A conducting rod of mass $m$ and length $\ell$ is placed over a smooth table. A uniform magnetic field is acting perpendicular to the rod. Charge $q$ is suddenly passed through the rod and it acquires a velocity $v$ on the surface, then $q$ is equal to

Question

$\begin {array} {1 1} (a)\;\large\frac{2mv}{B\ell} & \quad (b)\;\large\frac{mv}{B\ell} \\ (c)\;\large\frac{B\ell}{mv} & \quad (d)\;\large\frac{B\ell}{2mv} \end {array}$