Question

When the magnet as shown in the diagram, is moved towards the coil at a speed of 5 ms\(^{-1}\), the galvanometer shows a certain deflection to the right.

How will the direction and magnitude of deflection change when the coil also moves with a speed of 5 ms\(^{-1}\):
(a) in the direction of the motion of the magnet?
(b) in the opposite direction of the motion of the magnet?

Hint:

Induced current depends only on the *relative* motion between the magnet and the coil. No relative motion means no induced current.

Answer 1

Step 1: Understanding the Concept:
Faraday's Law of Electromagnetic Induction states that an EMF is induced in a coil only when there is a change in the magnetic flux linked with it. This change is caused by relative motion between the magnet and the coil.
Step 2: Detailed Explanation:
In the given scenario, the magnet moves to the left at \( 5 \text{ ms}^{-1} \) and the coil also moves to the left at \( 5 \text{ ms}^{-1} \).
Since both are moving with the same velocity in the same direction, the distance between them remains constant.
Relative velocity = \( 5 \text{ ms}^{-1} - 5 \text{ ms}^{-1} = 0 \text{ ms}^{-1} \).
Because there is no relative motion, there is no change in the magnetic flux linked with the coil.
Consequently, no current is induced, and the galvanometer shows zero deflection.
Step 3: Final Answer:
The deflection becomes zero because the relative velocity between the magnet and the coil is zero.
(b)
Step 1: Understanding the Concept:
The magnitude of induced EMF is proportional to the rate of relative motion. The direction of induced current depends on whether the magnetic flux is increasing or decreasing.
Step 2: Detailed Explanation:
The magnet moves to the left at \( 5 \text{ ms}^{-1} \).
The coil moves to the right at \( 5 \text{ ms}^{-1} \).
Since they move toward each other, their relative speed is the sum of their individual speeds:
Relative Velocity = \( 5 \text{ ms}^{-1} + 5 \text{ ms}^{-1} = 10 \text{ ms}^{-1} \).
1. Magnitude: The relative speed is now double the original speed (\( 10 \text{ ms}^{-1} \) vs \( 5 \text{ ms}^{-1} \)). Therefore, the rate of change of flux is doubled, leading to a doubling of the induced current and deflection magnitude.
2. Direction: The magnet's North pole is still approaching the coil (flux is increasing). According to Lenz's Law, the direction of the induced current will be the same as in the original case (to the right).
Step 3: Final Answer:
The deflection magnitude increases (doubles) and the direction remains to the right.