Consider a small bar magnet undergoing simple harmonic motion (SHM) al...
Explanation:
When a magnet moves in and out of a coil, it induces an electromotive force (EMF) in the coil due to the changing magnetic field. This induced EMF can cause an induced current to flow in the coil.
The induced EMF depends on the rate of change of the magnetic field, which in turn depends on the velocity of the magnet. As the magnet moves in and out of the coil during SHM, its velocity changes, which causes the induced EMF to change.
Now, we need to determine at which point the induced EMF is minimum during the SHM of the magnet.
The correct option is 'A', i.e., induced EMF is minimum when the center of the bar magnet crosses the coil. This can be explained as follows:
When the magnet is at the center of its motion and crosses the coil, its velocity is zero. Therefore, there is no change in the magnetic field, and hence no induced EMF is generated in the coil.
As the magnet moves away from the center, its velocity increases, causing a change in the magnetic field and inducing an EMF in the coil. Similarly, as the magnet moves towards the center from the other side, its velocity decreases, inducing an EMF in the opposite direction.
Thus, the induced EMF is maximum when the magnet is moving at maximum velocity, and it is zero when the magnet is at the center of its motion.
Therefore, option 'A' is the correct answer.
Note: The frequency of the induced current in the coil is the same as the frequency of the SHM of the magnet, not half of it (option 'B' is incorrect). The sign of the induced EMF depends on the direction of the magnetic field, not the pole face of the magnet (option 'D' is incorrect). The induced EMF depends on the velocity of the magnet (option 'C' is incorrect).