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. \(r \gg a\).

Hint:

Electric field due to a dipole: On axial line: \[ E_{\text{axial}} = \frac{1}{4\pi\varepsilon_0} \frac{2p}{r^3} \] On equatorial line: \[ E_{\text{equatorial}} = \frac{1}{4\pi\varepsilon_0} \frac{p}{r^3} \] The equatorial field is opposite to the direction of the dipole moment.

Answer 1