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

The Correct Option is B

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.