question_answer

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:             [JEE Main 09-Jan-2019 Morning]

A) \[R\sqrt{2}\]

B) R         

C)             \[\frac{R}{\sqrt{5}}\]     

D) \[\frac{R}{\sqrt{2}}\]

Correct Answer: D

Solution :

[d]

\[E\,\,\,\,=\,\,\,\,\frac{kQx}{{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}\]

For \[{{E}_{\max }}\]

\[\frac{dE}{dx}\,\,=\,\,0\]

On solving we get \[x\,\,=\,\,\frac{R}{\sqrt{2}}\]

So, option [d] is correct.