A current carrying 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 :
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Question

A current carrying 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 :

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G1 Physics · Accepted Answer

The magnetic field inside the vertical solenoid is directed along the solenoid axis. The charged particle is released from rest and then acquires velocity along the same vertical axis because of gravity. Therefore the particle velocity is parallel or antiparallel to the magnetic field. Magnetic force is F⃗₍ʙ₎ = Q(v⃗ × B⃗). Since v⃗ is parallel or antiparallel to B⃗, v⃗ × B⃗ = 0. Hence, F₍ʙ₎ = 0. The only force producing acceleration along the axis is the weight mg. Therefore, ma = mg, so a = g.…