On the Clausius-Mossotti-Lorenz-Lorentz formula

The usual way to describe the electromagnetic field in a material is to employ the macroscopic Maxwell equations together with constitutive relations and boundary conditions. The most popular form of all these relations is to introduce the permittivity and permeability. Though the problem of permittivity averaging in composites has a long history, there are still unclear aspects. One aspect concerns the local field E/sub local/ which acts on a separate inclusion. The most widespread approximation for E/sub local/ is the Clausius-Mossotti-Lorenz-Lorentz (CMLL) formula: E/sub local/=+4/spl pi/P/3 where P is the mean polarization of the material. The well-known Lorentz derivation of the CMLL formula leads to many questions. Even popular text books contain omissions and inaccurate speculations. The rigorous description of the problem is dispersed over several original articles. Here we summarise the results, critically reviewing different approaches.