Problem 18 - Master Resource Book in JEE Main Physics

Question

There are two coils \(A\) and \(B\) as shown in figure. A current starts flowing in \(B\) as shown, when \(A\) is moved towards \(B\) and stops when A stops moving. The current in \(A\) is counterclockwise. \(B\) is kept stationary when \(A\) moves. We can infer that \(\quad\) [NCERT Exemplar] (a) there is a constant current in the clockwise direction in \(A\). (b) there is a varying curent in \(A\). (c) there is no current in \(A\). (d) there is a constant current in the counterclockwise direction in \(A\)

Step-by-Step Solution

Answer

Option (b): There is a varying current in A.

Step 1: Understanding Lenz's Law

When coil A is moved towards coil B, an induced current is generated in coil B. Lenz's Law tells us that the direction of this induced current will be such that its magnetic field opposes the change in magnetic flux through coil B due to A's movement.

Step 2: Determine the Effect of Coil A's Motion

Since coil A is moving towards coil B, the magnetic field of A is increasing as perceived by coil B. The induced current in coil B is in a direction that opposes this increase.

Step 3: Examine Induced Current Direction in B

The problem states that the current in B starts when A moves and stops when A stops moving. Therefore, an electromotive force (EMF) is induced in coil B only when there's a change in magnetic flux due to A's motion.

Step 4: Evaluate the Current in Coil A

For an EMF to be induced in coil B, there needs to be a change in the magnetic field produced by A near B. If the current in A were constant, the magnetic field would be uniform and not change when A moves, meaning no EMF would be induced in B. Therefore, the current in A must vary when A moves.

Step 5: Conclusion

The varying current in A, as it moves, results in a changing magnetic field at coil B, thus inducing the observed current in B. Thus, option (b) is correct, as there is a varying current in A when it is in motion.

Key Concepts

Lenz's Law

Lenz’s Law is a fundamental principle of electromagnetic induction discovered by the physicist Heinrich Lenz. This law helps us understand the direction of an induced current. When a conductor, like our coil B in the exercise, is exposed to a changing magnetic field, an electromotive force (EMF) is induced. According to Lenz's Law, the direction of this induced current is such that it creates its own magnetic field which opposes the change in the original magnetic flux through the conductor. This is nature's way of preserving balance and preventing drastic changes.
This means in our scenario, when coil A moves closer to coil B, the magnetic flux through B changes. The induced current in B will produce a magnetic field to counteract this change, hence opposing the increasing effect of A’s magnetic field. This clever self-regulating mechanism ensures that systems remain stable during such interactions.

Induced Current

An induced current is a result of a changing magnetic environment around a conductor. In simpler terms, any time the magnetic conditions around a loop of wire or coil, like coil B, change, an EMF is generated which causes a current to flow if there is a closed path available. This process is the heart of how generators work, turning mechanical energy into electrical energy by rotating coils in magnetic fields.
In our exercise, when coil A approaches coil B, the changing magnetic field from A is what triggers an induced current in B. This current doesn't just appear out of nowhere, it's the effect of pushing and jostling of magnetic lines of force due to movement. The current only exists while this change is happening, explaining why it appears when A moves and disappears when A stops.

Magnetic Flux

Magnetic flux is a measure of the number of magnetic field lines passing through a given area, like the loops in a coil. Think of it as how many "lines" of magnetic influence are cutting through a surface. It's quantified in units of webers (Wb) and crucially depends on the strength of the magnetic field, the area it covers, and the orientation of that area relative to the field.
In our exercise, as coil A approaches B, the magnetic flux through coil B changes. This change is necessary for an induced current to be generated, as per Faraday’s Law, which states that it is the change in magnetic flux that induces an EMF. Therefore, when A moves, the flux associated with B is altered, "cutting" more field lines through its area, and when A stops, the flux becomes constant and the induced current stops.