Derive an expression for electric field intensity due to an electric dipole at a point on its axial line.
Electric field due to dipole on axial line
Explanation
Electric field due to +q charge
E1=14πε0q(r−d)2 along BP
Electric field due to -q charge
E2=14πε0q(r+d)2 along PA
E=E1+(−E2) or E=E1−E2
E=q4πε0[1(r−d)2−1(r+d)2]
E=q4πε0[4rd(r2−d2)2] along BP
p=q2d
When r>>d, d2 can be neglected.
E=14πε02Pr3
E acts in the direction of dipole moment.