Question

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

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

Answer 1

Answer: (B)

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

Answer 2

Magnetic Force on a Moving Charge:
When a charged particle, such as an electron, moves in a magnetic field, it experiences a force given by:
$\vec{F} = q (\vec{v} \times \vec{B})$
where $\vec{v}$ is the velocity of the particle and $\vec{B}$ is the magnetic field.
The direction of the force is perpendicular to both $\vec{v}$ and $\vec{B}$.

Magnetic Field Inside a Solenoid:
Inside a long solenoid carrying current, the magnetic field $\vec{B}$ is uniform and directed along the axis of the solenoid.
Since the electron is moving along the axis, its velocity $\vec{v}$ is also parallel to $\vec{B}$.

No Magnetic Force Due to Parallel $\vec{v}$ and $\vec{B}$:
Since $\vec{v} \parallel \vec{B}$, the cross product $\vec{v} \times \vec{B} = 0$.

Therefore, the magnetic force $\vec{F} = 0$, and the electron will not experience any force due to the magnetic field.

Conclusion:
The electron will continue to move with uniform velocity along the axis of the solenoid, as there is no force acting on it to change its state of motion.