JEE Physics 2023 Question with Solution

Given: An electron moves with constant velocity along the axis of a current-carrying solenoid.

Find: Which statements about magnetic force and motion are correct.

The magnetic force experienced by a charged particle is

$$\vec{F}_m = q(\vec{v} \times \vec{B})$$

Inside a solenoid, the magnetic field $\vec{B}$ is directed along the axis of the solenoid. The electron is also moving along the axis, so $\vec{v}$ is parallel to $\vec{B}$.

Therefore,

$$\vec{v} \times \vec{B} = 0$$

and hence

$$\vec{F}_m = 0$$

Since the magnetic force is zero, the electron will not experience magnetic force and it will continue to move along the axis of the solenoid with constant velocity. It will neither be accelerated along the axis nor follow a parabolic path.

Therefore, the correct statements are B and C, so the correct option is D.

Given: The electron moves along the axis of a straight current-carrying solenoid.

Find: Whether force acts on it and how it moves.

For magnetic force, only the component of velocity perpendicular to the magnetic field contributes. Here, the solenoid field is along its axis, and the electron velocity is also along the same axis.

So the angle between $\vec{v}$ and $\vec{B}$ is $0^\circ$, and

$$|\vec{F}_m| = |q|vB\sin 0^\circ = 0$$

Thus statement A is false and statement B is true.

Because there is no magnetic force, there is no change in velocity due to the field. Hence the electron continues along the axis, so statement C is true.

Since force is zero, there is no acceleration caused by the magnetic field, so statement D is false. Also, without a transverse force, a parabolic path is impossible, so statement E is false.

Therefore, the correct option is D.