A bar magnet is placed near and lying along the axis of a solenoid connected to a galvanometer. The pointer of the galvanometer shows no deflection when?

The galvanometer is an instrument used to measure the current flowing in a circuit. When current flows through the solenoid, it creates a magnetic field around it. When a bar magnet is placed near the solenoid, the magnetic field of the magnet interacts with the magnetic field of the solenoid. The interaction between these magnetic fields can cause a current to flow through the solenoid and hence through the galvanometer. The direction and strength of the current flowing through the galvanometer depends on the relative motion between the magnet and the solenoid. In the given options, when the magnet is moved towards the stationary solenoid or when the solenoid is moved away from the stationary magnet, there will be a change in the relative motion between the two, and hence a current will flow through the galvanometer. However, when there is no relative motion between the magnet and the solenoid, the interaction between their magnetic fields remains constant and there will be no induced current flowing through the solenoid or the galvanometer. Therefore, the pointer of the galvanometer shows no deflection when there is no relative motion between the magnet and the solenoid. So, the correct option is "there is no relative motion."