Question

An electric dipole consists of two point charges q and −q separated by a distance 2a. Derive an expression for the electric field `vec E` due to this dipole at a point distant r from the centre of the dipole on the equatorial plane. Write the expression for the electric field at a far off point, i.e. r >> a.

Answer 1

Distance of point from each charge (d) = `sqrt(r^2 + a^2)`

Magnitude of field due to one charge (E) = `1/(4 pi epsilon_0) q/d^2`

Resultant field (E_eq) = `1/(4 pi epsilon_0) (2 qa)/((r^2 + a^2)^(3//2))`

Since p = 2qa;

E_eq = `1/(4 pi epsilon_0) p/((r^2 + a^2)^(3//2))`

The direction is opposite to the dipole moment.

For r >> a:

r² + a² ≈ r²

E_eq = `1/(4 pi epsilon_0) p/r^3`