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Electromagnetic Induction

JEE Main level, single correct, medium

118 of 153

Question 118 of 153

Three identical coils $C_{1}, C_{2}$ and $C_{3}$ are closely placed such that they share a common axis. $C_{2}$ is exactly midway. $C_{1}$ carries current $I$ in anti-clockwise direction while $C_{3}$ carries current $I$ in clockwise direction. An induced current flows through $C_{2}$ will be in clockwise direction when

Show answer and solution

Answer: (C) $C_{1}$ moves towards $C_{2}$ and $C_{3}$ moves away from $C_{2}$

Let the common axis be the z-axis.

C_1

is at

z = -d

C_2

is at

z = 0

, and

C_3

is at

z = +d

.
Current in

C_1

is anti-clockwise (ACW), producing a magnetic field

B_1

in the

+z

direction at

C_2

.
Current in

C_3

is clockwise (CW), producing a magnetic field

B_3

in the

-z

direction at

C_2

.
The net magnetic field at

C_2

B_{net} = B_1 - B_3

. Since

C_1

and

C_3

are equidistant and carry equal current, initially

B_{net} = 0

.

To induce a clockwise current in

C_2

, Lenz's law states that the induced current must oppose the change in flux. A clockwise induced current produces a magnetic field in the

-z

direction.
This happens if there is an increasing flux in the

+z

direction or a decreasing flux in the

-z

direction.

Case 1:

C_1

moves towards

C_2

. The distance decreases, so

B_1

(in

+z

direction) increases. This causes an increasing flux in the

+z

direction.

Case 2:

C_3

moves away from

C_2

. The distance increases, so

B_3

(in

-z

direction) decreases. This causes a decreasing flux in the

-z

direction.

Both actions (moving

C_1

towards

C_2

and moving

C_3

away from

C_2

) result in a net change in flux that induces a clockwise current in

C_2

to oppose the change.
Therefore, option (3) is correct.

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JEE Main 2025 Apr 2 Shift 1 question paper

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