Let us calculate the electric potential at any point P due to an electric dipole, consisting of two charges -q and +q at A and B respectively separated from each other by a distance 2a from each other. Let 'r' be the distance of the point P from the center O of the dipole and r1 and r2 be the distances of P from the centers of charges +q and -q respectively.
....(i)
In ∆OBP,
r1 = BP = MP = OP - OM
= r - a cos θ
In ∆ANP,
r2 = PN = NO + OP = OP + NO
= r + a cos θ
So Eq. (i) becomes
(ii) At equatorial line,
θ = 90°
V = \(\frac{pcos90^\circ}{r^2}\) = 0