Write an equation of electric potential at a point on the axis of an electric dipole.

(N/A) Consider an electric dipole consisting of two charges $+q$ and $-q$ separated by a distance $2a$. Let $P$ be a point on the axis of the dipole at a distance $r$ from the center $O$ of the dipole.
The distance of point $P$ from the charge $+q$ is $(r - a)$ and from the charge $-q$ is $(r + a)$.
The electric potential $V$ at point $P$ is the algebraic sum of the potentials due to both charges:
$V = V_{+q} + V_{-q}$
$V = \frac{1}{4\pi\epsilon_0} \left( \frac{q}{r-a} - \frac{q}{r+a} \right)$
$V = \frac{q}{4\pi\epsilon_0} \left( \frac{r+a - (r-a)}{r^2 - a^2} \right)$
$V = \frac{q}{4\pi\epsilon_0} \left( \frac{2a}{r^2 - a^2} \right)$
Since the dipole moment $p = q \times 2a$,we can write:
$V = \frac{1}{4\pi\epsilon_0} \frac{p}{r^2 - a^2}$
For a short dipole where $r \gg a$,the equation simplifies to:
$V = \frac{1}{4\pi\epsilon_0} \frac{p}{r^2}$