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MULTIPLE CHOICE PROBLEMS for
ELECTROMAGNETISM
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A Student
10/28/2014
.
MULTIPLE CHOICE PROBLEMS
f or t he
STUDY
of
ELECTROMAGNETISM
MAGNETIC FLUX DENSITY
7. A 0.50 T magnetic field is directed perpendicular to the plane of a circular loop of radius 0.25 m.
What is the magnitude of the magnetic flux through the loop?
A) 0.049 Wb
B) 0.098 Wb
C) 0.20 Wb
D) 0.39 Wb
E) zero Wb
8. The Earth's magnetic field passes through a square tabletop with a magnitude of 4.95 x 10 5 T and directed at an
angle of 165° relative to the normal of the tabletop. If the tabletop has 1.50 m sides, what is the magnitude of the
magnetic flux through it?
A) 1.08 x 104 Wb
5 Wb
5 Wb
6 Wb
5 Wb
11. A uniform magnetic field passes through two areas, A1 and A2.
The angles between the magnetic field and the normals of areas A1and A2 are 30.0° and 60.0°, respectively.
If the magnetic flux through the two areas is the same, what is the ratio A1/A2?
A) 0.577
B) 0.816
C) 1.00
D) 1.23
E) 1.73
MOTIONAL EMF
2. The units of motional emf may be written
A) T • m/s
B) V • m2/s
C) J/s
D) kg • m2/(C • s2)
E) T • m
4. A conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown.
As a result of the bar moving through a constant magnetic field, a current I is induced in the indicated direction.
Which one of the following directions is that of the magnetic field?
A) Toward the right
D) Into the page
B) Toward the left
E) out of the page
C) parallel to the long axis of the bar
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5. A 0.45 m metal rod moves 0.11 m in a direction that is perpendicular to a 0.80 T magnetic field in an elapsed time of
0.036 s. Assuming that the acceleration of the rod is 0 m/s2, determine the emf that exists between the ends of the rod.
A) 1.1 V
B) 0.27 V
C) 0.076 V
D) 9.1 x 10 5 V
E) This cannot be determined without knowing the orientation of the rod relative to the magnetic field.
6. A 2.0 kg rod has a length of 1.0 m and a resistance of 4.0 . It slides with constant speed down a pair of frictionless
vertical conducting rails that are joined at the bottom. Other than the rod, the rest of the circuit is resistanceless.
A uniform magnetic field of magnitude 3.0 T is perpendicular to the plane formed by the rod and the rails as shown.
Determine the speed of the rod.
A) 0.38 m/s
B) 0.90 m/s
C) 2.6 m/s
D) 5.6 m/s
E) 8.7 m/s
Use the following to answer questions 25-26:
A circuit is pulled with a 16-N force toward the right to maintain a constant speed v.
At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper.
As the circuit moves, a 6.0 A current flows through a 4.0- resistor.
25. Which one of the following statements concerning this situation is true?
A) The temperature of the circuit remains constant.
B) The induced current flows clockwise around the circuit.
C) Since the circuit moves with constant speed, the force F does zero work.
D) If the circuit were replaced with a wooden loop, there would be no induced emf.
E) As the circuit moves through the field, the field does work to produce the current.
26. With what speed does the circuit move?
A) 1.5 m/s
B) 3.0 m/s
C) 6.4 m/s
D) 9.0 m/s
E) 12 m/s
Use the following to answer questions 62-64:
A loop is pulled with a force F to the right to maintain a constant speed of 8.0 m/s. The loop has a length of 0.15 m, a
width of 0.08 m, and a resistance of 200.0 . At the instant shown, the loop is partially in and partially out of a uniform
magnetic field that is directed into the paper. The magnitude of the field is 1.2 T.
62. What is the magnitude of the emf induced in the loop?
A) Zero volts
B) 0.77 V
C) 1.4 V
D) 4.9 V
E) 9.6 V
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63. What is the induced current in the loop?
A) 0.048 A
B) 0.024 A
C) 7.2  10 -3 A
D) 3.8 x 10 -3 A
E) Zero amperes
64. Determine the magnitude of the force F required to pull the loop.
A) 1.3 x 10 -4 N
D) 6.8 x 10-4 N
B) 2.1 x 10-4 N
E) 9.0 x 10-4 N
C) 3.7 x 10-4 N
Use the following to answer questions 65-69:
A loop with a resistance of 2.0 is pushed to the left at a constant speed of 4.0 m/s by a 32 N force. At the instant
shown in the figure, the loop is partially in and partially out of a uniform magnetic field. An induced current flows from
left to right through the resistor. The length and width of the loop are 2.0 m and 1.0 m, respectively.
65. What is the direction of the magnetic field?
A) To the left
D) Into the paper
B) To the right
E) Toward the top of the page
C) out of the paper
66. Determine the magnitude of the induced current through the resistor.
A) 2.0 A
B) 4.0 A
C) 8.0 A
D) 16 A
E) 32 A
67. Determine the magnitude of the induced emf in the loop.
A) 2.0 V
B) 4.0 V
C) 8.0 V
D) 12 V
E) 16 V
68. Determine the magnitude of the uniform magnetic field.
A) 2 T
B) 4 T
C) 6 T
D) 8 T
E) 12 T
69. At what rate is energy dissipated by the resistor?
A) 128 W
B) 96 W
C) 32 W
D) 16 W
E) 8.0 W
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FARADAY'S LAW of INDUCTION: INDUCED EMF and Currents
9. A circular copper loop is placed perpendicular to a uniform magnetic field of 0.50 T. Due to external forces, the area
of the loop decreases at a rate of 1.26 x 13 m2/s. Determine the induced emf in the loop.
A) 3.1 x 104 V
B) 6.3 x 104 V
C) 1.2 x 103 V
D) 7.9 x 103 V
E) 3.1 V
1. A conducting loop of wire is placed in a magnetic field that is normal to the plane of the loop.
Which one of the following actions will not result in an induced current in the loop?
A) Rotate the loop about an axis that is parallel to the field and passes through the center of the loop.
B) Increase the strength of the magnetic field.
C) Decrease the area of the loop.
D) Decrease the strength of the magnetic field.
E) Rotate the loop about an axis that is perpendicular to the field and passes through the center of the loop.
3. The figure shows a uniform magnetic field that is normal to the plane of a conducting loop, which has a
resistance R. Which one of the following changes will cause an induced current to flow through the resistor?
A) Decreasing the area of the loop
B) Decreasing the magnitude of the magnetic field
C) Increasing the magnitude of the magnetic field
D) Rotating the loop through 90° into the plane of the paper
E) all of the above
10. A conducting loop has an area of 0.065 m2 and is positioned such that a uniform magnetic field is perpendicular to
the plane of the loop. When the magnitude of the magnetic field decreases to 0.30 T in 0.087 s, the average induced
emf in the loop is 1.2 V. What is the initial value of the magnetic field?
A) 0.42 T
B) 0.75 T
C) 0.87 T
D) 1.2 T
E) 1.9 T
13. A magnetic field is directed perpendicular to the plane of the 0.15 m  0.30-m rectangular coil
comprised of 120 loops of wire. To induce an average emf of
.2 V in the coil, the magnetic field is increased from
0.1 T to 1.5 T during a time interval t. Determine t.
A) 0.053 s
B) 0.13 s
C) 1.6 s
D) 6.3 s
E) 7.6 s
14. The area of a 333 turn conducting coil is 7.85 x 103 m2. The resistance of the coil is 10.4 . If the coil is oriented
as shown in a magnetic field B, at what rate in T/s should the magnitude of B change to induce a current of 2.50 x 103
A in the coil?
A) 0.0155 T/s
B) 0.0996 T/s
C) 0.228 T/s
D) 0.757 T/s
E) 1.52 T/s
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15. A circular coil of wire has 25 turns and has a radius of 0.075 m. The coil is located in a variable magnetic field
whose behavior is shown on the graph. At all times, the magnetic field is directed at an angle of 75° relative to the
normal to the plane of a loop. What is the average emf induced in the coil in the time interval from t = 5.00 s to 7.50 s?
A) 18 mV
B49 mV
C) 92 mV
D) 140 mV
E) 180 mV
Use the following to answer questions 16-19:
The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of a conducting, circular loop with a
resistance of 1.5 and a radius of 0.024 m. The magnetic field is directed out of the paper as shown.
Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular loop.
16. What is the magnitude of the average induced emf in the loop if the magnitude of the magnetic field is doubled in
0.4 s?
A) 0.43 V
B) 0.65 V
C) 0.014 V
D) 0.027 V
E) 0.038 V
17. What is the average current around the loop if the magnitude of the magnetic field is doubled in 0.4 s?
A) 2.8  1 3 A, clockwise
D) 9.0 x 10-3 A, clockwise
B) 4.5 x 10-3 A, clockwise
E) 9.0 x 10-3 A, counterclockwise
C) 4.5 x 10-3 A, counterclockwise
18. If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s,
what is the magnitude of the average induced emf in the loop?
A) 8.6 x 10-3 V
D) 5.4 x 10-2 V
B) 9.8 x 10-3 V
E) 6.4 x 10-2 V
C) 2.7 x 10-2 V
19. If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s,
at what rate is energy dissipated in R?
A) 1.8 x 10-2 W
D) 2.7 x 10-4 W
B) 3.6 x 10-2 W
E) 4.9 x 10-4 W
C) 3.8 x 10-3 W
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59. A circular loop of copper wire with an area of 2.0 m2 lies in a plane perpendicular to a time-dependent magnetic
field oriented as shown. The time-dependence of the field is shown in the graph.
Which one of the entries in the table below is incorrect?
Time
Induced emf
A)
1s
zero volts
B)
4s
2.5 V, counterclockwise
C)
5s
2.5 V, counterclockwise
D)
7s
10 V, clockwise
E)
9s
10 V, counterclockwise
Use the following to answer questions 60-61:
The figure shows a uniform magnetic field that is normal to the plane of the conducting loop of resistance R.
Note: the area of the non-circular portion of the circuit is negligible compared to that of the loop.
60. Which entry in the table below correctly pairs the change in the system with the direction of the induced current
through R?
Change in the system
direction of current through R
A) Decrease the area of the loop
from top toward bottom
B) Rotate loop into the paper
no induced current
C) Increase the area of the loop
from bottom toward top
D) Decrease the magnitude of B
from bottom toward top
E) Pull loop to the right
from top toward bottom
61. Suppose that the radius of the loop is 0.50 m.
At what rate must B change with time if the emf induced in the loop is 3 volts?
A) 12.0 T/s
B) 18.8 T/s
C) 24.0 T/s
D) 37.7 T/s
E) 49.2 T/s
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Use the following to answer questions 70-72:
loop is pulled on opposite sides by equal forces and stretched until its enclosed area is essentially zero m 2, as
suggested in the drawings. It takes 0.30 s to close the loop.
70. Determine the magnitude of the emf induced in the loop.
A) 1.2 x 10-1 V
-2 V
D)
-2 V
B) 1.8
2
E)
V
2V
C)
71. At what rate is heat generated in the loop?
A) 3.6 x 10 -3 W
5W
-4 W
-5 W
4W
72. Which one of the following phrases best describes the direction of the induced magnetic field generated by the
current induced in the loop while the loop is being stretched?
A) Clockwise
D) out of the page
B) Counterclockwise
E) The induced field is zero.
C) Into the page
LENZ’S LAW
20. A long, straight wire is in the same plane as a wooden, non-conducting loop.
The wire carries an increasing current I in the direction shown.
A) There will be no induced emf and no induced current.
B) There will be a counterclockwise induced emf, but no induced current.
C) There will be a clockwise induced emf, but no induced current.
D) There will be a clockwise induced current in the loop.
E) There will be a counterclockwise induced current in the loop.
21. A long, straight wire is in the same plane as a rectangular, conducting loop. The wire carries a constant current I as
shown. Which one of the following statements is true if the wire is suddenly moved toward the loop?
A) There will be no induced emf and no induced current.
B) There will be an induced emf, but no induced current.
C) There will be an induced current that is clockwise around the loop.
D) There will be an induced current that is counterclockwise around the loop.
E) There will be an induced electric field that is clockwise around the loop.
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22. A metal ring is dropped from rest below a bar magnet that is fixed in position as suggested in the figure.
An observer views the ring from below. Which one of the following statements concerning this situation is true
A) As the ring falls, an induced current will flow counterclockwise as viewed by the observer.
B) As the ring falls, an induced current will flow clockwise as viewed by the observer.
C) As the ring falls, there will be an induced magnetic field around the ring
that appears counterclockwise as viewed by the observer.
D) As the ring falls, there will be an induced magnetic field around the ring
that appears clockwise as viewed by the observer.
E) Since the magnet is stationary, there will be no induced current in the ring.
23. Two conducting loops carry equal currents I in the same direction as shown in the figure. If the current in the upper
loop suddenly drops to zero, what will happen to the current in the bottom loop according to Lenz's law?
A) The current will decrease.
D) The current will also drop to zero.
B) The current will increase.
E) The current will reverse its direction.
C) The current will not change.
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Answer Key -- Chapter 22: Electromagnetic Induction
1. A
21. D
2. D
22. A
3. C
23. B
4. E
25. B
5. E
26. D
6. E
59. E
7. B
60. D
8. A
61. A
9. B
62. B
10. E
63. D
11. A
64. C
13. D
65. D
14. A
66. C
15. A
67. E
16. C
68. B
17. D
69. A
18. C
70. D
19. E
71. B
20. B
72. C
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