Question 1

Electric fields can be generated by
A) charges.
B) changing magnetic fields.
C) both of the above.
D) none of the above; electric fields can be neither created nor destroyed.

Accepted Answer

Electric fields can be generated by static charges, as described by Coulomb's law, and also by changing magnetic fields, as described by Faraday's law of electromagnetic induction.

Question 2

A statement equivalent to Lenz's law is the following:
A) Induced currents produce magnetic fields that reinforce the magnetic field that induced them in the first place.
B) Induced currents produce magnetic fields that reinforce the change in the magnetic field that induced them in the first place.
C) Induced currents produce magnetic fields that oppose the magnetic field that induced them in the first place.
D) Induced currents produce magnetic fields that oppose the change in the magnetic field that induced them in the first place.

Accepted Answer

Lenz's law states that the direction of the induced current will be such that it opposes the change in the magnetic field that produced it, which is accurately reflected in option D.

Question 3

A circular coil lies in the horizontal plane, having a bar magnet suspended above the coil's center with its south pole pointing down. When the magnet is released and approaches the coil, it induces
A) no current in the coil.
B) a current in the clockwise direction (when viewed from above).
C) a current in the counterclockwise direction (when viewed from above).
D) a large current in the coil.
E) a small current in the coil.

Accepted Answer

As the magnet approaches the coil, the magnetic flux through the coil increases, inducing an emf and a current in the coil. The direction of the current is such that the magnetic field produced by the coil opposes the change in magnetic flux, so the current flows in the counterclockwise direction (when viewed from above).

Question 4

An adjustable single loop positioned in the plane of the page is placed in a magnetic field B = 1.5 T pointing out of page. When the cross-sectional area of the loop is reduced from 0.50 m² to 0.35 m² in 0.30 s, the average emf induced in the coil is A) 75 V. B) 30 V. C) 23 V. D) 0.75 V E) 0.30 V.

Accepted Answer

The answer of An adjustable single loop positioned in the...

Question 5

An adjustable single loop positioned in the plane of the page is placed in a magnetic field B = 1.5 T, making an angle of 30^o with the page. When the cross-sectional area of the loop is reduced from 0.50 m² to 0.35 m² in 0.30 s, the average emf induced in the coil is A) 87 V. B) 65 V. C) 0.87 V. D) 0.65 V. E) 0.38 V.

Accepted Answer

The average emf induced in the coil can be calculated using Faraday's law of electromagnetic induction, which states that the induced emf (ε) in a coil is equal to the negative rate of change of magnetic flux (ΦB) through the coil. The magnetic flux is given by ΦB = B * A * cos(θ), where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the plane of the coil. Given that θ = 30°, B = 1.5 T, the initial area A1 = 0.50 m^2, the final area A2 = 0.35 m^2, and the time interval Δt = 0.30 s, we can calculate the change in flux and hence the induced emf.First, calculate the initial and final flux:ΦB1 = B * A1 * cos(30°) = 1.5 * 0.50 * cos(30°)ΦB2 = B * A2 * cos(30°) = 1.5 * 0.35 * cos(30°)Then, find the change in flux ΔΦB = ΦB2 - ΦB1 and divide by the time Δt to find the average emf ε = -ΔΦB / Δt.The calculation will show that the correct answer is D) 0.65 V, as it reflects the magnitude of the average induced emf based on the given parameters and the correct application of Faraday's law.

Question 6

A circular loop is placed in a magnetic field, with the plane of the loop perpendicular to the field lines. Which of the following will not cause a current to be induced in the loop?
A) Crushing the loop.
B) Rotating the loop about an axis perpendicular to the field lines.
C) Pulling the loop out of the field.
D) Keeping the orientation of the loop fixed and moving it along the field lines.

Accepted Answer

According to Faraday's law of electromagnetic induction, a current is induced in a loop if the magnetic flux through the loop changes. Crushing the loop (A) changes the area and thus the flux. Rotating the loop (B) changes the angle between the field lines and the normal to the plane of the loop, altering the flux. Pulling the loop out of the field (C) changes the amount of field the loop is exposed to, again changing the flux. However, keeping the orientation of the loop fixed and moving it along the field lines (D) does not change the flux through the loop, as both the area and the angle relative to the field lines remain constant, and thus, no current is induced.

Question 7

A rod lies in the plane of the page and moves at constant velocity, perpendicular to the rod, toward the top of the page, through a magnetic field that points out of the page. The correct statement concerning the potential induced across the rod is
A) no potential is induced across the rod.
B) the top part of the rod is at lower potential than the lower part.
C) the top part of the rod is at higher potential than the lower part.
D) the right end of the rod is at higher potential than the left end.

Accepted Answer

The answer of A rod lies in the plane of...

Question 8

A conducting square loop is placed around a bar magnet. As the loop moves away from the magnet,
A) the magnet and the loop attract one another.
B) the magnet and the loop repel one another.
C) the magnet repels the loop, but the loop attracts the magnet.
D) the magnet attracts the loop, but the loop repels the magnet.
E) there is neither attraction nor repulsion between the loop and the magnet.

Accepted Answer

When a conducting loop moves away from a magnet, a current is induced in the loop due to the changing magnetic flux, according to Faraday's law of electromagnetic induction. According to Lenz's law, the direction of the induced current will be such that it opposes the change that caused it. In this case, the induced current will create a magnetic field that opposes the loop's motion away from the magnet, effectively attracting the loop towards the magnet. This means the magnet and the loop attract one another.

Question 9

A circular loop of wire is rotated at constant angular speed about its symmetry axis, whose direction can be varied, in a uniform magnetic field pointing vertically upward. To get a maximum induced emf, the loop's axis of rotation should A) make an angle of 30^o with the vertical. B) make an angle of 45^o with the vertical. C) make an angle of 60^o with the vertical. D) be vertical. E) be horizontal.

Accepted Answer

The induced emf in a rotating loop is maximum when the plane of the loop rotates perpendicular to the magnetic field lines. This condition is met when the loop's axis of rotation is horizontal, making the plane of the loop perpendicular to the vertical magnetic field.

Question 10

A circular loop of wire is rotated at constant angular speed about its symmetry axis, whose direction can be varied, in a uniform magnetic field pointing vertically upward. To get no induced emf, the loop's axis of rotation should A) make an angle of 30^o with the vertical. B) make an angle of 45^o with the vertical. C) make an angle of 60^o with the vertical. D) be vertical. E) be horizontal.

Accepted Answer

When the axis of rotation of the loop is vertical, it aligns with the direction of the magnetic field. This means the magnetic flux through the loop remains constant as it rotates, resulting in no induced emf according to Faraday's law of electromagnetic induction.

Question 11

A conducting coil is rotated at constant speed in a uniform magnetic field as shown in the figure here. The time required by the loop to make a full rotation is T. The graph that most likely represents the current generated in the coil as a function of time is
 
A) A
B) B
C) C
D) D
E) E

Accepted Answer

The answer of A conducting coil is rotated at constant...

Question 12

A conducting coil is rotated at constant speed in a uniform magnetic field as shown in the figure here. The time required by the loop to make a full rotation is T. The graph that most likely represents the force exerted on an electron within the coil as a function of the angle $\theta$ made by the coil's plane with the magnetic field is

A) A
B) B
C) C
D) D
E) E

Accepted Answer

The answer of A conducting coil is rotated at constant...

Question 13

A conducting coil is rotated at constant speed in a uniform magnetic field as shown in the figure here. The time required by the loop to make a full rotation is T. The current generated in the coil would increase

A) if the angular speed of the coil increases.
B) if the area of the coil increases.
C) if the strength of the magnetic field increases.
D) All of the above are correct.
E) None of the above id correct.

Accepted Answer

The answer of A conducting coil is rotated at constant...

Question 14

A conducting bar is slid at constant velocity toward the positive x direction, along two conducting rods connected across a resistor R, as shown in the figure here. The graph that most likely shows the current generated by the apparatus is
 
A) A
B) B
C) C
D) D
E) E

Accepted Answer

The answer of A conducting bar is slid at constant...

Question 15

A conducting bar is slid at constant velocity toward the positive x direction, along two conducting rods connected across a resistor R, as shown in the figure here. The current generated by the apparatus increases if the following quantities increase except for

A) the speed of the bar.
B) the strength of the magnetic field.
C) the distance between the two conducting rods.
D) the resistance of the resistor.
E) All of the above increase the current generated by the apparatus; there are no exceptions.

Accepted Answer

The answer of A conducting bar is slid at constant...

Question 16

A conducting bar is slid at constant velocity toward the positive x direction, along two conducting rods connected across a resistor R, as shown in the figure here. At moment t₁, the conducting bar is slid at constant velocity toward the negative x direction. The graph that most likely shows the current generated by the apparatus is A) A B) B C) C D) D E) E

Accepted Answer

The answer of A conducting bar is slid at constant...

Question 17

When the number of loops of wire in a coil is doubled, assuming all the other factors stay constant, the induced emf
A) becomes four times larger.
B) becomes two times larger.
C) stays the same.
D) becomes two times smaller.
E) becomes four times smaller.

Accepted Answer

The induced emf in a coil is directly proportional to the number of loops, so doubling the number of loops doubles the induced emf.

Question 18

A long solenoid is surrounded by a circular coil. If the current changes in the solenoid, the emf induced in the coil as measured between the terminals of the coil is directly proportional to all of the following except
A) the number of turns in the solenoid.
B) the number of turns in the coil.
C) the radius of the coil.
D) All of the above are true.

Accepted Answer

The answer of A long solenoid is surrounded by a...

Question 19

A long solenoid is surrounded by a circular coil. The solenoid is replaced with an ideal toroid that produces the same average magnetic field in its interior as was present in the solenoid (and no magnetic field outside its enclosed region). The emf induced in the coil if the current in the toroid changes at the same rate is
A) considerably greater than for the case of the solenoid.
B) approximately equal to the case of the solenoid.
C) considerably less than for the case of the solenoid.
D) zero because there is no magnetic field at the location of the coil.

Accepted Answer

The magnetic field inside the toroid is the same as that inside the solenoid, so the emf induced in the coil will be the same in both cases.

Question 20

A solid conducting cube is placed on your page near the left side and oriented square with the page. When the cube is moved toward the right side of the page, in a uniform magnetic field pointing out of the page, an emf develops between the two surfaces
A) nearest the top and the bottom of the page.
B) nearest the left and right sides of the page.
C) parallel to the face and the backside of the page.
D) None of the above is correct.

Accepted Answer

The emf is developed between the two surfaces nearest the top and the bottom of the page because the magnetic field is pointing out of the page and the cube is moving toward the right side of the page. This causes the electrons in the cube to move toward the left side of the page, creating a positive charge on the right side of the cube and a negative charge on the left side of the cube. The emf is the potential difference between the two sides of the cube.

Quiz 31: Electromagnetic Induction

Electric fields can be generated by

A statement equivalent to Lenz's law is the following:

A circular coil lies in the horizontal plane, having a bar magnet suspended above the coil's center with its south pole pointing down. When the magnet is released and approaches the coil, it induces

An adjustable single loop positioned in the plane of the page is placed in a magnetic field B = 1.5 T pointing out of page. When the cross-sectional area of the loop is reduced from 0.50 m2 to 0.35 m2 in 0.30 s, the average emf induced in the coil is

An adjustable single loop positioned in the plane of the page is placed in a magnetic field B = 1.5 T, making an angle of 30o with the page. When the cross-sectional area of the loop is reduced from 0.50 m2 to 0.35 m2 in 0.30 s, the average emf induced in the coil is

A circular loop is placed in a magnetic field, with the plane of the loop perpendicular to the field lines. Which of the following will not cause a current to be induced in the loop?

A rod lies in the plane of the page and moves at constant velocity, perpendicular to the rod, toward the top of the page, through a magnetic field that points out of the page. The correct statement concerning the potential induced across the rod is

A conducting square loop is placed around a bar magnet. As the loop moves away from the magnet,

A circular loop of wire is rotated at constant angular speed about its symmetry axis, whose direction can be varied, in a uniform magnetic field pointing vertically upward. To get a maximum induced emf, the loop's axis of rotation should

A circular loop of wire is rotated at constant angular speed about its symmetry axis, whose direction can be varied, in a uniform magnetic field pointing vertically upward. To get no induced emf, the loop's axis of rotation should

A conducting coil is rotated at constant speed in a uniform magnetic field as shown in the figure here. The time required by the loop to make a full rotation is T. The graph that most likely represents the current generated in the coil as a function of time is

A conducting coil is rotated at constant speed in a uniform magnetic field as shown in the figure here. The time required by the loop to make a full rotation is T. The current generated in the coil would increase

A conducting bar is slid at constant velocity toward the positive x direction, along two conducting rods connected across a resistor R, as shown in the figure here. The graph that most likely shows the current generated by the apparatus is

A conducting bar is slid at constant velocity toward the positive x direction, along two conducting rods connected across a resistor R, as shown in the figure here. The current generated by the apparatus increases if the following quantities increase except for

When the number of loops of wire in a coil is doubled, assuming all the other factors stay constant, the induced emf

A long solenoid is surrounded by a circular coil. If the current changes in the solenoid, the emf induced in the coil as measured between the terminals of the coil is directly proportional to all of the following except

A solid conducting cube is placed on your page near the left side and oriented square with the page. When the cube is moved toward the right side of the page, in a uniform magnetic field pointing out of the page, an emf develops between the two surfaces

An adjustable single loop positioned in the plane of the page is placed in a magnetic field B = 1.5 T pointing out of page. When the cross-sectional area of the loop is reduced from 0.50 m² to 0.35 m² in 0.30 s, the average emf induced in the coil is

An adjustable single loop positioned in the plane of the page is placed in a magnetic field B = 1.5 T, making an angle of 30^o with the page. When the cross-sectional area of the loop is reduced from 0.50 m² to 0.35 m² in 0.30 s, the average emf induced in the coil is