(a) For points on the axis
Let the point P be at distance r from the centre of the dipole on the side of the charge q, as shown in Fig. (a).
The dipole moment vector p of an electric dipole is defined by
that is, it is a vector whose magnitude is charge q times the separation 2a (between the pair of charges q, –q) and the direction is along the line from –q to q.
At a point on the dipole axis
(b) For points on the equatorial plane
The magnitudes of the electric fields due to the two charges +q and –q are given by
and are equal. The directions of E+q and E–q are as shown in Fig. (b). The components normal to the dipole axis cancel away. The components along the dipole axis add up. The total electric field is opposite to ˆp . We have
it is clear that the dipole field at large distances does not involve q and a separately; it depends on the product qa. This suggests the definition of dipole moment. The dipole moment vector p of an electric dipole is defined by p = q × 2a ˆp that is, it is a vector whose magnitude is charge q times the separation 2a (between the pair of charges q, –q) and the direction is along the line from –q to q. At a point on the equatorial plane
