Question 1

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

Accepted Answer

A changing magnetic flux through a closed loop induces an electromotive force (emf) in the loop: $$\epsilon = -\frac{d\Phi_B}{dt}$$

Question 2

A coil is placed in a region where the magnetic field is perpendicular to its plane. If the magnetic field increases linearly with time, what is the direction of the induced current as seen from above?

Accepted Answer

Counterclockwise, to oppose the increase in magnetic flux.

Question 3

The magnetic flux $$\Phi_B$$ through a surface of area $$A in a $$uniform magnetic field $$\vec{B} is $$given by:

Accepted Answer

$$\Phi_B = B A \cos 	heta$$

Question 4

A rectangular loop of wire is pulled out of a region of uniform magnetic field pointing out of the page. What is the direction of the induced current in the loop?

Accepted Answer

Counterclockwise, to oppose the decrease in magnetic flux.

Question 5

Which of the following statements about the induced electric field due to a changing magnetic field is correct?

Accepted Answer

It forms closed loops and is non-conservative.

Question 6

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

Accepted Answer

$$\epsilon = B v l$$

Question 7

In an ideal transformer, the ratio of the secondary voltage $$V_s to $$the primary voltage $$V_p is$$:

Accepted Answer

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

Question 8

A solenoid with $$N$$ turns, length $$l$$, and cross-sectional area $$A$$ carries a current $$I. $$What is the self-inductance $$L of $$the solenoid?

Accepted Answer

$$L = \mu_0$ N^2$ A / l$$

Question 9

The energy stored in an inductor with inductance $$L$$ carrying current $$I is$$:

Accepted Answer

$$U = \frac{1}{2} L I^2$

Question 10

Why are high voltages used for long-distance transmission of electrical power?

Accepted Answer

To decrease the current and reduce power loss due to resistance: $$P_L = I^2$ R$$

Question 11

A generator coil rotates in a uniform magnetic field. If the coil rotates with angular velocity $$\omega$$, what is the expression for the induced emf?

Accepted Answer

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

Question 12

Which of the following is a real-world application of eddy currents?

Accepted Answer

Metal detectors

Question 13

If the current in the primary coil of a transformer is suddenly switched off, what happens in the secondary coil?

Accepted Answer

A voltage spike is induced.

Question 14

The mutual inductance $$M$$ between two coils depends on:

Accepted Answer

The geometry and relative position of both coils.

Question 15

Which equation correctly relates the induced emf $$\epsilon in a $$coil to the rate of change of current $$I in $$another coil via mutual inductance $$M$$?

Accepted Answer

$$\epsilon = -M \frac{dI}{dt}$$

Question 16

A transformer has 100 turns on the primary coil and 1000 turns on the secondary coil. If the input voltage is 120 V, what is the output voltage (ideal case)?

Accepted Answer

1200 V

Question 17

Which of the following best explains why a constant magnetic field does NOT induce an emf in a stationary loop?

Accepted Answer

The magnetic flux through the loop is not changing with time.

Question 18

The energy density $$u of a $$magnetic field $$B in $$free space is given by:

Accepted Answer

$$u = \frac{1}{2} \frac{B^2$}{\mu_0$}$$

Question 19

Which of the following is NOT a consequence of Lenz's Law?

Accepted Answer

The induced emf can create perpetual motion.

Question 20

A long solenoid is connected to a battery and a switch. When the switch is closed, what happens to the current and the magnetic field inside the solenoid?

Accepted Answer

The current and magnetic field gradually increase due to self-inductance.

Electromagnetic Induction and Faraday's Law: Study Notes

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