Question

A charge $Q$ is uniformly on a ring of radius $R.$ Find the electric potential on the axis of ring at distance $x$ from the centre of the ring :

• A. $\frac{1}{4 \pi \left(\epsilon \right)_{0}}\frac{Q}{\left(R^{2} + x^{2}\right)^{1 / 2}}$
• B. $\frac{1}{4 \pi \left(\epsilon \right)_{0}}\frac{2 Q}{\left(R^{2} + x^{2}\right)}$
• C. $\frac{1}{2 \pi \left(\epsilon \right)_{0}}\frac{Q}{\left(R^{2} + x^{2}\right)^{1 / 2}}$
• D. $\frac{1}{4 \pi \left(\epsilon \right)_{0}}\frac{Q}{\left(R^{2} + x^{2}\right)}$

Answer 1

Answer: (A)

Small potential at $P$ due to $dq$
$dV=\frac{1}{4 \pi ϵ_{0}}\cdot \frac{d q}{\sqrt{R^{2} + x^{2}}}$
$V_{P}=\Sigma dV=\frac{1}{4 \pi ϵ_{0}}\cdot \frac{\Sigma d q}{\sqrt{R^{2} + x^{2}}}$
$=\frac{1}{4 \pi ϵ_{0}}\cdot \frac{Q}{\sqrt{R^{2} + x^{2}}}$