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 will continue to move with uniform velocity along the axis of the solenoid.
• B. The electron will be accelerated along the axis.
• C. The electron will experience a force at 45 to the axis and hence execute a helical path.
• D. The electron path will be circular about the axis.

Answer 1

The correct option is A

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

Explanation for the correct option:

1. When an electron ($e$) is projected with a uniform velocity ($v$) in a uniform magnetic field ($B$), the magnitude of force ($F$) on the electron is given by the formula, $\left|\overrightarrow{F}\right|=-e\left|\overrightarrow{v}·\overrightarrow{B}\right|=-evB\sin \theta$, where $\theta$ is the angle between the velocity vector of the electron and the magnetic field vector.
2. Thus, when $\theta =0$, the magnitude of the force on the electron will be $0$, and thus it will continue to move with uniform velocity along the axis of the solenoid.

Hence, option A is correct.