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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.
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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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