Consider a circular loop that is uniformly charged and has a radius...

Consider a circular loop that is uniformly charged and has a radius

\mathrm{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 :

Options

A $\frac{a}{\sqrt{2}}$
B $\frac{a}{2}$
Ca
D0

Correct answer

C. a

Step-by-step solution

\begin{aligned} & \mathrm{E}=\frac{\mathrm{KQr}}{\left(\mathrm{x}^2+\mathrm{R}^2\right)^{3 / 2}} \\ & \frac{\mathrm{dE}}{\mathrm{dx}}=0 \\ & \therefore \mathrm{x}=\frac{\mathrm{R}}{\sqrt{2}}=\frac{\sqrt{2} \mathrm{a}}{\sqrt{2}}=\mathrm{a}\end{aligned}

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