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. $\frac{1}{4\pi {\left(ϵ\right)}_0}\frac{Q}{{\left(R^2+x^2\right)}^{1/2}}$
• B. $\frac{1}{4\pi {\left(ϵ\right)}_0}\frac{2Q}{\left(R^2+x^2\right)}$
• C. $\frac{1}{2\pi {\left(ϵ\right)}_0}\frac{Q}{{\left(R^2+x^2\right)}^{1/2}}$
• D. $\frac{1}{4\pi {\left(ϵ\right)}_0}\frac{Q}{\left(R^2+x^2\right)}$

Answer 1

Answer: (A)

Small potential at $P$ due to $dq$
$dV=\frac{1}{4\pi {ϵ}_0}\cdot \frac{dq}{\sqrt{R^2+x^2}}$
$V_P=\Sigma dV=\frac{1}{4\pi {ϵ}_0}\cdot \frac{\Sigma dq}{\sqrt{R^2+x^2}}$
$=\frac{1}{4\pi {ϵ}_0}\cdot \frac{Q}{\sqrt{R^2+x^2}}$