Derive an expression for the electric field E due to a dipole of length 2a at a point distant r from the centre of the dipole on the axial line.

Electric field at point P at a distance r from centre of dipole due to +q
EB=14πϵ0qBP2along BP =14πϵ0q(r−a)2
Electric field at point P due to -q is
EA=14πϵ0qAP2along PA =14πϵ0q(r+a)2
Net field at P is given by
EP=EB−EA=14πϵ0(q(r−a)2−q(r+a)2)=q4πϵ04ar(r2−a2)2=14πϵ02pr(r2−a2)2along BP .Where p is the dipole=2qa