Q: A circular loop of radius $$0.05\ \mathrm{m}$$ lies flat on a table. The Earth's magnetic field at this location is $$50\ \mu\mathrm{T}$$, directed $$60^\circ$$ below the horizontal. What is the magnetic flux through the loop?

$$3.4 \times 10$$^{-7}$$\ \mathrm{Wb}$$

Q: According to Faraday's law, what is the magnitude of the induced emf in a coil of $$N$$ turns if the magnetic flux through each turn changes by $$\Delta \Phi in $$time $$\Delta t$$?

$$\mathcal{E}_{\text{ind, coil}} = N \dfrac{\Delta \Phi}{\Delta t}$$

Question 1

A Boeing 747 with a wingspan of 65 m is flying at 260 m/s perpendicular to Earth's magnetic field of $$50 	imes 10$$^{-6}$$ T. What is the motional emf generated between the wingtips?

Accepted Answer

$$0.845\ \mathrm{V}$$

Question 2

Which of the following best describes the physical meaning of magnetic flux $$\Phi$$ through a loop?

Accepted Answer

The total number of magnetic field lines passing through the effective area of the loop.

Question 3

A rectangular loop of wire with area $$A is $$placed in a uniform magnetic field $$B at an $$angle $$	heta to $$the field. What is the correct formula for the magnetic flux through the loop?

Accepted Answer

$$\Phi = AB \cos 	heta$$

Question 4

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 downward?

Accepted Answer

Counterclockwise, to create an upward magnetic field opposing the increase.

Question 5

A conducting bar of length $$l$$ moves to the right at speed $$v on $$conducting rails in a uniform magnetic field $$B$$ directed into the page. What is the induced emf across the bar?

Accepted Answer

$$\mathcal{E} = v l B$$

Question 6

If the resistance of the loop in the previous question is $$R$$, what is the magnitude of the induced current?

Accepted Answer

$$I = \dfrac{v l B}{R}$$

Question 7

A circular loop of radius $$0.05\ \mathrm{m}$$ lies flat on a table. The Earth's magnetic field at this location is $$50\ \mu\mathrm{T}$$, directed $$60^\circ$$ below the horizontal. What is the magnetic flux through the loop?

Accepted Answer

$$3.4 	imes 10$$^{-7}$$\ \mathrm{Wb}$$

Question 8

Which of the following actions will NOT induce a current in a closed loop of wire?

Accepted Answer

Placing the loop in a constant magnetic field without moving it.

Question 9

A metal rod of length $$l$$ moves at velocity $$v$$ perpendicular to a magnetic field $$B. $$What is the direction of the induced electric field inside the rod?

Accepted Answer

Perpendicular to both the velocity and the magnetic field, as given by the right-hand rule.

Question 10

A generator coil rotates in a magnetic field, producing an alternating emf. What is the physical reason for the emf being alternating (AC) rather than direct (DC)?

Accepted Answer

The angle between the coil and the magnetic field changes continuously, causing the magnetic flux and thus the emf to oscillate in sign.

Question 11

Which of the following best explains why eddy currents are produced in a copper sheet moving through a magnetic field?

Accepted Answer

Changing magnetic flux through regions of the sheet induces circulating currents according to Faraday's law.

Question 12

A rectangular loop is moving toward a long straight current-carrying wire. As the loop approaches the wire, what is the direction of the induced current in the loop (as viewed from above)?

Accepted Answer

Counterclockwise

Question 13

According to Faraday's law, what is the magnitude of the induced emf in a coil of $$N$$ turns if the magnetic flux through each turn changes by $$\Delta \Phi in $$time $$\Delta t$$?

Accepted Answer

$$\mathcal{E}_{	ext{ind, coil}} = N \dfrac{\Delta \Phi}{\Delta t}$$

Question 14

A bar magnet is held stationary above a coil of wire. What happens to the current in the coil?

Accepted Answer

No current is induced because the magnetic flux is not changing.

Question 15

A conducting loop is pulled out of a region with a uniform magnetic field. What is the direction of the induced current as the loop leaves the field?

Accepted Answer

Clockwise, to maintain the original direction of the magnetic flux inside the loop.

Question 16

In the system where a wire slides on rails in a magnetic field, what is the relationship between the power supplied by the pulling force and the power dissipated in the resistor?

Accepted Answer

They are equal: $$P_{	ext{input}} = P_{	ext{dissipated}}$$

Question 17

Which of the following statements about electromagnetic induction is correct?

Accepted Answer

A changing magnetic flux through a loop induces an emf and possibly a current in the loop.

Electromagnetic Induction and Electromagnetic Waves: Study Notes

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