c
The applied magnetic field provides the required centripetal force to the charge particle, so it can move in circular path of radius $\frac{d}{2}$
$\therefore \mathrm{Bqv}=\frac{\mathrm{mv}^{2}}{\mathrm{d} / 2}$
or, $B = \frac{{2{\text{mv}}}}{{{\text{qd}}}}$
Time interval for which a uniform magnetic field is applied
$\Delta t=\frac{\pi \cdot \frac{d}{2}}{v}$
(particle reverses its direction after time $\Delta t$ by covering semi circle).
$\Delta \mathrm{t}=\frac{\pi \mathrm{d}}{2 \mathrm{v}}$