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10.13 Electric Dipole
The arrangement of a pair of equal and opposite charges separated by some distance is called an electric dipole. Any molecule in which the centres of the positive and negative charges do not coincide may, to a first approximation, be treated as a dipole. Molecules such as HCl, CO and H2O have permanent dipoles and are called polar molecules. An electric field may also induce a charge separation in an atom or a nonpolar molecule. Figure (a) shows an atom as a positive point charge surrounded by a sphere of equal negative charge. When an external electric field is applied, these charges are displaced in opposite directions, as shown in Figure (b), thereby creating an induced dipole. Such an induced dipole vanishes when the external field is removed.
The characteristic of a dipole is its dipole moment (p). It is defined as the product of one of the charges and their separation.
p = qd
It is a vector quantity that points from the negative to the positive charges. The SI unit for the electric dipole moment is C m.
10.13.1 Electric field intensity due to Dipole
(i) Along the axis
E|| = 
The direction of electric field along the axis is in the same direction as that of the dipole moment.
(ii) Along the bisector
E^= 
The direction of electric field along the bisector is opposite to that of the dipole moment
10.13.2 Electric Potential Due to a Dipole
(i) Along the axis
V|| = 
(ii) Along the bisector
V^ = 0
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