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Question
Consider a uniformly charged ring of radius R. Find the point on the axis where the electric field is maximum.
Solution
Let the total charge of the ring be Q.
Radius of the ring = R
The electric field at distance x from the centre of ring,
\[E = \frac{Qx}{4\pi \epsilon_0 \left( R^2 + x^2 \right)^{3/2}} . . . (1)\]
For maximum value of electric field,
\[\frac{dE}{dx} = 0\]
From equation (1),
\[\Rightarrow R^2 + x^2 - 3 x^2 = 0\]
\[ \Rightarrow 3 x^2 = R^2 \]
\[ \Rightarrow x = \frac{R}{\sqrt{2}}\]
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