The field of an electric dipole :
The electric field of the pair of charges (–q and q) at any point in space can be found out from Coulomb’s law and the superposition principle.
The results are simple for the following two cases :
1. when the point is on the dipole axis, and
2. when it is in the equatorial plane of the dipole, i.e., on a plane perpendicular to the dipole axis through its centre.
The electric field at any general point P is obtained by adding the electric fields E1 due to the charge q and E2 due to the charge -q, by the parallelogram law of vectors.
1. For points on the axis :
AB is an electric dipole of two point charges –q and +q separated by a small distance 2d (Fig). P is a point along the axial line of the dipole at a distance r from the midpoint O of the electric dipole.
The electric field at the point P due to +q placed at B is,
E1= q / [4πεo (r-d)^2 ] (along BP)
The electric field at the point P due to –q placed at A is,
E2= q / [4πεo (r+d)^2 ] (along PA)
E1 and E2 act in opposite directions.
Therefore, the magnitude of resultant electric field (E) acts in the direction of the vector with a greater magnitude. The resultant electric field at P is,
E = E1 + (-E2)
E = { q / [4πεo (r-d)^2 ] - q / [4πεo (r+d)^2 ] } (along BP)
E = q/4πεo (1/ [ (r-d)^2 ] - 1/ [ (r+d)^2 ] ) (along BP)
E = q/4πεo[4 rd / (r^2-d^2)^2] (along BP)
If the point P is far away from the dipole, then d <<r
