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?
Show Hint
Induced current depends only on the *relative* motion between the magnet and the coil. No relative motion means no induced current.
Step 1: Understanding Electromagnetic Induction:
According to Faraday's law of electromagnetic induction, an electromotive force (e.m.f.) and hence a current is induced in a coil only when there is a change in the magnetic flux linked with it. This change in flux is caused by the relative motion between the magnet and the coil. The magnitude of the induced current is proportional to the rate of change of flux, which depends on the relative speed. The direction is given by Lenz's law. (a) Coil moves in the same direction as the magnet:
- Speed of magnet = 5 ms\(^{-1}\) (let's say, to the left).
- Speed of coil = 5 ms\(^{-1}\) (also to the left).
- The relative speed between the magnet and the coil is \(5 - 5 = 0\).
- Since there is no relative motion, the magnetic flux linked with the coil does not change.
- Therefore, no current is induced, and the galvanometer shows zero deflection. (b) Coil moves in the opposite direction of the magnet:
- Speed of magnet = 5 ms\(^{-1}\) (to the left).
- Speed of coil = 5 ms\(^{-1}\) (to the right, i.e., in the opposite direction).
- The magnet and coil are moving towards each other. Their relative speed of approach is \(5 + 5 = 10\) ms\(^{-1}\).
- This relative speed (10 ms\(^{-1}\)) is double the original relative speed (5 ms\(^{-1}\)).
- Magnitude: Since the rate of change of flux is now doubled, the magnitude of the induced current and the resulting deflection will be larger (specifically, double the original deflection).
- Direction: The magnet is still approaching the coil, which is the same direction of relative motion as the initial case. According to Lenz's law, the direction of the induced current depends on whether the flux is increasing or decreasing. Since the relative motion is still 'approaching', the direction of the induced current will be the same as before (to the right).
