Question

The four separate figures below involve a cylindrical magnet and a light bulb connected to the ends of a loop of copper wire. These figures are to be used in the following question. The plane of the wire loop is perpendicular to the reference axis. The states of motion of the magnet and the loop of wire are indicated in the diagram. Speed is represented by $v$ and CCW represents counterclockwise. In which of the following figures will the bulb glow?

A) 1, 2, 3
B) 2, 3, 4
C) 1, 3, 4
D) 1, 2, 4
E) 1, 2, 3, 4

Answer 1

The bulb will glow when a current passes through it i.e. when an emf is induced in the loop. According to Faraday’s law of induction, when the magnetic flux associated with the loop changes an emf is induced in it. This then causes the bulb connected to the loop to glow.

Complete step by step answer.
Step 1: Sketch the first figure and based on Faraday’s law of induction determine if the bulb glows.

In the first figure, we see that the magnet moves towards the left while the lip is held stationary. So we can say that the magnet moves away from the loop. This motion of the magnet causes the magnetic flux associated with the loop to change. A change in the magnetic flux of the loop induces an emf in the loop. So the bulb in figure 1 will glow.
Step 2: Sketch the second figure and based on Faraday’s law of induction determine if the bulb glows.

In the second figure, we see that the magnet is held stationary while the loop collapses. The collapsing of the loop causes the magnetic flux associated with it to change. This change in the magnetic flux will then induce an emf in the loop. So the bulb in figure 2 will glow.
Step 3: Sketch the first figure and based on Faraday’s law of induction determine if the bulb glows.

In the third figure, we observe that the magnet is held stationary while the loop rotates in the counterclockwise direction. Here the Lorentz force is found to be perpendicular to the direction of motion of the loop. So the magnetic flux associated with the loop will be zero and hence no flux change is observed. So the bulb in figure 3 will not glow.
Step 4: Sketch the first figure and based on Faraday’s law of induction determine if the bulb glows.

In the fourth figure, the magnet is held stationary while the loop moves left i.e., it moves towards the magnet. This causes the magnetic flux associated with the loop to increase and will thus induce an emf in the loop. So the bulb in figure 4 will glow.

Thus the bulb in figures 1, 2 and 4 glow and so the correct option is D.

Note: When the magnet moves away from the loop, the magnetic flux decreases and if it were to move towards the loop the flux would have increased. The velocity $v$ with which the loop or the magnet moves is also important. If the magnitude of the velocity is greater in magnitude then the change in the flux associated with the loop will also be more.