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 r = f∈_r1 + (1 − f)∈_r2, where f is the number fraction of species 1 dipoles in the composite, and where ∈_r1 and ∈_r2 are the dielectric constants that the unmixed species would have if each had number density N.