Question

A wire is bent to form the double loop shown as figure. There is a uniform magnetic field directed into the plane of the loop. If the magnitude of this field is decreasing, the current will flow from

A) a to b and c to d
B) b to a and d to c
C) a to b and d to c
D) b to a and c to d
E) answer required

Answer 1

This question can be solved by using Right hand rule and lenz’s law, which gives a clear idea about how the direction of current varies with direction of magnetic field.

Complete step by step answer:
First, we understand the right hand thumb rule and lenz’s law.
As per right hand thumb rule, if you wrap your right hand around the conductor, your right-hand thumb gives the direction of current in the wire and the curled fingers give the direction of the magnetic field. As per Lenz's law, an induced electric current flow in a direction such that the current opposes the change that induced it.
First, we consider the arm AB and apply the right hand thumb rule. As per Lenz’s law, since the magnetic field is inwards, the direction of current is anticlockwise. But as the field decreases the flux also decreases. Hence the magnetic field induced inside AB also in the same direction. Hence again magnetic fields also inside the plane. Now, again apply the right-hand rule for the inner side of AB. Then the current should be in the direction of A to B.
As the field decreases the flux through the loop decreases. By Lenz's Law, to counter this the current in the clockwise direction will flow so that it adds to the decreasing field and hence opposes the decreasing flux. By Lenz's law clockwise current is induced in a closed loop.
For clockwise direction of current, current will flow from a to b and from d to c.
Hence the correct answer is (C)

Note: Lenz’s law also states that when a voltage is created by a change in magnetic flux, the induced voltage must create a current whose magnetic field is in opposition to the change which produces it.