Q: A generator coil rotates in a magnetic field. What is the expression for the induced EMF in the coil with $$N$$ turns, area $$A$$, magnetic field $$B$$, and angular frequency $$\omega$$?

$$\mathcal{E}_{\text{coil}} = \omega ABN \sin \omega t$$

Question 1

According to Faraday’s law, what is required to induce an electromotive force (EMF) in a circuit?

Accepted Answer

A changing magnetic flux through the circuit.

Question 2

In the experiment with two coils (one connected to a battery and the other to an ammeter), when does current flow in the second coil?

Accepted Answer

While the switch is being opened or closed.

Question 3

A metal bar moves to the right with velocity $$\vec{v}$$ through a uniform magnetic field $$\vec{B}$$ directed into the page. What is the direction of the force on positive charge carriers in the bar?

Accepted Answer

Upward

Question 4

What is the expression for the induced current $$I in a $$conducting loop when a metal bar of length $$l$$ moves with velocity $$v$$ through a magnetic field $$B$$, and the loop has resistance $$R$$?

Accepted Answer

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

Question 5

A metal bar is pulled to the right at constant speed through a magnetic field, inducing a current in the loop. If the resistance of the loop is increased, what happens to the force required to keep the bar moving at the same speed?

Accepted Answer

It decreases.

Question 6

If you push a metal bar with a fixed force $$F_{	ext{push}}$$ and the resistance of the wire is doubled, what happens to the speed of the bar?

Accepted Answer

Reduced by a factor of 2.

Question 7

What is the formula for the power required to pull a metal bar of length $$l at $$speed $$v$$ through a magnetic field $$B$$ with resistance $$R$$?

Accepted Answer

$$P = \frac{v^2$l^2B^2$}{R}$$

Question 8

A loop of wire is moved to the right through a uniform magnetic field directed into the screen. What happens to the magnetic flux through the loop?

Accepted Answer

It remains the same.

Question 9

A loop of wire is moved to the right through a non-uniform magnetic field that gets weaker as you move right. What happens to the magnetic flux through the loop?

Accepted Answer

It decreases.

Question 10

According to Lenz’s law, what is the direction of the induced current in a loop when a bar magnet is pushed toward the center of the loop (with the north pole entering first)?

Accepted Answer

Counterclockwise (looking down from the top)

Question 11

What is the mathematical expression for magnetic flux $$\Phi_m$$ through a loop of area $$A in a $$uniform magnetic field $$B at an $$angle $$	heta$$?

Accepted Answer

$$\Phi_m = AB \cos 	heta$$

Question 12

A conducting loop is halfway into a region of uniform magnetic field. If the magnetic field begins to increase rapidly in strength, what happens to the loop?

Accepted Answer

The loop is pulled to the left, into the magnetic field.

Question 13

Which plot best represents the current through a wire loop as a bar magnet moves toward and then away from the loop?

Accepted Answer

Current increases as the magnet approaches, then reverses as it moves away.

Question 14

What is the induced EMF $$\mathcal{E} in a $$loop according to Faraday’s law?

Accepted Answer

$$\mathcal{E} = \left| \frac{d\Phi_m}{dt} \right|$$

Question 15

A generator coil rotates in a magnetic field. What is the expression for the induced EMF in the coil with $$N$$ turns, area $$A$$, magnetic field $$B$$, and angular frequency $$\omega$$?

Accepted Answer

$$\mathcal{E}_{	ext{coil}} = \omega ABN \sin \omega t$$

Question 16

Which of the following statements best describes Lenz’s law?

Accepted Answer

The induced current in a loop opposes the change in magnetic flux.

Question 17

A hydroelectric power plant uses a generator to convert mechanical energy into electrical energy. Which principle is primarily responsible for the generation of electricity?

Accepted Answer

Faraday’s law of electromagnetic induction

Question 18

A rectangular loop is rotated in a uniform magnetic field. At what angle $$	heta$$ between the loop’s area vector and the magnetic field is the magnetic flux through the loop maximized?

Accepted Answer

$$	heta = 0^\circ$$

Question 19

A metal bar moves through a magnetic field, and an induced current flows in the loop. What is the direction of the magnetic force on the bar?

Accepted Answer

Opposite to the direction of motion

Electromagnetic Induction and Faraday’s Law: Motional EMF, Magnetic Flux, and Lenz’s Law Ch 30

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