Electric Dipole

System of two charges equal in magnitude but opposite in nature separated by certain distance is called an electric dipole.
Dipole moment is given as
P = qL, directed from -ve charge to +ve charge.

Electric potential due to electric dipole
Let us consider an electric dipole Ab of length L formed by charges +q and -q. Let p be a point at a distance r from centre of dipole where electric potential is to be found.
We know
V = V1+V2
V1 = 1/4πEo(q/PB)
V2 = 1/4πEo(q/AP)

if we consider dipole of very short length we can have AP = PN and PM = PB
also we know
PM = r-l/2cos(theta)
PN = r+l/2cos(theta)
Now
V = q/4πEo(1/r-l/2cos(theta) - 1/r+l/2cos(theta))
V = q/4πEo(lcos(theta)/r^2-l^2/4cos^2(theta))
since l^2/4cos^2(theta <<< r^2 we can have
V = pcos(theta)/4πEor^2