Question 1

A bar magnet is held vertically with its upper end a little bit below the center of a horizontal metal ring.The upper end of the magnet is its north pole,as shown in the figure.The bar magnet is now dropped.An observer views the ring from above its center.To this observer,how will the induced current in the ring behave as the magnet falls? 
A) The current will flow clockwise and be increasing.
B) The current will flow clockwise and be decreasing.
C) The current will flow counter-clockwise and be increasing.
D) The current will flow counter-clockwise and be decreasing.
E) The induced current will be zero.

Accepted Answer

The answer of A bar magnet is held vertically with...

Question 2

In the figure,the inner loop carries a clockwise current I that is increasing.The resistor R is in the outer loop and both loops are in the same plane.The induced current through the resistor R is 
A) from a to b.
B) from b to a.
C) There is no induced current through the resistor.

Accepted Answer

The answer of In the figure,the inner loop carries a...

Question 3

A capacitor is charging in a simple RC circuit with a dc battery.Which one of the following statements about this capacitor is accurate?
A) There is a magnetic field between the capacitor plates because charge travels between the plates by jumping from one plate to the other.
B) There is no magnetic field between the capacitor plates because no charge travels between the plates.
C) There is a magnetic field between the capacitor plates, even though no charge travels between them, because the magnetic flux between the plates is changing.
D) There is a magnetic field between the capacitor plates, even though no charge travels between them, because the electric flux between the plates is changing.
E) The magnetic field between the capacitor plates is increasing with time because the charge on the plates is increasing.

Accepted Answer

When a capacitor is charging, an electric current flows in the circuit, which leads to a changing electric flux between the plates. According to Maxwell's equations, a changing electric flux induces a magnetic field, even though no charge actually travels through the vacuum between the capacitor plates.

Question 4

In the figure,two parallel wires carry currents of magnitude I in opposite directions.A rectangular loop is midway between the wires.The current I is decreasing with time.The induced current through the resistor R is 
A) from a to b.
B) from b to a.
C) There is no induced current through the resistor.

Accepted Answer

The answer of In the figure,two parallel wires carry currents...

Question 5

The figure shows a bar magnet moving vertically upward toward a horizontal coil.The poles of the bar magnets are labeled X and Y.As the bar magnet approaches the coil it induces an electric current in the direction indicated on the figure (counter-clockwise as viewed from above).What are the correct polarities of the magnet? 
A) X is a south pole, Y is a north pole.
B) X is a north pole, Y is a south pole.
C) Both X and Y are north poles.
D) Both X and Y are south poles.
E) The polarities of the magnet cannot be determined from the information given.

Accepted Answer

The answer of The figure shows a bar magnet moving...

Question 6

In the figure,a straight wire carries a current I.The wire passes through the center of a toroidal coil.If the current in the wire is quickly reduced to zero,the induced current through the resistor R is 
A) from a to b.
B) from b to a.
C) There is no induced current through the resistor.

Accepted Answer

According to Lenz's Law, the direction of the induced current will be such that it opposes the change in the magnetic field that caused it. When the current in the wire is quickly reduced to zero, the magnetic field inside the toroidal coil will change. The induced current will flow in a direction that produces a magnetic field that opposes the change in the original magnetic field. The induced current will flow counterclockwise around the toroidal coil (looking from above). This current will produce a magnetic field that opposes the original magnetic field, which was directed into the page. The induced current will therefore produce a magnetic field that is directed out of the page in the center of the toroidal coil. This will induce a clockwise current in the resistor, looking from above. Therefore, the induced current through the resistor will be from b to a.

Question 7

A circular metal ring is situated above a long straight wire,as shown in the figure.The straight wire has a current flowing to the right,and the current is increasing in time at a constant rate.Which statement is true? 
A) There is an induced current in the metal ring, flowing in a clockwise direction.
B) There is an induced current in the metal ring, flowing in a counter-clockwise direction.
C) There is no induced current in the metal ring because the current in the wire is changing at a constant rate.

Accepted Answer

The answer of A circular metal ring is situated above...

Question 8

In the figure,a C-shaped conductor is in a uniform magnetic field B,which is increasing.The polarity of the induced emf in terminals X and Y is 
A) X and Y are at the same potential.
B) X is positive and Y is negative.
C) X is negative and Y is positive.

Accepted Answer

According to Faraday's law of electromagnetic induction, an electromotive force (EMF) is induced in a conductor when there is a change in the magnetic field, which is indicated by the increasing magnetic field in this case. The induced EMF creates a current flow in the conductor. According to Lenz's law, the direction of the induced EMF opposes the change in magnetic flux. In this case, the magnetic field is increasing in the upward direction, so the induced EMF will create a current flow in the opposite direction, i.e. clockwise. This means that terminal X will be at a lower potential than terminal Y, making X negative and Y positive. Therefore, the best choice is C.

Question 9

A 2.0-m long conducting wire is formed into a square and placed in the horizontal xy-plane.A uniform magnetic field is oriented 30.0° above the horizontal with a strength of 9.0 T.What is the magnetic flux through the square? A) 1.1 T • m² B) 1.9 T • m² C) 2.3 T • m² D) 18 T • m²

Accepted Answer

The magnetic flux through a closed loop is given by the formula:

Φ = BAcosθ

where B is the magnetic field strength, A is the area enclosed by the loop, and θ is the angle between the magnetic field and the normal to the loop.

In this case, the loop is a square of side length 2.0 m, so the area is A = (2.0 m)² = 4.0 m². The magnetic field is given as B = 9.0 T and the angle between the magnetic field and the normal to the loop is θ = 30°.

Substituting these values into the formula, we get:

Φ = (9.0 T) × (4.0 m²) × cos(30°) 
    = (9.0 T) × (4.0 m²) × (sqrt(3)/2) 
    = 18.0 T·m²·sqrt(3)

Therefore, the magnetic flux through the square is 18.0 T·m²·sqrt(3).

The closest answer choice is A, 1.1 T·m², which is equivalent to 18.0 T·m²·sqrt(3)/(10√3).

Question 10

A circular loop of wire lies in the plane of the paper.An increasing magnetic field points out of the paper.What is the direction of the induced current in the loop?
A) counter-clockwise then clockwise
B) clockwise then counter-clockwise
C) clockwise
D) counter-clockwise
E) There is no current induced in the loop.

Accepted Answer

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

Question 11

In the figure,a copper bar is in contact with a pair of parallel metal rails and is in motion with
Velocity ν.A uniform magnetic field is present pointing downward,as shown.The bar,the rails,
And the resistor R are all in the same plane.The induced current through the resistor R is 
A) from a to b.
B) from b to a.
C) There is no induced current through the resistor.

Accepted Answer

The answer of In the figure,a copper bar is in...

Question 12

In the figure,two solenoids are approaching each other with speed v as shown.The induced current through the resistor R is 
A) from a to b.
B) from b to a.
C) There is no induced current through the resistor.

Accepted Answer

The answer of In the figure,two solenoids are approaching each...

Question 13

The figure shows three metal coils labeled A,B,and C heading towards a region where a uniform static magnetic field exists.The coils move with the same constant velocity and all have the same resistance.Their relative sizes are indicated by the background grid.As they enter the magnetic field the coils will have an induced electric current in them.For which coil will the current be the greatest? 
A) A
B) B
C) C
D) The current is the same in all three cases since all the coils move with the same velocity.
E) There is no induced current in any of the coils since they move at constant velocity.

Accepted Answer

The answer of The figure shows three metal coils labeled...

Question 14

In the figure,two solenoids are side by side.The switch S,initially open,is closed.The induced current through the resistor R is 
A) from a to b.
B) from b to a.
C) There is no induced current through the resistor.

Accepted Answer

The answer of In the figure,two solenoids are side by...

Question 15

In the figure,a bar magnet moves away from the solenoid.The induced current through the resistor R is 
A) from a to b.
B) from b to a.
C) There is no induced current through the resistor.

Accepted Answer

The answer of In the figure,a bar magnet moves away...

Question 16

A coil lies flat on a tabletop in a region where the magnetic field vector points straight up.The magnetic field vanishes suddenly.When viewed from above,what is the direction of the induced current in this coil as the field fades?
A) counter-clockwise then clockwise
B) clockwise then counter-clockwise
C) clockwise
D) counter-clockwise
E) There is no current induced in the coil.

Accepted Answer

According to Faraday's law of electromagnetic induction, a change in magnetic field induces an electromotive force (EMF) that drives a current in the loop. In this case, the sudden disappearance of the magnetic field produces an EMF that tends to maintain the original field, which is upward. By Lenz's law, the induced current must create a magnetic field that opposes the original field. This means the induced current must flow in a direction such that the magnetic field it produces points downward. Using the right-hand rule for the direction of magnetic fields around a current-carrying conductor, we can see that the induced current must flow counter-clockwise.

Question 17

The long straight wire in the figure carries a current I that is decreasing with time at a constant rate.The circular loops A,B,and C all lie in a plane containing the wire.The induced emf in each of the loops A,B,and C is such that 
A) no emf is induced in any of the loops.
B) a counterclockwise emf is induced in all the loops.
C) loop A has a clockwise emf, loop B has no induced emf, and loop C has a counterclockwise emf.
D) loop A has a counter-clockwise emf, loop B has no induced emf, and loop C has a clockwise emf.
E) loop A has a counter-clockwise emf, loops B and C have clockwise emfs.

Accepted Answer

According to Faraday's Law of electromagnetic induction, the induced emf in a closed loop is given by the rate of change of magnetic flux linked with the loop.

For loop A, as the current in the wire decreases with time, the magnetic field around the wire also decreases. This change in magnetic field induces an emf in loop A in such a way that it opposes the decrease in flux. This can be achieved by inducing a magnetic field around loop A which is directed in the clockwise direction. Therefore, loop A has a clockwise emf.

For loop B, as it is just a straight wire, it does not enclose any magnetic field and hence there is no change in flux linked with it. Therefore, no emf is induced in loop B.

For loop C, as the current in the wire decreases with time, the magnetic field around the wire also decreases. This change in magnetic field induces an emf in loop C in such a way that it opposes the decrease in flux. This can be achieved by inducing a magnetic field around loop C which is directed in the clockwise direction. Therefore, loop C has a clockwise emf.

Hence, the best choice is D: loop A has a counter-clockwise emf, loop B has no induced emf, and loop C has a clockwise emf.

Question 18

A closed,circular loop has a counter-clockwise current flowing through it as viewed by a person on the right,as shown in the figure.If a second closed circular loop with the same radius approaches this loop with constant velocity along a common axis as shown,in what direction will a current flow in the approaching loop as viewed by the person on the right? 
A) clockwise
B) counter-clockwise
C) No current will be induced because the velocity of approach is constant.

Accepted Answer

According to Faraday's law of electromagnetic induction, when a conductor (the approaching loop) is moved through a magnetic field (created by the current in the first loop), an electric current is induced in the conductor. The direction of the induced current is such that it opposes the change in flux that is causing it. In this case, the approaching loop is moving towards the first loop, which means that the magnetic field is increasing in the region of the approaching loop. Therefore, the induced current in the approaching loop will flow in a direction such that it opposes this increase in magnetic flux. To do so, the induced current must create a magnetic field that opposes that of the first loop, which means that the induced current must flow in a clockwise direction as viewed by the person on the right.

Question 19

A circular loop of radius 0.10 m is rotating in a uniform external magnetic field of 0.20 T. Find the magnetic flux through the loop due to the external field when the plane of the loop and the magnetic field vector are
(a)parallel.
(b)perpendicular.
(c)at an angle of 30° with each other.

Accepted Answer

The answer of A circular loop of radius 0.10 m...

Question 20

In the figure,a straight wire carries a steady current I perpendicular to the plane of the page.A bar is in contact with a pair of circular rails,and rotates about the straight wire.The direction of the induced current through the resistor R is 
A) from a to b.
B) from b to a.
C) There is no induced current through the resistor.

Accepted Answer

The answer of In the figure,a straight wire carries a...

Quiz 1: A: Foundations

In the figure,the inner loop carries a clockwise current I that is increasing.The resistor R is in the outer loop and both loops are in the same plane.The induced current through the resistor R is

A capacitor is charging in a simple RC circuit with a dc battery.Which one of the following statements about this capacitor is accurate?

In the figure,two parallel wires carry currents of magnitude I in opposite directions.A rectangular loop is midway between the wires.The current I is decreasing with time.The induced current through the resistor R is

In the figure,a straight wire carries a current I.The wire passes through the center of a toroidal coil.If the current in the wire is quickly reduced to zero,the induced current through the resistor R is

A circular metal ring is situated above a long straight wire,as shown in the figure.The straight wire has a current flowing to the right,and the current is increasing in time at a constant rate.Which statement is true?

In the figure,a C-shaped conductor is in a uniform magnetic field B,which is increasing.The polarity of the induced emf in terminals X and Y is

A 2.0-m long conducting wire is formed into a square and placed in the horizontal xy-plane.A uniform magnetic field is oriented 30.0° above the horizontal with a strength of 9.0 T.What is the magnetic flux through the square?

A circular loop of wire lies in the plane of the paper.An increasing magnetic field points out of the paper.What is the direction of the induced current in the loop?

In the figure,a copper bar is in contact with a pair of parallel metal rails and is in motion with Velocity ν.A uniform magnetic field is present pointing downward,as shown.The bar,the rails, And the resistor R are all in the same plane.The induced current through the resistor R is

In the figure,two solenoids are approaching each other with speed v as shown.The induced current through the resistor R is

In the figure,two solenoids are side by side.The switch S,initially open,is closed.The induced current through the resistor R is

In the figure,a bar magnet moves away from the solenoid.The induced current through the resistor R is

A coil lies flat on a tabletop in a region where the magnetic field vector points straight up.The magnetic field vanishes suddenly.When viewed from above,what is the direction of the induced current in this coil as the field fades?

The long straight wire in the figure carries a current I that is decreasing with time at a constant rate.The circular loops A,B,and C all lie in a plane containing the wire.The induced emf in each of the loops A,B,and C is such that

A circular loop of radius 0.10 m is rotating in a uniform external magnetic field of 0.20 T. Find the magnetic flux through the loop due to the external field when the plane of the loop and the magnetic field vector are (a)parallel. (b)perpendicular. (c)at an angle of 30° with each other.

In the figure,a straight wire carries a steady current I perpendicular to the plane of the page.A bar is in contact with a pair of circular rails,and rotates about the straight wire.The direction of the induced current through the resistor R is