Question

If a current- carrying loop is placed in a non- uniform magnetic field, then the loop
(a) Experiences a force
(b) Experiences a torque
(c) Will develop induced current
(d) Oscillates

(A) a, c are correct
(B) a, b, c are correct
(C) b, c, d are correct
(A) a, b, d are correct

Answer 1

Hint The question is saying that a current- carrying loop is placed in a non- uniform magnetic field. Since the magnetic flux is non-uniform the change in magnetic field intensity will apply a force on the current- carrying loop and as a result, it'll also apply a torque that is generated during the process. So let’s start solving this problem.

Complete Step-by-step solution
1. When a current- carrying conductor is placed in a magnetic field, it will experience a force. The force on a current- carrying coil placed in a magnetic field is given by Fleming's left- hand rule.
 ${\overrightarrow F _m} = i\left( {\overrightarrow l \times \overrightarrow B } \right)$
Where F is the force on the conductor
B is the magnitude of the magnetic field
i is the current in the conductor
l is the length of the current- carrying wire
From the above formula, force is directly proportional to the magnitude of the magnetic field, current in the wire, and the length of the wire.
 2. The change in magnetic field intensity will insert a force on the loop and as a result, it’ll also insert a torque. The torque on a loop, with magnetic dipole moment $\overrightarrow \mu $ immersed in a magnetic field $\overrightarrow B $ is given by:
 $\tau = \mu B\sin \theta $
The direction of the magnetic dipole moment is given by the right-hand rule for axial vectors. If a closed- loop having a current $I$ the magnetic dipole moment vector $\mu $ is defined as:
 $\mu = IA$
Where $A$ is the area enclosed by the loop.
3. A current can be induced in a current- carrying conductor if it is exposed to a changing magnetic field. Then the strength of the current is proportional to the change of magnetic flux, as suggested by Faraday’s law of induction.
 ${\phi _B} = \iint_A {B.dA}$
The direction of the current can be determined by considering Lenz’s law, which says that an induced current will flow in such a way that it generates a magnetic field that opposes the change within the field that generated it.

The correct answer is (B) a, b, c are correct.

Note The change in the magnetic field to induce current may be produced in several ways; you can change the strength of the magnetic field, move the conductor in and out of the field, or change the distance between a magnet and the conductor, or change the area of a loop placed in a magnetic field.