Relative Permittivity
The linear permittivity of a homogeneous material is usually given relative to that of free space, as a relative permittivity εr (also called dielectric constant, although this sometimes only refers to the static, zero-frequency relative permittivity). In an anisotropic material, the relative permittivity may be a tensor, causing birefringence. The actual permittivity is then calculated by multiplying the relative permittivity by ε0:
where
- χ (frequently written χe) is the electric susceptibility of the material.
The susceptibility is defined as the constant of proportionality (which may be a tensor) relating an electric field E to the induced dielectric polarization density P such that
where ε_0 is the electric permittivity of free space.
The susceptibility of a medium is related to its relative permittivity εr by
So in the case of a vacuum,
The susceptibility is also related to the polarizability of individual particles in the medium by the Clausius-Mossotti relation.
The electric displacement D is related to the polarization density P by
The permittivity ε and permeability µ of a medium together determine the phase velocity v = c/n of electromagnetic radiation through that medium:
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