Question 1

Which of the following statements best describes Faraday's Law of Induction?

Accepted Answer

The induced emf in a circuit is proportional to the time rate of change of magnetic flux through the circuit: $$\varepsilon = -\frac{d\Phi_B}{dt}.$$

Question 2

A circular loop of radius $$r is $$placed in a uniform magnetic field $$B$$ perpendicular to its plane. If the field increases from $$0 to$$ $$B_0 in $$time $$t$$, what is the magnitude of the average induced emf in the loop?

Accepted Answer

$$\varepsilon = \frac{\pi r^2$ B_0$}{t}$$

Question 3

A square coil with $$N$$ turns and side length $$d is $$placed in a uniform magnetic field $$B$$ perpendicular to its plane. If $$B$$ changes linearly from $$0 to$$ $$B_1 in $$time $$\Delta t$$, what is the induced emf?

Accepted Answer

$$\varepsilon = N d^2$ \frac{\Delta B}{\Delta t}$$

Question 4

Which of the following will NOT induce an emf in a stationary conducting loop?

Accepted Answer

Keeping the magnetic field, area, and orientation constant.

Question 5

A metal bar of length $$L$$ moves with velocity $$v$$ perpendicular to a uniform magnetic field $$B. $$What is the potential difference between the ends of the bar?

Accepted Answer

$$V = BvL$$

Question 6

A conducting bar moves to the right on frictionless rails in a region with a uniform magnetic field pointing into the screen. If the induced current flows clockwise, what is the direction of the magnetic field?

Accepted Answer

Into the screen

Question 7

A flexible circular loop of radius $$r in a $$uniform magnetic field $$B is $$stretched so its area decreases to nearly zero in time $$\Delta t. $$What is the average induced emf?

Accepted Answer

$$\varepsilon = \frac{B \pi r^2$}{\Delta t}$$

Question 8

A rod of length $$L = 0.10 m $$moves at $$v = 2.0 m/s $$perpendicular to a uniform magnetic field. If a constant force of $$0.60 N is $$required to keep the rod moving at constant velocity and the circuit has a $$12\ \Omega$$ resistor, what is the current through the resistor?

Accepted Answer

$$I = \frac{F}{v}$$

Question 9

Three coils A, B, and C with identical resistance move at the same velocity into a region of uniform magnetic field. Coil A has the largest area, B is medium, and C is smallest. Which coil will have the greatest induced current as it enters the field?

Accepted Answer

Coil A

Question 10

A long solenoid of radius $$R$$ has turn density $$n$$ and carries a current that increases linearly from $$0 to$$ $$I in $$time $$t. $$What is the induced emf in a wire loop of resistance $$R_{loop}$$ placed perpendicular to the solenoid axis and enclosing the solenoid?

Accepted Answer

$$\varepsilon = \mu_0$ n \pi R^2$ \frac{\Delta I}{\Delta t}$$

Question 11

According to Lenz's Law, the direction of the induced current in a loop is such that:

Accepted Answer

It opposes the change in magnetic flux through the loop.

Question 12

A magnet is pushed toward a stationary metal loop. What is the direction of the induced current in the loop?

Accepted Answer

It creates a magnetic field that opposes the approaching magnet.

Question 13

A metal loop is being pulled out of a region with a uniform magnetic field pointing into the screen. What is the direction of the induced current?

Accepted Answer

Clockwise

Question 14

A rotating loop of area $$A in a $$uniform magnetic field $$B$$ rotates with angular velocity $$\omega. $$What is the expression for the induced emf?

Accepted Answer

$$\varepsilon = B A \omega \sin(\omega t)$$

Question 15

Which of the following best explains why the induced electric field from a changing magnetic field is non-conservative?

Accepted Answer

Because the induced electric field lines always make closed loops.

Question 16

A transformer has a primary coil with $$N_p$$ turns and a secondary coil with $$N_s$$ turns. If the input voltage is $$V_p$$, what is the output voltage $$V_s$$?

Accepted Answer

$$V_s = V_p \frac{N_s}{N_p}$$

Question 17

A solenoid of length $$l$$ and radius $$r$$ has $$N$$ turns. What is its inductance $$L$$?

Accepted Answer

$$L = \mu_0$ \frac{N^2$ \pi r^2$}{l}$$

Question 18

Which statement about inductors in circuits is correct?

Accepted Answer

Inductors oppose changes in current in a circuit.

Electromagnetic Induction (Chapter 30) – Study Notes

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