Effect of an External Field on a Polar Molecule

Those molecules for which the centres of gravity of positive and negative charges do not coincide are called polar molecules. Polar molecules have built-in, permanent dipole moments. Examples of polar molecules are HCI, NH₃, CO, H₂0, CH₃OH etc.

In the water molecule, the electrons tend to cluster around the oxygen atom. Since the molecule is bent at 105^o, this leaves a negative charge at the opposite end. The dipole moment of water is unusually large 6.1x 10^-30 Cm.

(i)    Uniform Electric Field

When a polar molecule is placed in a uniform electric filed, the force on the positive end, F+ = qE, exactly cancels the force on the negative end, F = -qE.
The positive charge e2xperiences a force F+ in the direction of the field and the negative charge experiences a force F in the opposite direction of the field. These two forces constitute of torque. The torque is given by

            N = (r x F) + (r x F)
            = [(s/2) x (qE)] + [(-s/2) x (-qE) = qs x E = p x E

Here, we are assuming centre of the dipole as the origin of the coordinates. Thus a dipole p in a uniform field E experiences a torque
            N = p x E

N is in such a direction as to line p up parallel to E. A polar molecule that is free to rotate will swing around until it points in the direction of the applied field.

The net force acting on the dipole in a uniform electric field, F does not exactly balance F. Hence there is a net force on the dipole, in addition to the torque. Let us derive an expression for the net translator force on the dipole.

Let dE be the difference between the field at the plus end and the field at the minus end. Then the formula for the force on a dipole in a non-uniform field is
            F = F+ + F- = q(E+ = E-) = q(dE)
Assuming the dipole is very short, the small change in Ex may be expressed as

            dEx = (∇E_x).s
Similarly        dE_y = (∇E_y).s
            dE_z = (∇E_z).s
            dE = (s.∇)E
            F = (p.∇)E
Here,            p.∇ = px ∂/∂x + py ∂/∂y + pz + ∂/∂z