Relaxation time point dipoles, electric polarization

It is of interest to compare these results with those for the field dependencies of the relaxation times and for T for the longitudinal and for the transverse polarization components of a polar fluid in a constant electric field Eq. As shown in [52, 55] the relaxation times and T are also given by Eqs. (5.55) and (5.56), where = nEJkT, p. is the dipole moment of a polar molecule and is the Debye rotational diffusion time with = 0. Thus, Eqs. (5.55) and (5.56) predict the same field dependencies of the relaxation times Tj and T for both a ferrofluid and a polar fluid. This is not unexpected because from a physical point of view the behavior of a suspension of fine ferromagnetic particles in a constant magnetic field Hg is similar to that of a system of electric dipoles (polar molecules) in a constant electric field Eg. 

Let us consider first a single dipole in an electric field. Given time, the dipole will line up with its axis parallel to the field (Figure 3.57c). Ifnow the field is reversed, the dipole will turn 180° to again lie parallel to the field, but it will take a finite time so if the frequency of the field reversal increases, a point will be reached when the dipole cannot keep up with the field, and the alteration of the dipole direction lags behind that of the field. For an assembly of dipoles in a dielectric, this condition results in an apparent reduction in the dielectric constant of the material. As the frequency of the field continues to increase, at some stage the dipoles will barely have started to move before the field reverses. Beyond this frequency, called the relaxation frequency, the dipoles make virtually no contribution to the polarization of the dielectric. 

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