Question

A magnet is brought towards a coil

1. speedily
2. slowly

What will be the induced e.m.f./induced charge respectively?

Answer 1

Induced Electromotive Force:

1. It is the potential difference in a coil due to the changes in the magnetic flux through it.
2. It is given as $InducedEMF=\frac{d\varnothing }{dt}$.
3. It is directly proportional to the rate of change in flux.

When the magnet is bought speedily:

When the magnet is bought speedily near the coil, the rate of change of flux will increase. So, the induced e.m.f will be higher in this case. However since the induced charge is independent of time, it will not be affected.

Induced Charge:

1. Induced current is the ratio of induced emf and resistance and it is the rate of change of induced charge.
2. Induced current is given as $i=\frac{\epsilon }{R}$, from which the induced charge is derived as $dq=-\frac{d\varnothing }{R}$.
3. It is independent of time.

When the magnet is bought slowly:

When the magnet is bought slowly the induced charge will remain the same, as it does not depend on time while the rate of change of flux will be lower.

Hence,

1. The induced e.m.f. will be higher if the magnet is bought near the coil speedily.
2. The induced charge will remain the same in both cases.