Question

A and B are 2 metallic rings placed at opposite sides of an infinitely long straight conducting wire as shown in the figure. If the current in the wire is slowly decreased, then the direction of the induced current will be:

A) clockwise in A and anticlockwise in B
B) anticlockwise in A and clockwise in B
C) clockwise in both A and B
D) anticlockwise in both A and B

Answer 1

Hint: Lenz’s law: The direction of current induced by a changing magnetic field will be such that the magnetic field created by the resulting induced current opposes the changing magnetic field.
Right-hand thumb rule: If the thumb of the right-hand points in the direction of the increasing current then the curl of the fingers gives the direction of the magnetic field.

Complete step by step solution:
We have to find the direction of current in metallic rings A and B.
Diagram: Fig 1 depicts the direction of the flow of current and situation presented in the question.

Step 1 of 3:
The changing current in a long straight wire produces a changing magnetic field in its vicinity.
Apply right-hand thumb rule to find the direction of the induced magnetic field for both the ring:
The amount of current passing through the long straight wire decreases, hence the thumb points in the downward direction. The fingers curl in an anticlockwise direction.
This means that for ring A: the magnetic field goes inside the plane of the paper.
For ring B: the magnetic field comes out of the plane of the paper.

Step 2 of 3:
Use Lenz’s law to determine the direction of flow of current in both the rings:
For ring A: the magnetic field produced by the induced current should point out of the plane of the paper.
For ring B: the magnetic field produced by the induced current should point inside the plane of the paper.

Step 3 of 3:
Again, apply the right-hand thumb rule to find the direction of induced current in both the rings:
For ring A: If the fingers curl out of the plane of the paper, then the direction of the thumb causes the current to flow anticlockwise.
For ring B: If the fingers curl inside the plane of the paper, then the direction of the thumb causes the current to flow clockwise.

$\therefore$ If the current in the wire is slowly decreased, then the direction of the induced current will be anticlockwise in A and clockwise in B. So, option (B) is correct.

Note:
In questions like these, apply the right-hand thumb rule to find the direction of the induced magnetic field. Then apply Lenz’s law to find the induced current generated in the rings to oppose it.