Q: The magnetic flux $$\Phi_m$$ through a single loop is given by which equation?

$$\Phi_m = B \cdot A \cdot \cos \theta$$

Q: A loop of wire is rotated in a magnetic field. Which of the following best describes the change in magnetic flux?

The magnetic flux changes as $$\cos \theta of $$the angle between the area vector and the field.

Question 1

A magnet is inserted into a coil connected to a galvanometer. Which of the following statements best explains why a current is induced in the coil?

Accepted Answer

The changing magnetic flux through the coil induces an electric field, causing a current.

Question 2

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

Accepted Answer

Keeping the loop stationary in a constant magnetic field.

Question 3

The magnetic flux $$\Phi_m$$ through a single loop is given by which equation?

Accepted Answer

$$\Phi_m = B \cdot A \cdot \cos 	heta$$

Question 4

A loop is placed in a magnetic field such that the area vector is perpendicular to the field lines ($$	heta = 0). $$What is the value of the magnetic flux?

Accepted Answer

$$\Phi_m = B \cdot A$$

Question 5

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 creates a magnetic field that opposes the increase in flux.

Question 6

A loop of wire with radius 5 cm and resistance 0.2 $$\Omega is $$placed perpendicular to a uniform magnetic field. The field increases from 0 T to 1.8 T in 3 seconds. What is the magnitude of the induced current?

Accepted Answer

$$0.0707\ 	ext{A}$$

Question 7

If the magnetic field through a loop is constant over time, what is the induced emf according to Faraday’s law?

Accepted Answer

$$\mathcal{E}_{induced} = 0$$

Question 8

A metal bar moves perpendicular to a uniform magnetic field. What is the expression for the motional emf generated across the bar?

Accepted Answer

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

Question 9

A square loop (area $$A) is $$placed in a region where the magnetic field is doubled, but the loop’s area is halved. What happens to the magnetic flux?

Accepted Answer

The magnetic flux remains unchanged.

Question 10

A loop is moving toward a current-carrying wire. What is the direction of the induced current in the loop?

Accepted Answer

Counterclockwise

Question 11

A coil with $$N$$ turns is placed in a changing magnetic field. What is the expression for the induced emf?

Accepted Answer

$$\mathcal{E}_{induced} = N \frac{\Delta \Phi_{m, per\ turn}}{\Delta t}$$

Question 12

A metal bar moves through a magnetic field, causing charge separation. What is the final condition inside the bar?

Accepted Answer

The electric and magnetic forces on the charge carriers balance each other.

Question 13

A loop of wire is rotated in a magnetic field. Which of the following best describes the change in magnetic flux?

Accepted Answer

The magnetic flux changes as $$\cos 	heta of $$the angle between the area vector and the field.

Question 14

A metallic bar moves along a U-shaped rail in a magnetic field pointing into the page. What is the direction of the induced current?

Accepted Answer

Counterclockwise

Question 15

Which scenario will result in zero magnetic flux through a loop?

Accepted Answer

The loop is oriented parallel to the magnetic field lines ($$	heta = 90^\circ).$$

Question 16

A loop of wire with resistance $$R is $$placed in a region where the magnetic field increases linearly with time. What is the induced current?

Accepted Answer

$$I = \frac{\mathcal{E}_{induced}}{R}$$

Question 17

A loop is pushed into a region with a constant magnetic field. What happens to the induced current as the loop enters and then stops moving?

Accepted Answer

Current is induced while entering, but stops once the loop is fully inside and stationary.

Question 18

A loop is moved away from a magnet. What is the direction of the induced current according to Lenz’s law?

Accepted Answer

The induced current creates a magnetic field in the same direction as the external field.

Question 19

A loop of wire is placed in a region where the magnetic field increases from 0 T to 1.8 T in 3 seconds, then stays constant for 2 seconds, and then drops to 0 in 1 second. What does the graph of induced current vs. time look like?

Accepted Answer

Current is positive during the increase, zero during the constant field, and negative during the decrease.

Electromagnetic Induction: Principles, Laws, and Applications

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