Question

A conductor of mass $m$ and length $l$ is placed horizontally perpendicular to a uniform horizontal magnetic field $B$. Suddenly a certain amount of charge is passed through it, so that it jumped to height $h$. The amount of charge that passes through the conductor is

Answer 1

Magnetic force on the conductor
$F=ilB$
as we know
$F=ma$
$ilB=ma$
$ilB=m\frac{dv}{dt}\{\because a=\frac{dv}{dt}\}$

$idtlB=mdv\{\because I=\frac{Q}{t}\}$
$QlB=mv$
velocity at height $h,$
$v=\sqrt{2gh}$
$Q=\frac{m\sqrt{2gh}}{lB}$