Question

A magnet is brought near a coil in two ways (i) rapidly (ii) slowly. The induced charge will be
A) More in case (i)
B) More in case (ii)
C) Equal in both the cases
D) More or less according to the radius of the coil

Answer 1

Induced emf is defined as the generation of a potential difference in a coil due to changes in the magnetic flux through it. To find the solution of the given question we will apply the formula of induced emf to find that the induced emf will be more in which case.

Formula used:
$e = N\dfrac{{d\phi }}{{dt}}$

Complete answer:
To find whether the induced charge will increase in both the cases or not, we will apply the concept of induced. EMF or electromotive force is known to be induced when the flux linking with a conductor or coil changes with respect to time.
Mathematically it can be written as,
$e = N\dfrac{{d\phi }}{{dt}}$
Where ‘N’ is the number of turns in the coil, and ‘$\phi$’ is the magnetic flux that passes through the coil.
(i) When magnet is brought near a coil rapidly
We know that when a magnet is brought near a current carrying coil rapidly, its magnetic flux increases which would result in the increase of the induced emf with respect to time.
(ii) When magnet is brought near a coil slowly
When a magnet is brought near a current carrying coil slowly, its magnetic flux increases slowly as compared to the first case which would result in the increase of the induced emf slowly with respect to time.
Thus, the induced charge will be more in case (i).

So, the correct answer is “Option A”.

Note:
When the magnetic flux through a coil changes, the emf ‘e’ is generated in the coil. This law is known as the Faraday’s Law. The change in flux is produced by moving the coil the field or changing the intensity of the magnetic field.