Question

Derive an expression for electric field due to an electric dipole (a) at a point on its axial line (b) at a point along the equatorial line.

Answer 1

Electric field on axial line of the electric dipole at the point of distance r from the centre of the electric dipole is given by $\mathbb{E}=\mathbf{\frac{1}{4\pi\epsilon_0}\frac{2pr}{(r^2-a^2)^2}}$
The direction of the electric field at a point on the axial line of a dipole is along the dipole moment.

Electric field on equatorial line of the electric dipole at the point of distance r from the centre of the electric dipole is given by $\mathbb{E}=\mathbf{\frac{1}{4\pi\epsilon_0}\frac{p}{(r^2+a^2)^{3/2}}}$

See attachment for derivation and sorry for bad handwriting :D.

Answer 2

Explanation:

see the above explanation. hope that it is very useful for you ...