A circular 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 displaced in the same plane in magnetic field
B. it is rotated about its axis
C. it is rotated about a diameter
D. it is converted into square loop in the same plane
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → C and D
By Faraday’s law an emf is induced only while the magnetic flux \( \Phi = BA\cos\theta \) through the loop changes. Here the flux can change only through the area \( A \) or the angle \( \theta \) between the field and the normal to the loop (initially \( \theta = 0^\circ \)).
(A) It is displaced in the same plane in magnetic field — Incorrect. The field is uniform, so \( B \), \( A \) and \( \theta \) stay the same and the flux does not change.
(B) It is rotated about its axis — Incorrect. The axis is perpendicular to the plane of the loop, so the plane stays perpendicular to the field and \( \theta \) stays \( 0^\circ \). The flux does not change.
(C) It is rotated about a diameter — Correct. The angle \( \theta \) between the field and the normal changes, so \( \cos\theta \) and the flux change continuously.
(D) It is converted into square loop in the same plane — Correct. For a given length of wire a circle encloses the greatest possible area, so the area \( A \) decreases and the flux changes.
NCERT (2026-27):
Faraday’s Law of Induction – “… From Eqs. (6.1) and (6.2), we see that the flux can be varied by changing any one or more of the terms B, A and θ. … The flux can also be altered by changing the shape of a coil (that is, by shrinking it or stretching it) in a magnetic field, or rotating a coil in a magnetic field such that the angle θ between B and A changes. In these cases too, an emf is induced in the respective coils.”