What is meant by an electric dipole? Derive an expression for electric field intensity due to an electric dipole in axial position at a point.

The dipole moment definition is given as the product of the magnitude of charges and the separation between them. The dipole moment determines the strength of an electric dipole to produce the electric field. It is denoted by P, and it is a vector quantity. Electric field due to an electric dipole at a point on its axial line: AB is an electric dipole of two point charges −q and +q separated by small distance 2d. 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 E 1 = 1 4 πε 0 r - d 2 along BP The electric field at the point P due to −q placed at A is, E 2 = 1 4 πε 0 r - d 2 along PA 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 = E 1 - - E 2 E = 1 × q 4 πε 0 r - d 2 - 1 × q 4 πε 0 r + d 2 along BP E = q 4 πε 0 1 r - d 2 - 1 r + d 2 along BP E = q 4 πε 0 4 rd r 2 - d 2 2 along BP If the point P is far away from the dipole, then d ≪ r ∴ E = q 4 πε 0 - 4 rd r 4 = q 4 πε 0 × 4 d r 3 E = 1 4 πε 0 2 p r 3 along BP ∵ Electric dipole moment p = q × 2 d E acts in the direction of dipole moment.