Clausius-Mossoti formula

For rarefied dielectrics, eq. (4.2.11) connecting the macroscopic characteristic k with the microscopic one a, which in tnrn provides access to the analysis of the molecule properties, was given. In more complex cases of the more condensed matter at no. noticeably larger than unity, the given simple ratio is not fair. In order to find the proper ratio in more dense substances we should substitute in the expression (4.2.10) the local field E by eq. (4.2.24)  

This is one of the forms of the Clausius-Mossoti law. It connects the macroscopic value of the susceptibility e with polarizability a of molecules. 

One can express a molecule concentration n in eq. (4.2.26) via the Avogadro constants and a molar volume MIp n = NJ(M/p) = Then the Clausius-Mossoti 

The Debye-Langevin formula is applicable to polar dielectrics at definite restrictions. It achieves good fulfillment for gases and vapors at low pressure, and for highly dissolved solutions of polar liquids in nonpolar solvents. This formula is of great importance in the interpretation of molecular structures. 

As was already mentioned in Section 4.2.5, the polarizability of molecules depends on the frequency of the alternative electric field, especially at high frequencies. In the Maxwell electromagnetic theory, the ratio between a refraction index n and the dielectric permeability s of substances is given. For low-magnetic substances, n = Ve. If in eq. (4.2.27) we substitute s by and take into account that at optical frequencies 

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