Question

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 :

• A. $\frac{R}{\sqrt{5}}$
• B. $R$
• C. $\frac{R}{\sqrt{2}}$
• D. $R \sqrt{2}$

Answer 1

Answer: (C)

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

Answer 2

Electric field on axis of ring
$E = \frac{kQh}{\left(h^{2}+R^{2}\right)^{3/2}}$
for maximum electric field
$\frac{dE}{dh} = 0$
$\Rightarrow h = \frac{R}{\sqrt{2}}$