Let an electric dipole consist of two charges -q and +q separated by a distance 2a as shown in the figure. Let us find electric potential at point P, at a distance r from the mid-point of the dipole.
The electric potential of OP due to the dipole is given by
For a short dipole: r >> a, so r2 - a2 ≃ r2
So V = \(\frac{1}{4\piɛ_o} \frac{p}{r^2}\).