Consider a composite material made up of two species, having number densities N1 and N2 molecules/m3, respectively. The two materials are uniformly mixed, yielding a total number density of N = N1 + N2. The presence of an electric field E induces molecular dipole moments p1 and p2 within the individual species, whether mixed or not. Show that the dielectric constant of the composite material is given by ϵr = f ϵr1 + (1 − f )ϵr 2, where f is the number fraction of species 1 dipoles in the composite, and where ϵr1and ϵr 2 are the dielectric constants that the unmixed species would have if each had number density N.
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