Question 1

A circular loop of wire with area $$A is $$placed in a uniform magnetic field $$\vec{B}$$, as shown in the first image. The angle between the normal to the loop and the magnetic field is $$	heta. $$What is the correct expression for the magnetic flux $$\Phi$$ through the loop?

Accepted Answer

$$\Phi = B A \cos 	heta$$

Question 2

Refer to the second image. Loop A is half as wide as Loop B, but the magnetic field in region A is twice as strong as in region B. Which loop has the larger magnetic flux through it?

Accepted Answer

The fluxes are the same.

Question 3

A bar magnet is moved toward a conducting loop as shown in the third image. According to Faraday's law, what causes the current in the loop?

Accepted Answer

The motion of the magnet, which changes the magnetic flux through the loop.

Question 4

In the fourth image, closing the switch in the right-hand circuit causes a current in the left-hand loop. What is the best explanation for this phenomenon?

Accepted Answer

A changing magnetic field in the right-hand loop induces an emf in the left-hand loop.

Question 5

A patient wears a copper bracelet of diameter $$6.0\ \mathrm{cm}$$ and resistance $$0.010\ \Omega$$ during an MRI scan. The magnetic field decreases from $$1.00\ \mathrm{T} to$$ $$0.40\ \mathrm{T} in$$ $$1.2\ \mathrm{s}. $$What is the magnitude of the induced current in the bracelet?

Accepted Answer

$$I = 0.47\ \mathrm{A}$$

Question 6

According to Lenz's law, what is the direction of the induced current in a loop when the magnetic flux through the loop is increasing?

Accepted Answer

The induced current creates a magnetic field that opposes the increase in flux.

Question 7

A bar magnet is moved upward away from a horizontal loop, as shown in the fifth image. What is the direction of the induced current in the loop?

Accepted Answer

Clockwise

Question 8

Which of the following statements best describes Faraday's law of electromagnetic induction?

Accepted Answer

An emf is induced in a loop when the magnetic flux through the loop changes.

Question 9

A coil with $$N$$ turns experiences a change in magnetic flux $$\Delta \Phi$$ over a time interval $$\Delta t. $$What is the induced emf $$\epsilon in $$the coil?

Accepted Answer

$$\epsilon = \dfrac{N \Delta \Phi}{\Delta t}$$

Question 10

A bar magnet is pushed toward the center of a wire loop, as shown in the sixth image. Which statement is true?

Accepted Answer

There is a counterclockwise induced current in the loop.

Question 11

If the magnetic field through a loop is constant but the area of the loop is decreasing, what happens to the magnetic flux and the induced emf?

Accepted Answer

The flux decreases and an emf is induced.

Question 12

A square loop of wire is placed in a region where the magnetic field is perpendicular to the plane of the loop and increases with time. What is the direction of the induced current as seen from above?

Accepted Answer

Clockwise

Question 13

Which of the following best explains why a current is only induced in the left-hand loop in the fourth image when the switch is opened or closed, but not when the current is steady?

Accepted Answer

A steady current produces a constant magnetic flux, so no emf is induced.

Question 14

A circular loop of radius $$r is $$placed in a uniform magnetic field $$B at an $$angle $$	heta to $$the field. If the field is doubled, what happens to the magnetic flux through the loop?

Accepted Answer

It is doubled.

Question 15

A metal ring is dropped over a long solenoid carrying a steady current. As the ring falls, what happens to the induced current in the ring?

Accepted Answer

An induced current opposes the motion of the ring as it enters and leaves the solenoid.

Electromagnetic Induction: Magnetic Flux, Faraday’s Law, and Lenz’s Law

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