An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.
A. The electron will experience magnetic force along the axis of the solenoid.
B. The electron will not experience magnetic force.
C. The electron will continue to move along the axis of the solenoid.
D. The electron will be accelerated along the axis of the solenoid.
E. The electron will follow parabolic path-inside the solenoid.
Choose the correct answer from the options given below:

Solution

Physics sir · 3 steps

Along the axis, velocity and field point the same way, so the cross product is zero and nothing pushes it.

1. Field on the axis. Inside a long straight solenoid the magnetic field is uniform and points along the axis. So an electron moving along the axis has v⃗ parallel or antiparallel to B⃗.

   F⃗ = q(v⃗ × B⃗), |F⃗| = qvB sin θ = 0 for θ = 0° or 180°

2. No force. With zero force there is no acceleration. The speed and the direction both stay the same, so the electron keeps moving in a straight line along the axis.

   Statement	True or false	Reason
   A: force along the axis	False	Magnetic force is always perpendicular to v⃗, and here it is zero anyway
   B: no magnetic force	True	sin 0° = 0
   C: keeps moving along the axis	True	No force, so velocity is unchanged
   D: accelerated along the axis	False	Zero force means zero acceleration
   E: parabolic path	False	A parabola needs a constant force, and there is none

3. So. Only B and C are correct, which is option (b).

The idea to keep. A magnetic field can only push a charge sideways to its motion. A charge moving parallel to B⃗ feels no force and coasts straight on.

Answer from the NTA final answer key. Solution by PrepWiser.