PSI AP Physics C – Electromagnetic Induction

Multiple Choice Questions

1. The induced current in the closed loop is largest in which one of these

diagrams?

(A) (B)

(C) (D)

(E)

2. A loop of wire is placed in a uniform magnetic field directed into the page as

shown above. The magnitude of the magnetic field increases at a constant

rate. What is the direction of the induced current in the loop?

(A) clockwise (B) counter clockwise (C) clockwise then counter clockwise

(D) counter clockwise then clockwise (E) no current in the loop

3. A loop of wire is placed in a uniform magnetic field directed out of the page

as shown above. The magnitude of the magnetic field decreases at a

constant rate. What is the direction of the induced current in the loop?

(A) clockwise (B) counter clockwise (C) clockwise then counter clockwise

(D) counter clockwise then clockwise (E) no current in the loop

4. A square loop of wire is moved at a constant velocity v through a uniform

magnetic field B directed into the page. What is the direction of the induced

current in the loop as it passes through the magnetic field?

Entering the field Leaving the field

(A) clockwise clockwise

(B) counter clockwise counter clockwise

(C) clockwise counter clockwise

(D) counter clockwise clockwise

(E) zero zero

5. A square loop of wire is moved at a constant velocity v through a uniform

magnetic field B directed into the page. What is the direction of the induced

magnetic force on the loop as it passes through the magnetic field?

Entering the field Leaving the field

(A) left right

(B) right left

(C) right right

(D) left left

(E) zero zero

6. A small ring of wire is placed inside a large loop connected to a battery and a

switch. What is the direction of the induced current in the ring just after the

switch is closed?

(A) clockwise (B) counter clockwise (C) clockwise then counter clockwise

(D) counter clockwise then clockwise (E) no induced current

7. A conducting rod is pulled to the right at a constant velocity v through a

uniform magnetic field B directed into the page. The rod rides on two

parallel conducting rails. What is the direction of the induced current in the

circuit?

(A) clockwise (B) counter clockwise (C) clockwise then counter clockwise

(D) counter clockwise then clockwise (E) no induced current

8. A conducting rod of length L is pulled to the right at a constant velocity v

through a uniform magnetic field B. The rod rides two conducting rails

connected to a resistor R. What is the induced current in the circuit? Ignore

the resistance of the rod and the rails.

(A) 𝐵𝐿𝑣𝑅 (B) 𝐵𝑣𝑅

𝐿 (C)

𝐵𝐿𝑣

𝑅 (D)

𝑣𝐿𝑅

𝐵 (E)

𝐵𝑅𝐿

𝑣

9. A conducting rod of length L is pulled to the right at a constant velocity v

through a uniform magnetic field B. The rod rides two metallic rails

connected to a resistor R. What is the rate of energy dissipation in the

circuit? Ignore the resistance of the rod and the rails.

(A) 𝐵𝐿𝑣𝑅 (B) 𝐵𝑣𝑅

𝐿 (C)

𝐵𝐿𝑣

𝑅 (D)

𝑣2𝑅2𝐿

𝐵 (E)

𝐵2 𝐿2 𝑣2

𝑅

10. A circular loop of wire is placed in the same plane as a long wire carrying a

steady current I. Which of the following actions will not induce the current

in the loop?

(A) increasing current in the wire

(B) decreasing current in the wire

(C) moving the away from the wire

(D) moving the loop in parallel to the wire

(E) rotating the loop with respect to its diameter

11. A bar magnet with the north pole facing down is dropped above a

conducting ring. As the magnet passes through the ring, what is the

direction of the induced current in the ring?

(A) always clockwise

(B) always counter clockwise

(C) first clockwise then counter clockwise

(D) first counter clockwise then clockwise

(E) no induced current in the ring

12. A bar magnet with the north pole facing down is dropped above a

conducting ring. Which one of the following is true about the magnet’s

acceleration as it passes through the ring?

(A) less than g (B) greater that g (C) equals g (D) twice g (E) zero

13. A conducting rod moves to the right at a constant velocity. The rod crosses

a uniform magnetic field directed out of the page. Which of the following

choices correctly describes the electric polarity of the rod as it moves

through the field?

Top End Bottom End

(A) positive positive

(B) negative negative

(C) positive negative

(D) negative positive

(E) zero zero

14. A square loop of wire with a side s and resistance R is placed in a uniform

magnetic field of magnitude B directed into the page. The field begins to

increase according to the formula B = β +γt, where β and γ are positive

constants. What is the direction and magnitude of the induced current I in

the loop?

(A) 𝑆2𝛾

𝑅, clockwise (B)

𝑆2𝛾

𝑅, counter clockwise (C)

𝑆2𝛽

𝑅, clockwise

(D) 𝑆2𝛽

𝑅, counter clockwise (E)

𝑆2𝛽𝛾

𝑅, clockwise

15. A circular loop of wire with radius a is placed in a uniform magnetic field

perpendicular to the plane of the loop. The magnetic field varies with time

generating an emf Ɛ = βπ𝑎2𝑡1

2, where β is a constant. What is the rate of

change of the magnetic field?

(A) 1

2 βπ𝑎2𝑡

1

2 (B) β𝑡1

2 (C) βπ𝑎2𝑡1

2 (D) 3

2βπ𝑎2𝑡

3

2 (E) 2

3βπ𝑎2𝑡

3

2

16. A circular loop of wire with radius a is placed in a uniform magnetic field

perpendicular to the plane of the loop. The magnetic field varies with time

generating an emf Ɛ = βπ𝑎2𝑡1

2, where β is a constant. Assuming B (t=0) = 0,

which of the following formulas represents the magnetic field as a function

of time?

(A) 1

2 βπ𝑎2𝑡

1

2 (B) β𝑡1

2 (C) βπ𝑎2𝑡1

2 (D) 3

2βπ𝑎2𝑡

3

2 (E) 2

3β𝑡

3

2

17. A rectangular loop of wire with dimensions a and b moves with a constant

speed v across a uniform magnetic field B directed out of the page. Which of

the following graphs represents the induced current in the loop as a

function of the position x of the leading edge of the loop?

(A) (B)

(C) (D)

(E)

18. A conducting rod moves to the right at a constant velocity. The rod crosses

a uniform magnetic field directed out of the page. Which of the following

graphs represents the induced voltage between the ends of the rod as a

function of time?

(A) (B)

(C) (D)

(E)

19. Which of the following equations states: “A changing magnetic field induces

an electric field?”

(A) ∮ 𝑑𝑙 = −𝑑𝛷𝐵

𝑑𝑡 (B) ∮ 𝑑𝐴 =

𝑄𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑

Ɛ0

(C) ∮ 𝑑𝐴 = 0 (D) ∮ 𝑑𝑙 = µ0𝑖𝑐 (E) ∮ 𝑑𝑙 = Ɛ0𝑑𝛷𝐵

𝑑𝑡

20. The magnetic field B at all points within the shaded circle has an initial

magnitude B. The magnetic field is directed into the page and begins

decreasing at a constant rate. What is the shape and direction of the electric

field lines induced in the circular space?

(A) parallel lines directed to the right

(B) parallel lines directed to the left

(C) concentric circles in the clockwise direction

(D) concentric circles in the counter clockwise direction

(E) parallel lines directed into the page

21. A circular loop of wire with an area of 6×10-3 m2 is placed in a uniform

magnetic field perpendicular to the plane of the loop. The magnetic field

decreases at a constant rate from 0.04 T to zero in 12 µs. What is the

induced emf in the loop?

(A) 10 V (B) 20 V (C) 40 V (D) 60 V (E) 80 V

22. A circular loop of wire with an area of 4.0×10-3 m2 is placed in a uniform

magnetic field perpendicular to the plane of the loop. The magnetic field

increases at a constant rate from zero to 0.050 T in 10.0 µs. If the electrical

resistance of the loop is 400.0 Ω, what is the rate at which energy is

dissipated in the loop as the field increases?

(A) 0.4 W (B) 1.6 W (C) 3.2 W (D) 1.2 W (E) 1.0 W

23. A conducting ring with radius r = 0.10 m is placed in a region of a spatially

uniform magnetic field perpendicular to the plane of the ring. The magnetic

field is directed into the page and is decreasing at a rate of 0.050 T/s. What

is the magnitude of the induced electric field in the ring?

(A) 5×10-3 V/m (B) 2.5×10-3 V/m (C) 1.5×10-4 V/m

(D) 1×10-5 V/m (E) 2×10-2 V/m

24. A conducting ring with a radius r = 0.10 m is placed in a region of a spatially

uniform magnetic field perpendicular to the plane of the ring. The magnetic

field is directed into the page and is decreasing at the rate 0.050 T/s. What is

the magnitude of the induced current in the ring if its resistance is 5.0 Ω?

(B) 5π×10-3 A (B) 2.5π×10-3 A (C) π ×10-4 A

(D) π×10-5 A (E) 2π×10-2 A

25. An electric circuit consists of a charged capacitor C, a resistor R and a

switch S. Initially, the switch is open and all devices are connected in series.

A circular loop of wire is placed in the same plane as the circuit. Which one

of the following is true about the induced current in the loop after the

switch is closed?

(A) it is clockwise and increases

(B) it is counter clockwise and increases

(C) it is clockwise and decreases

(D) it is counter clockwise and decreases

(E) it is clockwise and constant

Answer Key

1. A

2. B

3. B

4. D

5. D

6. B

7. B

8. C

9. E

10. D

11. D

12. A

13. D

14. B

15. B

16. E

17. D

18. E

19. A

20. C

21. B

22. E

23. B

24. C

25. D