Question

A magnet is moved towards a coil (i) quickly (ii) slowly, then the work done is.

Answer 1

Hint: In order to solve this question, we are going to analyze the condition given and what happens when a magnet is moved towards a coil quickly and slowly. The induced emf is noted in both the cases which directly means the work done and thus, we can tell the impact on work done.

Complete step-by-step solution:
The effect on the work done on the magnet , depends directly on the emf that is induced due to the movement of the magnet.
Now in the first case, i.e., when the magnet is moved towards the coil quickly, the change in the induced emf that is produced due to the movement of the magnet, is more. This can be explained in the following way.
Induced emf is defined as the work done on the charge per unit charge when there is no current flowing.
Emf induced in the coil is given by the formula
\[\varepsilon = - \dfrac{{d\phi }}{{dt}}\]
Thus emf induced is proportional to rate of change of magnetic flux.
When a magnet is moved towards the coil quickly, the rate of change of flux is larger, this means that if the magnetic is moved quickly, a larger emf is induced due to quick movement of the coil.
Thus, the work done is more in the case when the magnet is moved towards a coil (i) quickly.

Note: Alternatively, we can see as the magnet moves quickly, more energy it experiences due to the change in the magnetic fields and the movement of the magnet , similar is the impact for slow cases but to a lesser extent. Hence, change in work can be easily answered based on this.