Let the particle projected at the point $O$, undergo deflection due to the applied magnetic field $\overrightarrow{B}$ in a direction normally inwards and let it just miss hitting the wall at $A$.

Then, $\mathrm{r}=\frac{\mathrm{mv}}{\mathrm{qB}}$

For the particle not to hit the wall i.e. to just miss hitting the wall,

$r=d \Rightarrow \frac{m v}{q B}=d$

$\Rightarrow \mathrm{B}=\frac{\mathrm{mv}}{\mathrm{qd}}=\frac{\mathrm{v}}{\alpha \mathrm{d}}$