Physics: Electromagnetic Induction and Faraday's Law Worksheet

Question 1

A circular wire loop has an area of 0.25 m^2 and is placed perpendicular to a uniform magnetic field of 0.80 T. What is the magnetic flux through the loop?

Accepted Answer

The magnetic flux is 0.20 Wb because flux equals BA cos(theta), and the field is perpendicular to the loop so theta = 0 degrees. The calculation is (0.80 T)(0.25 m^2)(1) = 0.20 Wb.

Question 2

A 50-turn coil experiences a change in magnetic flux from 0.10 Wb to 0.40 Wb in 0.20 s. What is the magnitude of the average induced emf?

Accepted Answer

The magnitude of the average induced emf is 75 V. Using emf = N(Delta flux)/(Delta time), the result is 50(0.40 Wb - 0.10 Wb)/(0.20 s) = 75 V.

Question 3

State Faraday's law in words and explain what factor makes the induced emf larger.

Accepted Answer

Faraday's law states that a changing magnetic flux through a circuit induces an emf in the circuit. The induced emf becomes larger when the magnetic flux changes more quickly or when the coil has more turns.

Question 4

A bar magnet is pushed north-pole first toward a coil connected to a light bulb. Explain why the bulb lights while the magnet is moving but not when the magnet is held still.

Accepted Answer

The bulb lights while the magnet is moving because the magnetic flux through the coil is changing, which induces an emf and current. When the magnet is held still, the flux is constant, so no emf is induced and the bulb does not light.

Question 5

A square loop with side length 0.20 m is in a magnetic field that increases from 0.50 T to 1.10 T in 0.30 s. The field is perpendicular to the loop. What is the magnitude of the induced emf?

Accepted Answer

The induced emf has magnitude 0.080 V. The area is (0.20 m)(0.20 m) = 0.040 m^2, so the flux change is (1.10 T - 0.50 T)(0.040 m^2) = 0.024 Wb. Dividing by 0.30 s gives 0.080 V.

Question 6

According to Lenz's law, what is the direction of the induced magnetic field if the magnetic field into the page through a loop is increasing?

Accepted Answer

The induced magnetic field points out of the page. Lenz's law says the induced field opposes the increase in flux, so it must point opposite the increasing field into the page.

Question 7

For the situation in Problem 6, is the induced current clockwise or counterclockwise as viewed on the page?

Accepted Answer

The induced current is counterclockwise. By the right-hand rule, a counterclockwise current produces a magnetic field out of the page.

Question 8

A 200-turn coil has an induced emf of 12 V when the magnetic flux through each turn changes uniformly for 0.50 s. What is the magnitude of the flux change per turn?

Accepted Answer

The flux change per turn is 0.030 Wb. Rearranging Faraday's law gives Delta flux = emf times Delta time divided by N, so Delta flux = (12 V)(0.50 s)/200 = 0.030 Wb.

Question 9

A straight conducting rod of length 0.40 m moves at 6.0 m/s perpendicular to a 0.25 T magnetic field. What motional emf is induced across the rod?

Accepted Answer

The motional emf is 0.60 V. For a rod moving perpendicular to the field, emf = BLv = (0.25 T)(0.40 m)(6.0 m/s) = 0.60 V.

Question 10

A coil is rotated in a uniform magnetic field. At one instant, the coil's area vector is parallel to the magnetic field. At another instant, the area vector is perpendicular to the magnetic field. At which instant is the magnetic flux greatest?

Accepted Answer

The magnetic flux is greatest when the coil's area vector is parallel to the magnetic field. Since flux equals BA cos(theta), the maximum occurs when theta = 0 degrees and cos(theta) = 1.

Question 11

A single loop has an area of 0.060 m^2. The magnetic field through the loop changes from 0.20 T out of the page to 0.20 T into the page in 0.10 s. What is the magnitude of the average induced emf?

Accepted Answer

The magnitude of the average induced emf is 0.24 V. Treating out of the page as positive, the field changes from +0.20 T to -0.20 T, so the change in field is 0.40 T in magnitude. The flux change is (0.40 T)(0.060 m^2) = 0.024 Wb, and emf = 0.024 Wb/0.10 s = 0.24 V.

Question 12

A transformer has 400 turns on the primary coil and 100 turns on the secondary coil. If the primary voltage is 120 V AC, what is the secondary voltage, assuming an ideal transformer?

Accepted Answer

The secondary voltage is 30 V AC. For an ideal transformer, Vs/Vp = Ns/Np, so Vs = 120 V times 100/400 = 30 V.

Question 13

Why does a transformer require alternating current instead of steady direct current for normal operation?

Accepted Answer

A transformer requires alternating current because a changing current in the primary coil produces a changing magnetic flux in the core. That changing flux induces an emf in the secondary coil, while steady direct current would produce nearly constant flux after it is established.

Question 14

A metal ring is falling vertically through a region where a horizontal magnetic field is present. As it enters the field region, the magnetic flux through the ring changes. Explain how electromagnetic induction affects the ring's motion.

Accepted Answer

As the ring enters the magnetic field region, an induced current forms because the magnetic flux through the ring changes. By Lenz's law, the induced current creates a magnetic effect that opposes the change, which produces a force that resists the ring's motion and can slow it down.

Question 15

A coil has 80 turns and area 0.015 m^2 per turn. It is in a magnetic field perpendicular to the coil. The field decreases uniformly from 0.90 T to 0.10 T in 0.40 s. What is the magnitude of the induced emf?

Accepted Answer

The induced emf has magnitude 2.4 V. The change in flux per turn is (0.90 T - 0.10 T)(0.015 m^2) = 0.012 Wb. Multiplying by 80 turns and dividing by 0.40 s gives emf = 80(0.012 Wb)/(0.40 s) = 2.4 V.

Physics: Electromagnetic Induction and Faraday's Law

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