A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is relea

Question

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 :

Professor PC Thomas Classes · Answer

The magnetic field inside the solenoid is along its vertical axis. When the charged particle is released, it moves downwards along the axis due to gravity. Thus, its velocity vector is parallel to the magnetic field. The magnetic force on the particle is $F_m = Q(\vec{v} 	imes \vec{B}) = QvB\sin(0^\circ) = 0$. Since the only force acting on the particle is gravity, its acceleration is exactly equal to $g$.