0.234 m from the axis at time t=0.0208 s ?

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

Click these links for the keys:

#### Key: A2[edit | edit source]

1) A long solenoid has a radius of 0.845 m and 78 turns per meter; its current decreases with time according to , where 3 A and 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

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.708 m. The magnetic field is spatially uniform but decays in time according to , where 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

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

Click these links for the keys:

### Key: B0[edit | edit source]

1) A long solenoid has a radius of 0.845 m and 65 turns per meter; its current decreases with time according to , where 6 A and 30 s^{−1}.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

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

2) A recangular coil with an area of 0.432 m^{2} and 16 turns is placed in a uniform magnetic field of 3.7 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.020E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 55 s?

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

3) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

^{−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

Click these links for the keys:

#### Key: B1[edit | edit source]

1) A recangular coil with an area of 0.587 m^{2} and 13 turns is placed in a uniform magnetic field of 1.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.800E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 93 s?

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

2) A long solenoid has a radius of 0.845 m and 65 turns per meter; its current decreases with time according to , where 6 A and 30 s^{−1}.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

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

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

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

4) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

Click these links for the keys:

#### Key: B2[edit | edit source]

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

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

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

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

3) A long solenoid has a radius of 0.845 m and 65 turns per meter; its current decreases with time according to , where 6 A and 30 s^{−1}.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

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

4) A long solenoid has a radius of 0.517 m and 23 turns per meter; its current decreases with time according to , where 1 A and 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

Click these links for the keys:

### Key: C0[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.798 m. The magnetic field is spatially uniform but decays in time according to , where 4.63 s. What is the current in the coil if the impedance of the coil is 75.7 Ω?

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

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

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

--(

*Answer & Why this question is different.*)

- -a) 8.324E+00 cm
^{3}/s - -b) 9.157E+00 cm
^{3}/s - -c) 1.007E+01 cm
^{3}/s - -d) 1.108E+01 cm
^{3}/s - +e) 1.219E+01 cm
^{3}/s

4) A long solenoid has a radius of 0.857 m and 58 turns per meter; its current decreases with time according to , where 1 A and 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

Click these links for the keys:

#### Key: C1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to , where 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

- -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

--(

*Answer & Why this question is different.*)

- -a) 6.534E+01 cm
^{3}/s - -b) 7.188E+01 cm
^{3}/s - +c) 7.907E+01 cm
^{3}/s - -d) 8.697E+01 cm
^{3}/s - -e) 9.567E+01 cm
^{3}/s

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

- -a) 1.026E-05 V/m
- -b) 1.129E-05 V/m
- +c) 1.242E-05 V/m
- -d) 1.366E-05 V/m
- -e) 1.502E-05 V/m

Click these links for the keys:

#### Key: C2[edit | edit source]

1) A cylinder of height 1.48 cm and radius 7.74 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.76 cm from point O and moves at a speed of 3.09 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)--(

*Answer & Why this question is different.*)

- -a) 3.312E+01 cm
^{3}/s - +b) 3.643E+01 cm
^{3}/s - -c) 4.008E+01 cm
^{3}/s - -d) 4.408E+01 cm
^{3}/s - -e) 4.849E+01 cm
^{3}/s

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

- -a) 1.224E+04 V
- -b) 1.346E+04 V
- -c) 1.481E+04 V
- -d) 1.629E+04 V
- +e) 1.792E+04 V

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.477 m. The magnetic field is spatially uniform but decays in time according to , where 8.01 s. What is the current in the coil if the impedance of the coil is 75.6 Ω?

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

4) A long solenoid has a radius of 0.845 m and 78 turns per meter; its current decreases with time according to , where 3 A and 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

Click these links for the keys:

### Key: D0[edit | edit source]

^{−1}.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

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

2) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- -a) 1.215E-04 V
- -b) 1.337E-04 V
- -c) 1.470E-04 V
- -d) 1.617E-04 V
- +e) 1.779E-04 V

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

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

^{2} 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

Click these links for the keys:

#### Key: D1[edit | edit source]

1) A recangular coil with an area of 0.178 m^{2} and 17 turns is placed in a uniform magnetic field of 2.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.380E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 45 s?

- -a) 1.068E+04 V
- -b) 1.175E+04 V
- +c) 1.293E+04 V
- -d) 1.422E+04 V
- -e) 1.564E+04 V

2) A long solenoid has a radius of 0.749 m and 62 turns per meter; its current decreases with time according to , where 9 A and 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

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

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

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

Click these links for the keys:

#### Key: D2[edit | edit source]

1) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- -a) 1.215E-04 V
- -b) 1.337E-04 V
- -c) 1.470E-04 V
- -d) 1.617E-04 V
- +e) 1.779E-04 V

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

- -a) 1.026E-05 V/m
- -b) 1.129E-05 V/m
- +c) 1.242E-05 V/m
- -d) 1.366E-05 V/m
- -e) 1.502E-05 V/m

3) A recangular coil with an area of 0.479 m^{2} 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

- -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

Click these links for the keys:

### Key: E0[edit | edit source]

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

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

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

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.75 T and 1.740E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

--(

*Answer & Why this question is different.*)

- -a) 7.479E+00 cm
^{3}/s - -b) 8.227E+00 cm
^{3}/s - -c) 9.049E+00 cm
^{3}/s - -d) 9.954E+00 cm
^{3}/s - +e) 1.095E+01 cm
^{3}/s

Click these links for the keys:

#### Key: E1[edit | edit source]

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

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

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

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.97 T and 5.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

--(

*Answer & Why this question is different.*)

- -a) 3.054E+01 cm
^{3}/s - -b) 3.359E+01 cm
^{3}/s - +c) 3.695E+01 cm
^{3}/s - -d) 4.065E+01 cm
^{3}/s - -e) 4.471E+01 cm
^{3}/s

Click these links for the keys:

#### Key: E2[edit | edit source]

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

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

--(

*Answer & Why this question is different.*)

- +a) 1.372E+01 cm
^{3}/s - -b) 1.509E+01 cm
^{3}/s - -c) 1.660E+01 cm
^{3}/s - -d) 1.826E+01 cm
^{3}/s - -e) 2.009E+01 cm
^{3}/s

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 2.18 T and 4.840E+03 s^{−1}. Suppose the electric field is always zero at point , and consider a circle of radius 0.387 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral around the circle.

- -a) 1.928E+04 V
- -b) 2.120E+04 V
- -c) 2.332E+04 V
- +d) 2.566E+04 V
- -e) 2.822E+04 V

4) A long solenoid has a radius of 0.777 m and 67 turns per meter; its current decreases with time according to , where 6 A and 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

Click these links for the keys:

### Key: F0[edit | edit source]

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

2) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.8 T and 1.530E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

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

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

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

Click these links for the keys:

#### Key: F1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.8 m. The magnetic field is spatially uniform but decays in time according to , where 8.91 s. What is the current in the coil if the impedance of the coil is 61.7 Ω?

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

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

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

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.89 T and 1.710E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- -a) 7.262E+03 V
- -b) 7.988E+03 V
- -c) 8.787E+03 V
- +d) 9.666E+03 V
- -e) 1.063E+04 V

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

- -a) 2.609E+00 A
- -b) 2.870E+00 A
- +c) 3.157E+00 A
- -d) 3.473E+00 A
- -e) 3.820E+00 A

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#### Key: F2[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.274 m. The magnetic field is spatially uniform but decays in time according to , where 9.59 s. What is the current in the coil if the impedance of the coil is 33.0 Ω?

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

2) A square coil has sides that are L= 0.245 m long and is tightly wound with N=925 turns of wire. The resistance of the coil is R=8.0 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

4) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.97 T and 5.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

Click these links for the keys:

### Key: G0[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.58 T and 4.310E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

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

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

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.227 m. The magnetic field is spatially uniform but decays in time according to , where 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

- -a) 2.081E-04 V
- -b) 2.289E-04 V
- -c) 2.518E-04 V
- +d) 2.770E-04 V
- -e) 3.047E-04 V

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#### Key: G1[edit | edit source]

1) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.706 m. The magnetic field is spatially uniform but decays in time according to , where 9.53 s. What is the current in the coil if the impedance of the coil is 27.4 Ω?

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

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

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

^{−1}. Suppose the electric field is always zero at point , 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 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

Click these links for the keys:

#### Key: G2[edit | edit source]

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

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

- +a) 1.242E-04 V
- -b) 1.366E-04 V
- -c) 1.503E-04 V
- -d) 1.653E-04 V
- -e) 1.819E-04 V

3) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.31 T and 8.360E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- -a) 7.145E+04 V
- -b) 7.860E+04 V
- -c) 8.646E+04 V
- +d) 9.510E+04 V
- -e) 1.046E+05 V

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

- +a) 1.791E-01 A
- -b) 1.970E-01 A
- -c) 2.167E-01 A
- -d) 2.384E-01 A
- -e) 2.622E-01 A

Click these links for the keys:

### Key: H0[edit | edit source]

1) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.45 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- -a) 1.066E-04 V
- -b) 1.173E-04 V
- +c) 1.290E-04 V
- -d) 1.419E-04 V
- -e) 1.561E-04 V

2) A recangular coil with an area of 0.315 m^{2} and 20 turns is placed in a uniform magnetic field of 3.45 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 9.480E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 26 s?

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

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

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

^{−1}.What is the induced electric fied at a distance 0.106 m from the axis at time t=0.055 s ?

- -a) 1.026E-05 V/m
- -b) 1.129E-05 V/m
- +c) 1.242E-05 V/m
- -d) 1.366E-05 V/m
- -e) 1.502E-05 V/m

Click these links for the keys:

#### Key: H1[edit | edit source]

^{−1}.What is the induced electric fied at a distance 0.203 m from the axis at time t=0.0448 s ?

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

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

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

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

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

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

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

Click these links for the keys:

#### Key: H2[edit | edit source]

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

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

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

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

3) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm. A small coil consisting of N=23turns wraped in a circle of diameter 1.7 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- -a) 1.215E-04 V
- -b) 1.337E-04 V
- -c) 1.470E-04 V
- -d) 1.617E-04 V
- +e) 1.779E-04 V

4) A long solenoid has a radius of 0.887 m and 45 turns per meter; its current decreases with time according to , where 3 A and 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

Click these links for the keys:

### Key: I0[edit | edit source]

1) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

--(

*Answer & Why this question is different.*)

- -a) 1.128E+02 cm
^{3}/s - -b) 1.241E+02 cm
^{3}/s - -c) 1.365E+02 cm
^{3}/s - +d) 1.502E+02 cm
^{3}/s - -e) 1.652E+02 cm
^{3}/s

4) A long solenoid has a radius of 0.596 m and 19 turns per meter; its current decreases with time according to , where 5 A and 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

Click these links for the keys:

#### Key: I1[edit | edit source]

1) A square coil has sides that are L= 0.458 m long and is tightly wound with N=742 turns of wire. The resistance of the coil is R=6.81 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0559 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

--(

*Answer & Why this question is different.*)

- -a) 3.312E+01 cm
^{3}/s - +b) 3.643E+01 cm
^{3}/s - -c) 4.008E+01 cm
^{3}/s - -d) 4.408E+01 cm
^{3}/s - -e) 4.849E+01 cm
^{3}/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

Click these links for the keys:

#### Key: I2[edit | edit source]

1) A square coil has sides that are L= 0.465 m long and is tightly wound with N=954 turns of wire. The resistance of the coil is R=6.06 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0367 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

3) A long solenoid has a radius of 0.732 m and 55 turns per meter; its current decreases with time according to , where 9 A and 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

--(

*Answer & Why this question is different.*)

- -a) 2.061E+02 cm
^{3}/s - -b) 2.267E+02 cm
^{3}/s - +c) 2.494E+02 cm
^{3}/s - -d) 2.743E+02 cm
^{3}/s - -e) 3.018E+02 cm
^{3}/s

Click these links for the keys:

### Key: J0[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.7 T and 8.100E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

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

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

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

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.78 m. The magnetic field is spatially uniform but decays in time according to , where 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

- -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

Click these links for the keys:

#### Key: J1[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.71 T and 4.780E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- +a) 1.510E+04 V
- -b) 1.661E+04 V
- -c) 1.827E+04 V
- -d) 2.010E+04 V
- -e) 2.211E+04 V

2) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns wraped in a circle of diameter 1.44 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

- -a) 1.602E-04 V
- -b) 1.762E-04 V
- +c) 1.939E-04 V
- -d) 2.132E-04 V
- -e) 2.346E-04 V

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

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

4) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to , where 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

Click these links for the keys:

#### Key: J2[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.84 T and 4.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- -a) 3.333E+04 V
- -b) 3.666E+04 V
- +c) 4.033E+04 V
- -d) 4.436E+04 V
- -e) 4.879E+04 V

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.861 m. The magnetic field is spatially uniform but decays in time according to , where 4.2 s. What is the current in the coil if the impedance of the coil is 19.8 Ω?

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

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

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

- -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

Click these links for the keys:

### Key: K0[edit | edit source]

1) A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)--(

*Answer & Why this question is different.*)

- -a) 7.479E+00 cm
^{3}/s - -b) 8.227E+00 cm
^{3}/s - -c) 9.049E+00 cm
^{3}/s - -d) 9.954E+00 cm
^{3}/s - +e) 1.095E+01 cm
^{3}/s

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

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

^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- -a) 1.168E+04 V
- -b) 1.284E+04 V
- -c) 1.413E+04 V
- -d) 1.554E+04 V
- +e) 1.710E+04 V

4) A long solenoid has a radius of 0.436 m and 87 turns per meter; its current decreases with time according to , where 4 A and 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

Click these links for the keys:

#### Key: K1[edit | edit source]

^{−1}.What is the induced electric fied at a distance 0.169 m from the axis at time t=0.072 s ?

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

2) A spatially uniform magnetic points in the z-direction and oscilates with time as where 1.89 T and 1.710E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

--(

*Answer & Why this question is different.*)

- -a) 6.534E+01 cm
^{3}/s - -b) 7.188E+01 cm
^{3}/s - +c) 7.907E+01 cm
^{3}/s - -d) 8.697E+01 cm
^{3}/s - -e) 9.567E+01 cm
^{3}/s

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

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

Click these links for the keys:

#### Key: K2[edit | edit source]

^{−1}. Suppose the electric field is always zero at point , 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 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

--(

*Answer & Why this question is different.*)

- -a) 3.312E+01 cm
^{3}/s - +b) 3.643E+01 cm
^{3}/s - -c) 4.008E+01 cm
^{3}/s - -d) 4.408E+01 cm
^{3}/s - -e) 4.849E+01 cm
^{3}/s

3) A long solenoid has a radius of 0.596 m and 19 turns per meter; its current decreases with time according to , where 5 A and 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

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

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### Key: L0[edit | edit source]

1) A long solenoid has a radius of 0.394 m and 13 turns per meter; its current decreases with time according to , where 9 A and 28 s^{−1}.What is the induced electric fied at a distance 1.8 m from the axis at time t=0.0757 s ?

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

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.549 m. The magnetic field is spatially uniform but decays in time according to , where 7.0 s. What is the current in the coil if the impedance of the coil is 46.7 Ω?

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

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

- -a) 1.026E-05 V/m
- -b) 1.129E-05 V/m
- +c) 1.242E-05 V/m
- -d) 1.366E-05 V/m
- -e) 1.502E-05 V/m

4) A recangular coil with an area of 0.291 m^{2} and 6 turns is placed in a uniform magnetic field of 2.63 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.130E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 35 s?

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

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#### Key: L1[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.419 m. The magnetic field is spatially uniform but decays in time according to , where 9.15 s. What is the current in the coil if the impedance of the coil is 67.8 Ω?

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

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

- -a) 1.598E-04 V/m
- +b) 1.758E-04 V/m
- -c) 1.934E-04 V/m
- -d) 2.127E-04 V/m
- -e) 2.340E-04 V/m

3) A recangular coil with an area of 0.182 m^{2} 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

^{−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

Click these links for the keys:

#### Key: L2[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.348 m. The magnetic field is spatially uniform but decays in time according to , where 7.57 s. What is the current in the coil if the impedance of the coil is 68.6 Ω?

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

2) A recangular coil with an area of 0.897 m^{2} and 8 turns is placed in a uniform magnetic field of 2.83 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 8.740E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 3 s?

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

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

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

4) A long solenoid has a radius of 0.793 m and 45 turns per meter; its current decreases with time according to , where 2 A and 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

Click these links for the keys:

### Key: M0[edit | edit source]

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

2) A long solenoid has a radius of 0.45 m and 35 turns per meter; its current decreases with time according to , where 1 A and 28 s^{−1}.What is the induced electric fied at a distance 2.35 m from the axis at time t=0.0709 s ?

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

3) A recangular coil with an area of 0.137 m^{2} and 18 turns is placed in a uniform magnetic field of 1.18 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.120E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 47 s?

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

4) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.79 T and 7.280E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

Click these links for the keys:

#### Key: M1[edit | edit source]

1) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.54 T and 1.860E+03 s^{−1}. Suppose the electric field is always zero at point , 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 around the circle.

- -a) 2.415E+04 V
- +b) 2.656E+04 V
- -c) 2.922E+04 V
- -d) 3.214E+04 V
- -e) 3.535E+04 V

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

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

^{2} and 18 turns is placed in a uniform magnetic field of 1.18 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.120E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 47 s?

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

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

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

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#### Key: M2[edit | edit source]

1) A recangular coil with an area of 0.315 m^{2} and 20 turns is placed in a uniform magnetic field of 3.45 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 9.480E+03 s^{−1}. What is the *magnitude* (absolute value) of the induced emf at t = 26 s?

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

2) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to , where 2 A and 21 s^{−1}.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?

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

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

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

4) A spatially uniform magnetic points in the z-direction and oscilates with time as where 3.84 T and 4.410E+03 s^{−1}. Suppose the electric field is always zero at point , 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 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

Click these links for the keys:

### Key: N0[edit | edit source]

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

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

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

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

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

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

4) A long solenoid has a radius of 0.447 m and 85 turns per meter; its current decreases with time according to , where 7 A and 23 s^{−1}.What is the induced electric fied at a distance 0.212 m from the axis at time t=0.0819 s ?

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

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#### Key: N1[edit | edit source]

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

- -a) 1.598E-04 V/m
- +b) 1.758E-04 V/m
- -c) 1.934E-04 V/m
- -d) 2.127E-04 V/m
- -e) 2.340E-04 V/m

2) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

- -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

^{−1}.What is the induced electric fied at a distance 0.234 m from the axis at time t=0.0208 s ?

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

Click these links for the keys:

#### Key: N2[edit | edit source]

1) A long solenoid has a radius of 0.517 m and 23 turns per meter; its current decreases with time according to , where 1 A and 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

- -a) 1.215E-04 V
- -b) 1.337E-04 V
- -c) 1.470E-04 V
- -d) 1.617E-04 V
- +e) 1.779E-04 V

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

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

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

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

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### Key: O0[edit | edit source]

1) A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)--(

*Answer & Why this question is different.*)

- -a) 7.479E+00 cm
^{3}/s - -b) 8.227E+00 cm
^{3}/s - -c) 9.049E+00 cm
^{3}/s - -d) 9.954E+00 cm
^{3}/s - +e) 1.095E+01 cm
^{3}/s

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

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

3) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

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#### Key: O1[edit | edit source]

1) A cylinder of height 1.48 cm and radius 7.74 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.76 cm from point O and moves at a speed of 3.09 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)--(

*Answer & Why this question is different.*)

- -a) 3.312E+01 cm
^{3}/s - +b) 3.643E+01 cm
^{3}/s - -c) 4.008E+01 cm
^{3}/s - -d) 4.408E+01 cm
^{3}/s - -e) 4.849E+01 cm
^{3}/s

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

- -a) 1.395E+04 V
- -b) 1.534E+04 V
- -c) 1.688E+04 V
- -d) 1.857E+04 V
- +e) 2.042E+04 V

3) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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

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#### Key: O2[edit | edit source]

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

--(

*Answer & Why this question is different.*)

- -a) 3.054E+01 cm
^{3}/s - -b) 3.359E+01 cm
^{3}/s - +c) 3.695E+01 cm
^{3}/s - -d) 4.065E+01 cm
^{3}/s - -e) 4.471E+01 cm
^{3}/s

3) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

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

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

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### Key: P0[edit | edit source]

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.869 m. The magnetic field is spatially uniform but decays in time according to , where 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

--(

*Answer & Why this question is different.*)

- -a) 4.057E+01 cm
^{3}/s - -b) 4.463E+01 cm
^{3}/s - -c) 4.909E+01 cm
^{3}/s - -d) 5.400E+01 cm
^{3}/s - +e) 5.940E+01 cm
^{3}/s

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

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

^{−1}.What is the induced electric fied at a distance 0.206 m from the axis at time t=0.0387 s ?

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

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#### Key: P1[edit | edit source]

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