Find an expression for electric field at any position on the axial line of an electric dipole.

Did: axial line of an electric dipole

Let us consider a dipole having charges  +q & -q and separation 2a let P be a point at a distance r from the centre of the dipole O. Electric field at P due to charge + Q is

E₁=1/4π∈₀   q/(r-a)²   along AP

Due to charge -q is

E₂=1/4π∈₀   q/(r+a)²   along PB

Hens resultant field

E=E₁+E₂=q/4π∈₀  {1/(r-a)²-1/(r+a)²}

=4aqr/4π∈₀(r²-a²)²

=2P/4π∈₀r³               (r>>a)