Dielectric - Electric Susceptibility

The electric susceptibility χ_e of a dielectric material is a measure of how easily it polarizes in response to an electric field. This, in turn, determines the electric permittivity of the material and thus influences many other phenomena in that medium, from the capacitance of capacitors to the speed of light.

It 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

${\mathbf P}=\varepsilon_0\chi_e{\mathbf E},$

where is the electric permittivity of free space.

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

So in the case of a vacuum,

The electric displacement D is related to the polarization density P by

$\mathbf{D} \ = \ \varepsilon_0\mathbf{E} + \mathbf{P} \ = \ \varepsilon_0 (1+\chi_e) \mathbf{E} \ = \ \varepsilon_r \varepsilon_0 \mathbf{E}.$

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