Polarization in the Dipolar Solid

The previous treatment assumed that the dipoles were free to rotate, which is true only in liquids and gases. In most dipolar solids, some form of potential barrier must be overcome in order to rotate a dipole. Assume a solid in which dipoles can only point to the right or to the left and let there be a potential barrier / that must be overcome in flipping a dipole back and forth. The rate at which dipoles on the left flip to the right is given by 

In this case, the average polarizability is three times greater than that for a gas or a liquid because the dipoles can only be ei er parallel or antiparaUel. It is interesting to note that the barrier height cancels out and does not appear in the final result. This result assumes that equilibrium has been reached, but does not say how long it takes to come to equilibrium. 

With no field present, the rate of change of the polarization is 

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