Question 1

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

Accepted Answer

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

Question 2

A circular coil with $$N$$ turns is rotated in a uniform magnetic field at a constant angular velocity $$\omega. $$What is the expression for the maximum amplitude of the induced emf?

Accepted Answer

$$\varepsilon_{max} = NB\omega A$$

Question 3

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 flows in a direction that opposes the change in magnetic flux.

Question 4

A conducting 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

$$\varepsilon = Blv$$

Question 5

In an electric generator, the induced emf is sinusoidal because:

Accepted Answer

The coil rotates at a constant speed, causing the angle between the magnetic field and the area vector to change sinusoidally.

Question 6

Why does a split-ring commutator in a DC generator produce a pulsed DC voltage rather than a steady DC voltage?

Accepted Answer

Because the commutator reverses the connection every half turn, resulting in the output voltage always being positive but varying in magnitude.

Question 7

A metal bob swings through a region of uniform magnetic field. What effect do eddy currents have on its motion?

Accepted Answer

Eddy currents create a magnetic force that opposes the motion, causing magnetic damping and slowing the bob.

Question 8

Which of the following is NOT a practical application of eddy currents?

Accepted Answer

Generating static electricity in batteries.

Question 9

A rectangular conducting loop is pulled to the right at constant velocity $$v$$ through a uniform magnetic field $$B$$ pointing out of the page. What is the direction of the induced current?

Accepted Answer

Counterclockwise around the loop.

Question 10

Which statement about induced electric fields due to changing magnetic flux is correct?

Accepted Answer

Induced electric fields are non-conservative and form closed loops.

Question 11

A coil with $$N$$ turns and area $$A$$ rotates in a uniform magnetic field $$B$$ with angular velocity $$\omega. $$What is the time-dependent expression for the induced emf?

Accepted Answer

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

Question 12

Which of the following best explains the difference between an electric generator and an electric motor?

Accepted Answer

A generator converts mechanical energy into electrical energy, while a motor converts electrical energy into mechanical energy.

Question 13

A slotted metal plate is dropped through a magnetic field. Compared to a solid metal plate, what happens to the eddy currents and magnetic damping?

Accepted Answer

Eddy currents are reduced because the slots break up the current loops, resulting in less magnetic damping.

Question 14

If the area of a coil inside a steady magnetic field is changed at a constant rate, what is the expression for the induced emf?

Accepted Answer

$$\varepsilon = -B \frac{dA}{dt}$$

Question 15

A metal rod is pulled through a uniform magnetic field at constant velocity. What force must be applied to keep the rod moving at constant speed?

Accepted Answer

A force equal in magnitude and opposite in direction to the magnetic force $$\vec{F}_m = q\vec{v} 	imes \vec{B}.$$

Question 16

Which of the following statements about the work done by the induced emf in a circuit is correct?

Accepted Answer

The work is done by the induced electric field $$\vec{E} on $$the conduction electrons.

Question 17

Which equation correctly relates the induced emf to the line integral of the induced electric field around a closed loop?

Accepted Answer

$$\varepsilon = \oint \vec{E} \cdot d\vec{l} = -\frac{d\Phi_m}{dt}$$

Question 18

Which of the following is a consequence of Lenz's Law in electromagnetic induction?

Accepted Answer

Energy is conserved because the induced current always opposes the change in magnetic flux.

Question 19

Which scenario will NOT produce a motional emf in a wire loop?

Accepted Answer

The loop is stationary in a uniform magnetic field.

LEC 5: Electromagnetic Induction II: Faraday’s Law, Motional EMF, and Eddy Currents

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