Consider a circular loop that is uniformly charged and has a radius . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin:

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Solution

Q.
Consider a circular loop that is uniformly charged and has a radius $a \sqrt{2}$ . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin: [2025]

1 $\frac{a}{\sqrt{2}}$

2 $\frac{a}{2}$

3 a

4 0

Ans.
(3)

$E = K \frac{Q r}{{(x^{2} + R^{2})}^{3 / 2}}$

For $E_{\max}, \frac{d E}{d x} = 0$

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

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