Show mathematically that the potential at a point on the equatorial line of an electric dipole is zero.

Explanation

Consider a point P situated on the equatorial line of the electric dipole at a distance r from mid-point of dipole.
Now electric potential at P is given by
`V = V_A + V_B = (-q)/ (4 pi epsi_0 sqrt(r^2 + a^2)) + q/(4pi epsi_0 sqrt(r^2 + a^2)) = 0` .
hus, potential at any point on equatorial line of an electric -9. dipole is zero irrespective of the position of that point.