A coil is placed in a magnetic field such that the plane of the coil is perpendicular to the direction of the magnetic field. The magnetic flux through the coil can be changed by-
(A) Changing the magnetic field within the coil.
(B) Changing the area of coil within the magnetic field.
(C) Changing the angle between the direction of the magnetic field and the plane of the coil.
(D) Reversing the magnetic field direction abruptly without changing its magnitude.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (B), (C) and (D)
The magnetic flux through a coil of area A is \( \Phi = BA\cos\theta \), where \( \theta \) is the angle between the field and the normal to the coil. Changing any factor in this product changes the flux.
\( \Phi = BA\cos\theta \)
(A) Changing the magnetic field within the coil. — Correct. The flux is proportional to B.
(B) Changing the area of coil within the magnetic field. — Correct. The flux is proportional to the area inside the field.
(C) Changing the angle between the direction of the magnetic field and the plane of the coil. — Correct. The angle with the plane and the angle with the normal add up to 90°, so changing one changes \( \cos\theta \). Turning the coil from perpendicular to parallel to the field reduces the flux from BA to zero.
(D) Reversing the magnetic field direction abruptly without changing its magnitude. — Correct. Flux has a sign: it changes from +BA to −BA.
\( \Delta\Phi = (-BA) - (+BA) = -2BA \)
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 \( \mathbf{B} \), \( \mathbf{A} \) and \( \theta \). … 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 \( \theta \) between \( \mathbf{B} \) and \( \mathbf{A} \) changes.”