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1. A circular current-carrying loop lies so that the plane of the loop is perpendicular to a constant magnetic field of
strength B. Suppose that the radius R of the loop could be made to increase with time t so that R = at , where a is a constant. What is the magnitude of the emf that would be generated around the loop as a function of t?
(A)
(B) (C) (D)
(E)
2. A circular loop of wire of radius R is perpendicular to a magnetic field whose magnitude as a function of time t is
given by the equation 𝐵 = 𝑏𝑡^2 + 𝑐𝑡 , where b and c are positive, nonzero constants. What is the magnitude of the emf induced in the loop as a function of time t?
(A)
(B)
(C)
(D)
(E)
A small, circular loop of conducting wire is near a long, straight wire that carries a steady electric current I to the right, as shown above. Which of the following actions will result in a clockwise induced electric current in the wire loop?
I. The wire loop is pulled vertically upward in the plane of the page (away from the wire) at a constant speed.
II. The current in the straight wire is steadily increasing.
III. The wire loop is rotated about a diameter through a small angle so that it is no longer in the plane of the page.
(A) I only
(B) II only
(C) III only (D) Either I or II (E) Either I or III
AP PHYSICS C: ELECTRICITY AND MAGNETISM Scoring Guide
MCQ 13.1-13.3 EM induction and Len's law
AP Physics C: Electricity and Magnetism Page 1 of 51
In the figure above, the north pole of the magnet is first moved down toward the loop of wire, then withdrawn upward. As viewed from above, the induced current in the loop is
(A) always clockwise with increasing magnitude (B) always clockwise with decreasing magnitude (C) always counterclockwise with increasing magnitude (D) always counterclockwise with decreasing magnitude
(E) first counterclockwise, then clockwise
When a rectangular conducting loop of resistance and vertical side of length is moved to the right with velocity through a magnetic field of magnitude , no current is induced in the loop. The loop is now placed in a region of space that contains two uniform magnetic fields of the same magnitude but in opposite directions, as shown in the figure. The conducting loop is moved to the right with velocity through the fields. The induced current in the loop at the moment shown is (A) 0
(B) clockwise
(C) counterclockwise
(D) clockwise
(E) counterclockwise
MCQ 13.1-13.3 EM induction and Len's law
Page 2 of 51 AP Physics C: Electricity and Magnetism
8. A loop of wire with resistance 2 ⯑ lies in a magnetic field. The magnetic flux ⯑𝑚 through the loop as a function of time t is given by ⯑𝑚 = (2 t^2 + 2 t) , where ⯑𝑚 is in tesla•meters squared and t is in seconds. What is the current in the loop at t = 3 s?
(A) 6 A
(B) 7 A
(C) 12 A (D) 14 A (E) 24 A
9. A magnetic field perpendicular to the plane of a wire loop is uniform in space but changes with time t in the region of the loop. If the induced emf in the loop increases linearly with time t , then the magnitude of the magnetic field must be proportional to
(A) t^3
(B) t^2
(C) t (D) t^0 (i.e., constant) (E) t 1/
A uniform magnetic field B of magnitude 1.2 T passes through a rectangular loop of wire, which measures 0.10 m by 0.20 m. The field is oriented 30° with respect to the plane of the loop, as shown above. What is the magnetic flux through the loop?
(A) Zero
(B)
(C) (D) (E)
MCQ 13.1-13.3 EM induction and Len's law
Page 4 of 51 AP Physics C: Electricity and Magnetism
A bar magnet with its south pole pointing down is released from rest and falls through a wire coil, as shown above. A resistor is connected across the two ends of the coil. What current would be produced in the coil, as observed by a person directly above the coil?
(A) A clockwise current only (B) A counterclockwise current only
(C) A current that is first clockwise and then counterclockwise
(D) A current that is first counterclockwise and then clockwise (E) No current would be produced.
MCQ 13.1-13.3 EM induction and Len's law
AP Physics C: Electricity and Magnetism Page 5 of 51
(A)
(B)
(C)
(D)
(E)
Students are to perform an experiment using a long solenoid, a magnetic field probe, a bar magnet, a power supply, connecting wires, and meters for collecting voltage and current data.
MCQ 13.1-13.3 EM induction and Len's law
AP Physics C: Electricity and Magnetism Page 7 of 51
The students disconnect the solenoid from the power supply and connect the solenoid to the voltmeter. They move the bar magnet into, through, and out of the solenoid at constant speed, as shown. The length of the bar magnet is much smaller than the length of the solenoid. When will the voltmeter detect an?
I. When the bar magnet is entering the solenoid II. When the bar magnet is moving through the center of the solenoid III. When the bar magnet is leaving the solenoid
(A) only (B) only (C) and
(D) and
(E) and
Answer D
Correct. Faraday’s law, , indicates that an emf is produced when the magnetic flux is
changing with time. When the bar magnet is entering the solenoid, flux is increasing, and when it is
leaving the solenoid, flux is decreasing. Therefore, an emf will be detected for conditions and , since
magnetic flux is changing in both of these conditions.
MCQ 13.1-13.3 EM induction and Len's law
Page 8 of 51 AP Physics C: Electricity and Magnetism
A rectangular conducting loop is located above a long, straight wire carrying a current to the right, as shown in the figure above. The wire and loop are both in the plane of the page. Which of the following will induce a clockwise current in the loop? (A) Decreasing the current in the wire (B) Moving the loop to the right (C) Moving the loop to the left (D) Moving the loop up away from the wire
(E) Moving the loop down toward the wire
Answer E
Correct. Using one of the right-hand rules, it can be determined that the magnetic field due to the current-
carrying wire it directed out of the page in the loop. Moving the loop closer to the wire will result in an
increase in the magnetic field directed out of the page in the loop. By Lenz’s law, the induced magnetic
field will oppose this increase and will point into the page in the loop. As a result, using another right-
hand rule, it can be determined that a clockwise current is induced in the loop.
A conducting loop of wire that is initially around a magnet is pulled away from the magnet to the right, as indicated in the figure above, inducing a current in the loop. What is the direction of the force on the magnet and the direction of the magnetic field at the center of the loop due to the induced current?
MCQ 13.1-13.3 EM induction and Len's law
Page 10 of 51 AP Physics C: Electricity and Magnetism
(A)
Direction of Force on the Magnet: To the right Direction of Magnetic Field at Center of Loop Due to Induced Current: To the right
(B) Direction of Force on the Magnet: To the right Direction of Magnetic Field at Center of Loop Due to Induced Current: To the left
(C) Direction of Force on the Magnet: To the left Direction of Magnetic Field at Center of Loop Due to Induced Current: To the right
(D) Direction of Force on the Magnet: To the left Direction of Magnetic Field at Center of Loop Due to Induced Current: To the left
(E) Direction of Force on the Magnet: No direction; the force is zero Direction of Magnetic Field at Center of Loop Due to Induced Current: To the left
A rectangular loop of wire with mass , width , length , and resistance is positioned a distance away from the center of a long wire that has a current , as shown in the figure. The current in the wire now decreases to zero in time .
17. Which of the following is a correct claim about the current induced in the loop and the net force on the loop as the current in the wire is decreasing?
(A) A clockwise current is induced in the loop, and there is a net force away from the wire exerted on the loop. (B) A clockwise current is induced in the loop, and there is a net force toward the wire exerted on the loop. (C) A clockwise current is induced in the loop, and there is a net force toward the right exerted on the loop.
(D) A counterclockwise current is induced in the loop, and there is a net force toward the right exerted on the loop.
(E) A counterclockwise current is induced in the loop, and there is a net force toward the wire exerted on the loop.
MCQ 13.1-13.3 EM induction and Len's law
AP Physics C: Electricity and Magnetism Page 11 of 51
A loop of wire of radius and resistance is inserted into the coil, as shown above. The power supply is adjusted so that the magnitude of the magnetic field in the coil as a function of time is , where μ and μ. The current induced in the loop is most nearly
(A) (B) (C)
(D)
(E)
Answer E
Correct. Faraday’s law, , is used to calculate the induced emf. Because the magnetic field,
and not the area of the loop, is changing with time, the magnitude of the emf is calculated by
. Numeric substitution yields
. Ohm’s law is then applied to calculate the
current in the loop.
MCQ 13.1-13.3 EM induction and Len's law
AP Physics C: Electricity and Magnetism Page 13 of 51
A rectangular conducting loop is moving at constant speed into a uniform magnetic field of magnitude that is directed into the page. At the two times and shown in the figures, the currents in the loop are and , respectively. Which of the following correctly compares currents and and provides evidence? (A) , because more of the loop is in the field at time. (B) , because it takes more force to move the loop at constant speed at time. (C) , because the current in the loop is zero at both times.
(D) , because the loop experiences the same rate of change in flux at both times.
(E) , because more of the loop is in the field at time.
Answer D
Correct. Current exists if there is induced potential, which requires that magnetic flux to change with
time. Magnetic flux is. In this problem, and is the
area of intersection of the loop and magnetic field. As the loop moves in the -direction into the
magnetic field at constant speed , the induced potential is calculated as follows:
. Because at times and , is the same, the induced
potential and current must also be the same.
Two identical rectangular conducting loops and a very long, straight wire lie in the plane of the page, as shown above.
The loops are equal distances from the wire, and there is a current to the right in the wire.
MCQ 13.1-13.3 EM induction and Len's law
Page 14 of 51 AP Physics C: Electricity and Magnetism
(A)
Loop X Loop Y
Counterclockwise Clockwise
(B)
Loop X Loop Y
Counterclockwise Counterclockwise
(C)
Loop X Loop Y
Clockwise Counterclockwise
(D)
Loop X Loop Y
Clockwise Clockwise
(E)
Loop XX Loop YY
None None
MCQ 13.1-13.3 EM induction and Len's law
Page 16 of 51 AP Physics C: Electricity and Magnetism
A uniform magnetic field of magnitude directed to the right exists in a certain region of space, as shown. A loop of wire is placed in the field such that a vector normal to the plane of the loop is at a angle relative to the field. Which of the following is a correct statement about the direction of the current induced in the loop? (A) The current starts clockwise and then becomes counterclockwise. (B) The current starts counterclockwise and then becomes clockwise. (C) The current is counterclockwise. (D) The current is clockwise.
(E) No current will be induced in the loop.
Answer E
Correct. Faraday’s law shows that current will be induced in a loop only by a changing magnetic flux.
Because the flux is not changing, no current will be induced in the loop.
MCQ 13.1-13.3 EM induction and Len's law
AP Physics C: Electricity and Magnetism Page 17 of 51
A conducting rod is sliding at a speed of along conducting rails that are apart. The rails are attached to a resistor, completing a loop. The loop is in a magnetic field that is directed out of the page, as shown. The current generated in the resistor is (A) 0 (B) counterclockwise
(C) clockwise
(D) counterclockwise (E) clockwise
Answer C
Correct. Using Faradays law to derive an expression for the emf yields. Then,
using Ohm’s law to calculate the current yields. Using
Lenz’s law to determine the direction of the current, the area of the loop is increasing. Therefore, the flux
is increasing out of the page, and the current created must create a magnetic field that is into the page;
thus, the current is clockwise around the loop.
An emf of 20 V is induced around a metal ring by increasing a uniform magnetic field at a constant rate from zero to a
final magnitude of 1.0 × 10–2^ T throughout the region enclosed by the ring. The field direction is perpendicular to the
plane of the ring.
25. If the area enclosed by the ring is 4.0 × 10–3^ m^2 , what is the time interval during which the field is increased?
(A) 2.0 μs
(B) 5.0 μs (C) 10 μs (D) 20 μs (E) 50 μs
MCQ 13.1-13.3 EM induction and Len's law
AP Physics C: Electricity and Magnetism Page 19 of 51
A loop of wire at location X is moving toward the right with constant speed v in a region of uniform magnetic field
, which is perpendicular to the plane of the loop. The magnetic field region ends at the dashed line, as shown in the figure above. Later, the loop is at location Y and exiting the magnetic field with the same constant speed v. The process is then repeated with the loop moving at a speed of 2 v. Which of the following best describes the emf in the loop at the two positions shown when the process is repeated at a speed of 2 v?
MCQ 13.1-13.3 EM induction and Len's law
Page 20 of 51 AP Physics C: Electricity and Magnetism
