Question 1

A copper hoop is held in a vertical east-west plane in a uniform magnetic field whose field lines run along the north-south direction. The largest induced emf is produced when the hoop is:
A) rotated about a north-south axis
B) rotated about an east-west axis
C) moved rapidly, without rotation, toward the east
D) moved rapidly, without rotation, toward the south
E) moved rapidly, without rotation, toward the northwest

Accepted Answer

When the hoop is rotated about an east-west axis, it cuts the maximum number of magnetic field lines per unit time, leading to the largest induced emf according to Faraday's law of induction.

Question 2

A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries an increasing current in the direction shown. The current in the rectangle is: 
A) zero
B) clockwise
C) counterclockwise
D) clockwise in the left side and counterclockwise in the right side
E) counterclockwise in the left side and clockwise in the right side

Accepted Answer

The answer of A long straight wire is in the...

Question 3

A square loop of wire lies in the plane of the page. A decreasing magnetic field is directed into the page. The induced current in the loop is:
A) counterclockwise
B) clockwise
C) zero
D) up the left edge and from right to left alongthe top edge
E) throught the middle of the page

Accepted Answer

The answer of A square loop of wire lies in...

Question 4

As a loop of wire with a resistance of 10 $\Omega$  moves in a constant non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced current in the loop:
A) is 0
B) is 2 mA
C) is 2.8 mA
D) is 20 mA
E) cannot be calculated from the given data

Accepted Answer

The answer of As a loop of wire with a...

Question 5

A rectangular loop of wire is placed midway between two long straight parallel conductors as shown. The conductors carry currents i₁ and i₂ as indicated. If i₁ is increasing and i₂ is constant, then the induced current in the loop is: A) zero B) clockwise C) counterclockwise D) depends on i₁ - i₂ E) depends on i₁ + i₂

Accepted Answer

The induced current in the rectangular loop is determined by Lenz's law which states that the direction of the induced current is such that it opposes the change in the magnetic flux causing it. 
In this case, the increasing current in the left conductor produces a magnetic field out of the page which interacts with the magnetic field produced by the constant current in the right conductor, resulting in a changing flux through the rectangular loop. To oppose this change, an induced current flows in the rectangular loop in a direction that produces a magnetic field into the page. This can be achieved by the current flowing counterclockwise around the loop, as shown in the diagram, so the correct answer is C.

Question 6

A copper penny slides on a horizontal frictionless table. There is a square region of constant uniform magnetic field perpendicular to the table, as shown. Which graph correctly shows the speed v of the penny as a function of time t? 
A) I
B) II
C) III
D) IV
E) V

Accepted Answer

The answer of A copper penny slides on a horizontal...

Question 7

A long straight wire is in the plane of a rectangular conducting loop. The straight wire initially carries a constant current i in the direction shown. While the current i is being shut off, the current in the rectangle is: 
A) zero
B) clockwise
C) counterclockwise
D) clockwise in the left side and counterclockwise in the right side
E) counterclockwise in the left side and clockwise in the right side

Accepted Answer

The answer of A long straight wire is in the...

Question 8

A rod with resistance R lies across frictionless conducting rails in a constant uniform magnetic field B, as shown. Assume the rails have negligible resistance. The magnitude of the force that must be applied by a person to pull the rod to the right at constant speed v is: A) 0 B) BLv C) BLv/R D) B²L²v/R E) B²Lxv/R

Accepted Answer

The answer of A rod with resistance R lies across...

Question 9

The diagram shows a circular loop of wire that rotates at a steady rate about a diameter O that is perpendicular to a uniform magnetic field. The maximum induced emf occurs when the point X on the loop passes: 
A) a
B) b
C) c
D) d
E) e

Accepted Answer

The answer of The diagram shows a circular loop of...

Question 10

A merry-go-round has an area of 300 m² and spins at 2 rpm about a vertical axis at a place where the Earth's magnetic field is vertical and has a magnitude of 5 *10^-⁵ T. The emf around the rim is: A) 0 B) 0.5 mV C) 3.1 mV D) 15 mV E) 30 mV

Accepted Answer

The emf induced around the rim of the merry-go-round is zero because the magnetic field is vertical and parallel to the axis of rotation, so there is no change in magnetic flux through the area enclosed by the rim.

Question 11

A 10 turn conducting loop with a radius of 3.0 cm spins at 60 revolutions per second in a magnetic field of 0.50 T. The maximum emf generated is:
A) 0.014 V
B) 0.53 V
C) 5.3 V
D) 18 V
E) 180 V

Accepted Answer

The maximum emf (ε) generated in a spinning loop is given by ε = NABω, where N is the number of turns, A is the area of the loop, B is the magnetic field, and ω is the angular velocity in radians per second. Here, N = 10, A = π(0.03 m)^2, B = 0.50 T, and ω = 2π(60) rad/s. Calculating this gives ε ≈ 5.3 V.

Question 12

A rod of length L and electrical resistance R moves through a constant uniform magnetic field perpendicular to the rod. The force that must be applied by a person to keep the rod moving with constant velocity is: A) 0 B) BLv C) BLv/R D) B²L²v/R E) B²L²v²/R

Accepted Answer

The answer of A rod of length L and electrical...

Question 13

A rectangular loop of wire is placed perpendicular to a uniform magnetic field and then spun around one of its sides at frequency f. The induced emf is a maximum when:
A) the flux is zero
B) the flux is a maximum
C) the flux is half its maximum value
D) the derivative of the flux with respect to time is zero
E) none of the above

Accepted Answer

The answer of A rectangular loop of wire is placed...

Question 14

At any instant of time the total magnetic flux through a stationary conducting loop is less in magnitude than the flux associated with an externally applied field. This might occur because:
A) the applied field is normal to the loop and increasing in magnitude
B) the applied field is normal to the loop and decreasing in magnitude
C) the applied field is parallel to the plane of the loop and increasing in magnitude
D) the applied field is parallel to the plane of the loop and decreasing in magnitude
E) the applied field is tangent to the loop

Accepted Answer

The answer of At any instant of time the total...

Question 15

A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries a constant current i, as shown. While the wire is being moved toward the rectangle the current in the rectangle is: 
A) zero
B) clockwise
C) counterclockwise
D) clockwise in the left side and counterclockwise in the right side
E) counterclockwise in the left side and clockwise in the right side

Accepted Answer

The answer of A long straight wire is in the...

Question 16

A single loop of wire with a radius of 7.5 cm rotates about a diameter in a uniform magnetic field of 1.6 T. To produce a maximum emf of 1.0 V, it should rotate at:
A) 0
B) 2.7 rad/s
C) 5.6 rad/s
D) 35 rad/s
E) 71 rad/s

Accepted Answer

The answer of A single loop of wire with a...

Question 17

As an externally generated magnetic field through a certain conducting loop increases in magnitude, the field produced at points inside the loop by the current induced in the loop must be:
A) increasing in magnitude
B) decreasing in magnitude
C) in the same direction as the applied field
D) directed opposite to the applied field
E) perpendicular to the applied field

Accepted Answer

According to Faraday's Law of Electromagnetic Induction, when a magnetic field through a conducting loop changes, an electric field is induced, which produces a current in the loop. The direction of the induced current is such that it produces its own magnetic field that opposes the change in the applied field. This is known as Lenz's Law. Therefore, as the externally generated magnetic field through the loop increases in magnitude, the current induced in the loop will produce a magnetic field that is directed opposite to the applied field. Hence, the correct choice is D.

Question 18

The four wire loops shown have edge lengths of either L, 2L, or 3L. They will move with the same speed into a region of uniform magnetic field  directed out of the page. Rank them according to the maximum magnitude of the induced emf, least to greatest. 
A) 1 and 2 tie, then 3 and 4 tie
B) 3 and 4 tie, then 1 and 2 tie
C) 4, 2, 3, 1
D) 1, then 2 and 3 tie, then 4
E) 1, 2, 3, 4

Accepted Answer

The answer of The four wire loops shown have edge...

Question 19

As a loop of wire with a resistance of 10  $\Omega$ moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop:
A) is 0
B) is 0.2 V
C) is 0.28 V
D) is 2 V
E) cannot be calculated from the given data

Accepted Answer

The power loss due to resistance is given by P = I^2 * R. Given P = 5 mJ/s and R = 10 Ω, we can find I = sqrt(P/R) = sqrt(0.005/10) = 0.02236 A. The induced emf (E) is given by E = I * R = 0.02236 * 10 = 0.2236 V, which rounds to 0.2 V.

Question 20

You push a permanent magnet with its north pole away from you toward a loop of conducting wire in front of you. Before the north pole enters the loop the current in the loop is:
A) zero
B) clockwise
C) counterclockwise
D) to your left
E) to your right

Accepted Answer

The answer of You push a permanent magnet with its...

Quiz 30: Induction and Inductance

A copper hoop is held in a vertical east-west plane in a uniform magnetic field whose field lines run along the north-south direction. The largest induced emf is produced when the hoop is:

A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries an increasing current in the direction shown. The current in the rectangle is:

A square loop of wire lies in the plane of the page. A decreasing magnetic field is directed into the page. The induced current in the loop is:

As a loop of wire with a resistance of 10 Ω\OmegaΩ moves in a constant non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced current in the loop:

A rectangular loop of wire is placed midway between two long straight parallel conductors as shown. The conductors carry currents i1 and i2 as indicated. If i1 is increasing and i2 is constant, then the induced current in the loop is:

A copper penny slides on a horizontal frictionless table. There is a square region of constant uniform magnetic field perpendicular to the table, as shown. Which graph correctly shows the speed v of the penny as a function of time t?

A long straight wire is in the plane of a rectangular conducting loop. The straight wire initially carries a constant current i in the direction shown. While the current i is being shut off, the current in the rectangle is:

A rod with resistance R lies across frictionless conducting rails in a constant uniform magnetic field B, as shown. Assume the rails have negligible resistance. The magnitude of the force that must be applied by a person to pull the rod to the right at constant speed v is:

The diagram shows a circular loop of wire that rotates at a steady rate about a diameter O that is perpendicular to a uniform magnetic field. The maximum induced emf occurs when the point X on the loop passes:

A merry-go-round has an area of 300 m2 and spins at 2 rpm about a vertical axis at a place where the Earth's magnetic field is vertical and has a magnitude of 5 *10-5 T. The emf around the rim is:

A 10 turn conducting loop with a radius of 3.0 cm spins at 60 revolutions per second in a magnetic field of 0.50 T. The maximum emf generated is:

A rod of length L and electrical resistance R moves through a constant uniform magnetic field perpendicular to the rod. The force that must be applied by a person to keep the rod moving with constant velocity is:

A rectangular loop of wire is placed perpendicular to a uniform magnetic field and then spun around one of its sides at frequency f. The induced emf is a maximum when:

At any instant of time the total magnetic flux through a stationary conducting loop is less in magnitude than the flux associated with an externally applied field. This might occur because:

A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries a constant current i, as shown. While the wire is being moved toward the rectangle the current in the rectangle is:

A single loop of wire with a radius of 7.5 cm rotates about a diameter in a uniform magnetic field of 1.6 T. To produce a maximum emf of 1.0 V, it should rotate at:

As an externally generated magnetic field through a certain conducting loop increases in magnitude, the field produced at points inside the loop by the current induced in the loop must be:

The four wire loops shown have edge lengths of either L, 2L, or 3L. They will move with the same speed into a region of uniform magnetic field directed out of the page. Rank them according to the maximum magnitude of the induced emf, least to greatest.

As a loop of wire with a resistance of 10 Ω\OmegaΩ moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop:

You push a permanent magnet with its north pole away from you toward a loop of conducting wire in front of you. Before the north pole enters the loop the current in the loop is:

As a loop of wire with a resistance of 10 $\Omega$ moves in a constant non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced current in the loop:

A rectangular loop of wire is placed midway between two long straight parallel conductors as shown. The conductors carry currents i₁ and i₂ as indicated. If i₁ is increasing and i₂ is constant, then the induced current in the loop is:

A merry-go-round has an area of 300 m² and spins at 2 rpm about a vertical axis at a place where the Earth's magnetic field is vertical and has a magnitude of 5 *10^-⁵ T. The emf around the rim is:

As a loop of wire with a resistance of 10 $\Omega$ moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop: