For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is :

Electric filed on the axis of a ring of radius R at a distance h from the centre, $\mathrm{E}=\frac{\mathrm{kQh}}{{\left({\mathrm{h}}^2+{\mathrm{R}}^2\right)}^{3/2}}$Condition; for maximum electric field $\frac{\mathrm{dE}}{\mathrm{dh}}=0$
$\Rightarrow \frac{\mathrm{d}}{\mathrm{dh}}\left[\frac{\mathrm{kQh}}{{\left({\mathrm{R}}^2+{\mathrm{h}}^2\right)}^{3/2}}\right]=0$  By using the concept of maxima and minima we get, $\mathrm{h}=\frac{\mathrm{R}}{\sqrt{2}}$