For uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance $\text{'}h\text{'}$  from its centre. The value of  $h$ is

Electric field on axis of ring

                                 $E=\frac{KQx}{{\left(x^2+R^2\right)}^{3/2}}$

For maximum electric field$\frac{dE}{dx}=0$

$\Rightarrow \left(1\right) {(x^2+R^2)}^{-3/2} + \left(x\right) {\left(\frac{-3}{2}\right)(x^2+R^2)}^{-5/2} \left(2x\right) = 0$

By solving we get 

$x=\frac{R}{\sqrt{2}}$