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(A) The magnetic field $\vec{B}$ inside a long solenoid is directed along its axis.Since the particle is released from rest and moves along the axis o

Vedclass · Accepted Answer

$a = g$

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(A) The magnetic field $\vec{B}$ inside a long solenoid is directed along its axis.Since the particle is released from rest and moves along the axis of the solenoid, its velocity vector $\vec{v}$ is always parallel or anti-parallel to the magnetic field vector $\vec{B}$.The magnetic force on a moving charge is given by $\vec{F}_{B} = Q(\vec{v} 	imes \vec{B})$.Since $\vec{v}$ is parallel to $\vec{B}$, the cross product $\vec{v} 	imes \vec{B} = 0$, hence $\vec{F}_{B} = 0$.The only force acting on the particle is the gravitational force $\vec{F}_{g} = m\vec{g}$ acting downwards.Therefore, the net force $\vec{F}_{net} = m\vec{g}$.According to Newton's second law, $m\vec{a} = m\vec{g}$, which gives $\vec{a} = \vec{g}$.Thus, the acceleration of the particle is $a = g$.

$A$ 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 the solenoid. If $g$ is the acceleration due to gravity, then the acceleration $(a)$ of the charged particle will satisfy:

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