Question

A conducting loop is placed in a uniform magnetic field, with its plane perpendicular to the field. An emf is induced in the loop if

• A. It is rotated about its axis
• B. It is rotated about its diameter
• C. It is not moved
• D. It is given translational motion in the field

Answer 1

The correct option is B

It is rotated about its diameter

Explanation for correct option:

According to the laws of EMF-Electromotive force is induced only when there is a change in magnetic flux and the induced EMF opposes the change in magnetic flux. Magnetic flux can be changed by moving the loop in the magnetic field.

$Magneticflux=B(magneticfield)\times A(areaofcrosssection)\times \cos \theta$

1. If the loop is rotated about its diameter, B and A remain constant since B is uniform throughout the plane and A remains constant because the loop doesn't change its shape but the angle between them changes due to rotation.
2. In this case, EMF is induced as there is a change in magnetic flux.

Explanation for incorrect options:

Option A

1. If the loop is rotated about its axis (lies in the center of the loop), it will perform circular motion according to which B, A, and the angle between B and A doesn't change.
2. Since magnetic flux doesn't change when the loop is rotated about its axis, this option is incorrect.

Option C

1. If the loop is not moved, B, A, and the angle between them won't change and there won't be any change in magnetic flux due to which EMF would not be induced

Option D

1. If the loop is translated that is if it is moved in a translation motion (for example left or right), B doesn't change since B is uniform throughout the plane, A doesn't change because the loop maintains its shape and the angle between B and A doesn't change too.
2. Since magnetic flux doesn't change when the loop is translated, this option is incorrect.

Hence, option B is correct.