# Relative static permittivity

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The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. Technically, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum. Similarly, it is also the ratio of the capacitance of a capacitor using that material as a dielectric, compared to a similar capacitor which has a vacuum as its dielectric.

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.[5][6] 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.[7] Second, while in most modern usage "dielectric constant" refers to a relative permittivity[6][8], 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 electric constant.

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[8], that is ε = ε0, although there are theoretical nonlinear quantum effects in vacuum that have been predicted at high field strengths (but not yet observed).[9]

The relative permittivity of a medium is related to its electric susceptibility, χe, as εr(ω) = 1 + χe.