Question

A circular loop of wire is in a region of the spatially uniform magnetic field, as shown in Fig. 29.15 . The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or counterclockwise) of the induced current in the loop when (a) B is increasing; (b) B is decreasing; (c) B is constant with value ${\mathbf{B}}_{\mathbf{0}}$. Explain your reasoning.

Short answer

1. Anti-clockwise
2. Clockwise
3. No induced current

Step-by-step solution

Explanation when B is increasingTop of Form

According to Lenz’s law, the direction of the induced current is such that it opposes the cause which causes it.

When B is increasing, the direction of the induced current will be such that the magnetic field produced by it will oppose the increasing magnetic field.

Hence, the direction of the magnetic field due to the induced current should be out of the plane of the paper. The induced current will flow in the anti-clockwise direction.

Explanation when B is decreasing

When B is decreasing, the direction of the induced current will be such that the magnetic field produced by it will oppose the increasing magnetic field.

Hence, the direction of the magnetic field due to the induced current should be into the plane of the paper. The induced current will flow in the clockwise direction.

Explanation when B is constant

The flux associated with the circular loop remains constant. Thus, there is no induced current flowing through the loop.