## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## Relative permittiv

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:

$varepsilon = varepsilon_r varepsilon_0 = (1+chi)varepsilon_0$

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

${mathbf P}=varepsilon_0chi{mathbf E},$

where $, varepsilon_0$ is the electric permittivity of free space.

The susceptibility of a medium is related to its relative permittivity $, varepsilon_r$ by

$chi = varepsilon_r - 1.$

So in the case of a vacuum,

$chi = 0.$

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

$mathbf{D} = varepsilon_0mathbf{E} + mathbf{P} = varepsilon_0 (1+chi) mathbf{E} = varepsilon_r varepsilon_0 mathbf{E}.$

The permittivity ε and permeability µ of a medium together determine the phase velocity v = c/n of electromagnetic radiation through that medium:

$varepsilon mu = frac{1}{v^2}.$

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