A current carrying solenoid is placed vertically and a particle of mass m with charge Q is released from rest. The particle moves along the axis of solenoid. If g is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

Solution

Physics sir · 4 steps

Inside a solenoid the field runs along the axis, so a charge moving along the axis feels no magnetic force.

1. Field direction. Inside a long current-carrying solenoid the magnetic field B⃗ is uniform and points along the axis. With the solenoid vertical, B⃗ is vertical.
2. Velocity direction. The particle starts from rest and gravity pulls it straight down the axis. So its velocity v⃗ is vertical too, parallel or antiparallel to B⃗.

   |F⃗| = |Q v⃗ × B⃗| = QvB sin θ = QvB sin 0° = 0

3. Only gravity acts. With zero magnetic force, the only force on the particle is its weight mg. Since there is no sideways force, the velocity stays along the axis the whole way down.
4. So. a = mg/m = g, which is option (d).

The idea to keep. The magnetic force Qv⃗ × B⃗ vanishes whenever the velocity is along the field. Always check the angle between v⃗ and B⃗ before adding a magnetic force.

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