Editing Permittivity (section)

== Relative permittivity ==
{{main|Relative permittivity}}

The linear permittivity of a homogeneous material is usually given relative to that of free space, as a relative permittivity {{mvar|ε}}{{sub|r}} (also called [[dielectric constant]], although this term is deprecated and 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 {{mvar|ε}}{{sub|o}}:

<math display="block">\ \varepsilon = \varepsilon_\mathrm{r}\ \varepsilon_0 = (1 + \chi)\ \varepsilon_0\ ,</math>

where {{mvar|χ}} (frequently written {{mvar|χ}}{{sub|e}}) 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]] {{math|'''E'''}} to the induced [[dielectric]] [[polarization (electrostatics)|polarization density]] {{math|'''P'''}} such that

<math display="block">\ \mathbf{P}\ =\ \varepsilon_0\ \chi\ \mathbf{E}\; ,</math>

where {{mvar|ε}}{{sub|o}} is the [[Vacuum permittivity|electric permittivity of free space]].

The susceptibility of a medium is related to its relative permittivity {{mvar|ε}}{{sub|r}} by

<math display="block">\chi = \varepsilon_\mathrm{r} - 1 ~.</math>

So in the case of a vacuum,

<math display="block">\chi =  0 ~.</math>

The susceptibility is also related to the [[polarizability]] of individual particles in the medium by the [[Clausius-Mossotti relation]].

The [[electric displacement]] {{math|'''D'''}} is related to the polarization density {{math|'''P'''}} by

<math display="block">\mathbf{D} = \varepsilon_0\ \mathbf{E} + \mathbf{P} = \varepsilon_0\ (1+\chi)\ \mathbf{E} = \varepsilon_\mathrm{r}\ \varepsilon_0\ \mathbf{E} ~.</math>

The permittivity {{mvar|ε}} and [[permeability (electromagnetism)|permeability]] {{mvar|µ}} of a medium together determine the [[phase velocity]] {{math|''v'' {{=}} {{sfrac|''c''|''n''}}}} of [[electromagnetic radiation]] through that medium:

<math display="block">\varepsilon \mu = \frac{ 1 }{\ v^2 } ~.</math>