Calculate the electric potential on the axis of a ring of radius $R$ due to a charge $Q$ uniformly distributed along it.

(N/A) Suppose a charge $+Q$ is uniformly distributed on a ring of radius $R=a$.
Let us consider a point $P$ at a distance $x$ from the center of the ring along its axis.
The distance $r$ from any small charge element $dq$ on the ring to point $P$ is given by:
$r = \sqrt{x^{2} + a^{2}}$
The electric potential $dV$ at point $P$ due to the charge element $dq$ is:
$dV = \frac{k dq}{r} = \frac{k dq}{\sqrt{x^{2} + a^{2}}}$
To find the total potential $V$ at point $P$ due to the entire ring,we integrate over the whole charge $Q$:
$V = \int dV = \int \frac{k dq}{\sqrt{x^{2} + a^{2}}}$
Since $k$,$x$,and $a$ are constants for all points on the ring:
$V = \frac{k}{\sqrt{x^{2} + a^{2}}} \int dq$
Since $\int dq = Q$ and $k = \frac{1}{4 \pi \epsilon_{0}}$,we get:
$V = \frac{Q}{4 \pi \epsilon_{0} \sqrt{x^{2} + a^{2}}}$