A positive charge $\text{'}\mathrm{q}\text{'} \mathrm{of} \mathrm{mass} \text{'}\mathrm{m}\text{'}$ is moving along the +x axis with velocity v. We wish to apply a uniform magnetic field B for time $∆\mathrm{t}$ so that the charge reverses its direction crossing the y axis at a distance d. Then:

Given data: positive charge$\text{ 'q' }, mass\text{ 'm' }, magnetic field B and time \Delta t$

Concept used: moving charges and magnetism

Detailed solution:

Force needed to be applied while changing the direction of charge.

$\mathrm{qvB}=\frac{{\mathrm{mv}}^2}{\mathrm{r}}\text{ where }\mathrm{r}=\mathrm{d}/2$

Thereby,$\mathrm{B}=\frac{2\mathrm{mv}}{\mathrm{qd}}$

Total displacement is d when charge travels for time $∆t$

Therefore $∆t=\frac{\pi d}{2v}$