Editing Displacement current (section)

===Isotropic dielectric case===
In the case of a very simple dielectric material the [[constitutive relation]] holds:

<math display=block> \mathbf{D} = \varepsilon \, \mathbf{E} ~ , </math>

where the [[permittivity]] {{nowrap|<math>\varepsilon = \varepsilon_0 \,  \varepsilon_\mathrm{r}</math>}} is the product of:
* {{math|''ε''<sub>0</sub>}}, the ''[[permittivity of free space]]'', or the ''[[electric constant]]''; and
* {{math|''ε''<sub>r</sub>}}, the [[relative permittivity|''relative'' permittivity]] of the dielectric.

In the equation above, the use of  {{mvar|ε}}  accounts for
the polarization (if any) of the dielectric material.

The [[scalar (physics)|scalar]] value of displacement current may also be expressed in terms of [[electric flux]]:

<math display=block> I_\mathrm{D} = \varepsilon \, \frac{\, \partial \Phi_\mathrm{E}  \, }{\partial t} ~ .</math>

The forms in terms of [[scalar (physics)|scalar]]  {{mvar|ε}}  are correct only for linear [[isotropic]] materials. For linear non-isotropic materials, {{mvar|ε}}  becomes a [[matrix (mathematics)|matrix]]; even more generally,  {{mvar|ε}}  may be replaced by a [[tensor]], which may depend upon the electric field itself, or may exhibit frequency dependence (hence [[Dispersion (optics)|dispersion]]).

For a linear isotropic dielectric, the polarization {{math|'''P'''}} is given by:

<math display=block>\mathbf{P} = \varepsilon_0 \chi_\mathrm{e}  \, \mathbf{E} = \varepsilon_0 (\varepsilon_\mathrm{r} - 1) \, \mathbf{E} ~,</math>

where  {{math|''χ''<sub>e</sub>}} is known as the [[electric susceptibility|''susceptibility'']] of the dielectric to electric fields. Note that

<math display=block>\varepsilon = \varepsilon_\mathrm{r} \, \varepsilon_0 = \left( 1 + \chi_\mathrm{e} \right) \, \varepsilon_0 ~. </math>