Question

A short bar magnet passes at a steady speed right through a long solenoid. A galvanometer is connected across the solenoid which graph best represents the variation of the galvanometer deflection $\theta$ with time.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Galvanometer:

1. A galvanometer is an electric device that measures the current through a circuit.
2. In a galvanometer, the galvanometer deflection $\left(\theta \right)$ is proportional to the induced current $I$.

Induced current:

1. We know induced current on a circuit is proportional to the magnetic flux through it, i.e, $\varphi \propto I$, where, $\varphi$is the magnetic flux and i is the induced current through the circuit.
2. The flux due to a magnet in a circuit is defined by the form, $\varphi =B.ds$, where B is the magnetic field and ds is the area.

Explanation for the correct option:

Option (A)

1. In this case, the magnetic field due to the bar magnet is non-uniform. We know the induced current is proportional to the flux. And flux will change when the magnetic field and surface area associated with the circuit are changed.
2. When the magnet moves toward the coil flux will increase rapidly at a certain point, and this flux will increase the induced current in the circuit. According to Lenz's law, the direction of the current will be such as the entering section of the solenoid will produce a north pole.
3. After entering the magnet the current will decrease and at the time when the magnet is completely inside the solenoid, the current associated with the circuit will be zero.
4. When the magnet leaves the solenoid then according to Lenz's law the end becomes north and the direction of induced current becomes negative. In this case, the current will increase at a certain value, and after completely leaving the solenoid the current becomes zero.
5. All these events are suitable for the graph given in option (A).

Diagram

Explanation for the incorrect options:

1. Al the graph in options (D), (B), and (C) do not obey the electromagnetic induction theory.
2. So, these options are not correct.

Therefore, option (A) is correct.