Terminology
The relative permittivity of a material for a frequency of zero is known as its static relative permittivity or as its dielectric constant. Other terms used for the zero frequency relative permittivity include relative dielectric constant and static dielectric constant. While they remain very common, these terms are ambiguous and have been deprecated by some standards organizations. The reason for the potential ambiguity is twofold. First, some older authors used "dielectric constant" or "absolute dielectric constant" for the absolute permittivity ε rather than the relative permittivity. Second, while in most modern usage "dielectric constant" refers to a relative permittivity, it may be either the static or the frequency-dependent relative permittivity, depending on context.
Relative permittivity is typically denoted as εr(ω) (sometimes κ or K) and is defined as
where ε(ω) is the complex frequency-dependent absolute permittivity of the material, and ε0 is the vacuum permittivity.
Relative permittivity is a dimensionless number that is in general complex. The imaginary portion of the permittivity corresponds to a phase shift of the polarization P relative to E and leads to the attenuation of electromagnetic waves passing through the medium. By definition, the linear relative permittivity of vacuum is equal to 1, that is ε = ε0, although there are theoretical nonlinear quantum effects in vacuum that exist at high field strengths.
The relative permittivity of a medium is related to its electric susceptibility, χe, as εr(ω) = 1 + χe.
In anisotropic media (such as non cubic crystals) the relative permittivity is a second rank tensor.
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