Answer
$m=\frac{qB^2R^2}{2V}$
Work Step by Step
In the given scenario, potential energy is equal to the kinetic energy:
$qV=\frac{1}{2}mv^2$......eq(1)
We also know that magnetic force produces centripetal force i.e
$qvB=\frac{mv^2}{R}$
This simplifies to
$v=\frac{qBR}{m}$
Substituting this value of $v$ in equation(1), we obtain:
$qV=\frac{1}{2}m(\frac{qBR}{m})^2$
$qV=\frac{q^2B^2R^2}{2m}$
This simplifies to
$m=\frac{qB^2R^2}{2V}$
