A magnet is brought towards a coil (i) speedily and (ii) slowly then the induced emf/induced charge will be respectively.a)more in first case/equal in both caseb)less in first case/equal in both casec)less in first case/more is second cased)more in first case/more in first caseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

According to Faraday’s law.

The magnitude of induced emf is directly proportional to the rate of change of magnetic flux. So induced emf will be more in first case.

We also know ε = iR

So, induced charge in a coil is independent of time taken to charge the flux.
The correct answer is: more in first case/equal in both case

Answer

When a magnet is brought towards a coil, it induces an electromotive force (emf) and/or an induced charge in the coil. The magnitude of the induced emf and charge depends on the rate at which the magnet approaches the coil.

(i) Speedy Approach:
When the magnet is brought towards the coil speedily, the rate of change of magnetic field is higher. This leads to a larger induced emf and charge in the coil. According to Faraday's law of electromagnetic induction, the induced emf is directly proportional to the rate of change of magnetic flux through the coil. Since the magnetic field is changing rapidly, the induced emf in the coil will be larger.

(ii) Slow Approach:
When the magnet is brought towards the coil slowly, the rate of change of magnetic field is slower. This leads to a smaller induced emf and charge in the coil. The slower change in magnetic field results in a smaller rate of change of magnetic flux through the coil, resulting in a smaller induced emf according to Faraday's law.

Therefore, the induced emf and charge will be more in the first case (speedy approach) and equal in both cases.

To summarize:
- When the magnet is brought towards the coil speedily, the induced emf and charge are larger due to the faster rate of change of magnetic field.
- When the magnet is brought towards the coil slowly, the induced emf and charge are smaller due to the slower rate of change of magnetic field.
- In both cases, the induced emf and charge are present, but their magnitudes differ based on the rate of change of magnetic field.

In conclusion, the induced emf and charge will be more in the first case (speedy approach) and equal in both cases.

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