Question

An electron is projected with uniform velocity along the axis of a current-carrying long solenoid. Which of the following is true?

• A. The electron path will be circular about the axis
• B. The electron path will be accelerated along the path
• C. The electron will continue to move with uniform velocity along the axis of the solenoid
• D. The electron path will experience a force and will hence execute a helical path

Answer 1

The correct option is C

The electron will continue to move with uniform velocity along the axis of the solenoid

Explanation for correct option:

In case of option C:

1. An electron $\left(e\right)$ is projected with uniform velocity $\left(v\right)$ along the axis of a current-carrying long solenoid.
2. The force $\left(F\right)$ acting on a charge $\left(q\right)$ moving with a velocity $\left(v\right)$ in a magnetic field $\left(B\right)$ is given by $F=q\left(v\times B\right)=qvB\sin \theta$, where $\theta$ is the angle between the direction of velocity an magnetic field. Assume $e$ to be the charge of the electron.
3. The electron is moving in along the direction of axis and the magnetic field is always along the direction of axis. Thus, the velocity of electron and magnetic field is parallel to each other. Therefore, the angle between them is $\theta =0$.
4. Substitute the values in the formula

$\begin{array}{rcl}F& =& qvB\sin \theta \\ & =& evB\sin 0\\ & =& evB\times 0\\ & =& 0\end{array}$

Since the force acting on the electron is $0$, according to Newton's first law of motion, the electron will continue to move in the same direction with uniform velocity.

In case of option A:

1. For any body to move in a circular path centripetal force is required.
2. The electron will not move in a circular path because a force will be required for it.
3. Thus, this option is incorrect.

In case of option B:

1. For any body to be accelerated, its velocity must change and for that an external for is required.
2. Therefore, the electron will not be accelerated.
3. Thus, this option is incorrect.

In case of option D:

1. It has already been proved above that the electron will experience no force. therefore its path will also not change.
2. Thus, this option is incorrect.

Hence, option C is correct.