Q: A coil with 20 turns and area $$0.0015\ \text{m}^2 is $$placed perpendicular to a magnetic field that increases from $$0.050\ \text{T} to$$ $$0.060\ \text{T} in$$ $$0.10\ \text{s}. $$What is the magnitude of the average induced emf?

$$3.0 \times 10$$^{-3}$$\ \text{V}$$

Q: A coil is rotated in a magnetic field, changing the angle $$\theta$$ between the field and the normal to the coil. Which of the following will NOT induce an emf?

Keeping $$B$$, $$A$$, and $$\theta$$ constant.

Question 1

A bar magnet is pushed into a coil as shown in the image. Which statement best describes the direction of the induced current according to Lenz's Law?

Accepted Answer

The induced current flows in a direction that opposes the change in magnetic flux caused by the magnet.

Question 2

Which equation correctly expresses Faraday's Law for a coil with $$N$$ turns?

Accepted Answer

$$\mathcal{E} = -N \frac{\Delta \Phi_B}{\Delta t}$$

Question 3

A coil of wire with area $$A is $$placed in a magnetic field $$B at an $$angle $$	heta to $$the normal. What is the expression for the magnetic flux $$\Phi$$ through the coil?

Accepted Answer

$$\Phi = BA \cos 	heta$$

Question 4

A circular loop in a magnetic field is rotated from $$	heta = 0^\circ to$$ $$	heta = 90^\circ. $$What happens to the magnetic flux through the loop?

Accepted Answer

The flux decreases to zero.

Question 5

A rod of length $$l$$ moves with velocity $$v$$ perpendicular to a magnetic field $$B. $$What is the induced emf across the ends of the rod?

Accepted Answer

$$\mathcal{E} = Blv$$

Question 6

A coil with 20 turns and area $$0.0015\ 	ext{m}^2 is $$placed perpendicular to a magnetic field that increases from $$0.050\ 	ext{T} to$$ $$0.060\ 	ext{T} in$$ $$0.10\ 	ext{s}. $$What is the magnitude of the average induced emf?

Accepted Answer

$$3.0 	imes 10$$^{-3}$$\ 	ext{V}$$

Question 7

If the area of a loop in a constant magnetic field decreases, what is the direction of the induced current?

Accepted Answer

The induced current produces a magnetic field that opposes the decrease in flux.

Question 8

A coil is rotated in a magnetic field, changing the angle $$	heta$$ between the field and the normal to the coil. Which of the following will NOT induce an emf?

Accepted Answer

Keeping $$B$$, $$A$$, and $$	heta$$ constant.

Question 9

A permanent magnet is moved away from a loop of wire. What is the direction of the induced current?

Accepted Answer

The induced current produces a magnetic field that opposes the decrease in flux.

Question 10

A circular loop in a $$0.75\ 	ext{T}$$ magnetic field has its diameter changed from $$20.0\ 	ext{cm} to$$ $$6.0\ 	ext{cm} in$$ $$0.50\ 	ext{s}. If $$the coil resistance is $$2.5\ \Omega$$, what is the average induced current?

Accepted Answer

$$0.163\ 	ext{A}$$

Question 11

Which of the following best describes Lenz's Law?

Accepted Answer

The induced current opposes the change in magnetic flux.

Question 12

A coil with $$N$$ turns is placed in a changing magnetic field. If the magnetic flux through the coil changes by $$\Delta \Phi_B in $$time $$\Delta t$$, what is the average induced emf?

Accepted Answer

$$\mathcal{E} = -N \frac{\Delta \Phi_B}{\Delta t}$$

Question 13

A conducting rod moves with velocity $$v in a $$magnetic field $$B$$ and length $$l. If $$the resistance of the circuit is $$R$$, what is the induced current?

Accepted Answer

$$I = \frac{Blv}{R}$$

Question 14

A loop is moved into a region with a constant magnetic field. When will an induced current be observed?

Accepted Answer

Only when the magnetic flux through the loop changes.

Question 15

A coil is rotated in a magnetic field, and the flux decreases. What is the direction of the induced current?

Accepted Answer

The induced current produces a magnetic field that opposes the decrease in flux.

Question 16

A coil of wire is part of a complete circuit and is placed in a changing magnetic field. What is required for an induced current to flow?

Accepted Answer

The circuit must be closed.

Question 17

A bar magnet is moved toward a loop of wire. What happens to the induced current if the speed of the magnet is doubled?

Accepted Answer

The induced current is doubled.

Question 18

A coil is placed in a region where the magnetic field is perpendicular to its surface. If the area of the coil is changed, what happens to the magnetic flux?

Accepted Answer

The magnetic flux changes proportionally to the area.

Question 19

A loop is moved out of a region with a constant magnetic field. What is the direction of the induced current?

Accepted Answer

The induced current produces a magnetic field that opposes the decrease in flux.

Electromagnetic Induction: Faraday’s Law, Lenz’s Law, and Applications

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