Editing Gaussian units (section)

=== Dielectric and magnetic materials ===

Below are the expressions for the various fields in a dielectric medium. It is assumed here for simplicity that the medium is homogeneous, linear, isotropic, and nondispersive, so that the [[permittivity]] is a simple constant.

{| class="wikitable"
|+ Expressions for fields in dielectric media
|-
! scope="col" | Gaussian system
! scope="col" | {{abbr|ISQ|International System of Quantities}}
|-
| <math>\mathbf{D}^{_\mathrm{G}} = \mathbf{E}^{_\mathrm{G}}+4\pi\mathbf{P}^{_\mathrm{G}}</math>
| <math>\mathbf{D}^{_\mathrm{I}} = \varepsilon_0 \mathbf{E}^{_\mathrm{I}}+\mathbf{P}^{_\mathrm{I}}</math>
|-
| <math>\mathbf{P}^{_\mathrm{G}} = \chi^{_\mathrm{G}}_\mathrm{e}\mathbf{E}^{_\mathrm{G}}</math>
| <math>\mathbf{P}^{_\mathrm{I}} = \chi^{_\mathrm{I}}_\mathrm{e}\varepsilon_0\mathbf{E}^{_\mathrm{I}}</math>
|-
| <math>\mathbf{D}^{_\mathrm{G}} = \varepsilon^{_\mathrm{G}}\mathbf{E}^{_\mathrm{G}}</math>
| <math>\mathbf{D}^{_\mathrm{I}} = \varepsilon^{_\mathrm{I}}\mathbf{E}^{_\mathrm{I}}</math>
|-
| <math>\varepsilon^{_\mathrm{G}} = 1+4\pi\chi^{_\mathrm{G}}_\mathrm{e}</math>
| <math>\varepsilon^{_\mathrm{I}}/\varepsilon_0 = 1+\chi^{_\mathrm{I}}_\mathrm{e}</math>
|}
where
* {{math|'''E'''}} and {{math|'''D'''}} are the [[electric field]] and [[Electric displacement field|displacement field]], respectively;
* {{math|'''P'''}} is the [[polarization density]];
* <math>\varepsilon</math> is the [[permittivity]];
* <math>\varepsilon_0</math> is the [[permittivity of vacuum]] (used in the SI system, but meaningless in Gaussian units); and
* <math>\chi_\mathrm{e}</math> is the [[electric susceptibility]].

The quantities <math>\varepsilon^{_\mathrm{G}}</math> and <math>\varepsilon^{_\mathrm{I}}/\varepsilon_0</math> are both dimensionless, and they have the same numeric value. By contrast, the [[electric susceptibility]] <math>\chi_\mathrm{e}^{_\mathrm{G}}</math> and <math>\chi_\mathrm{e}^{_\mathrm{I}}</math> are both unitless, but have {{em|different numeric values}} for the same material:
<math display="block">4\pi \chi_\mathrm{e}^{_\mathrm{G}} = \chi_\mathrm{e}^{_\mathrm{I}}\,.</math>

Next, here are the expressions for the various fields in a magnetic medium. Again, it is assumed that the medium is homogeneous, linear, isotropic, and nondispersive, so that the [[Permeability (electromagnetism)|permeability]] is a simple constant.

{| class="wikitable"
|+ Expressions for fields in magnetic media
|-
! scope="col" | Gaussian system
! scope="col" | {{abbr|ISQ|International System of Quantities}}
|-
| <math>\mathbf{B}^{_\mathrm{G}} = \mathbf{H}^{_\mathrm{G}}+4\pi\mathbf{M}^{_\mathrm{G}}</math>
| <math>\mathbf{B}^{_\mathrm{I}} = \mu_0 (\mathbf{H}^{_\mathrm{I}}+\mathbf{M}^{_\mathrm{I}})</math>
|-
| <math>\mathbf{M}^{_\mathrm{G}} = \chi^{_\mathrm{G}}_\mathrm{m}\mathbf{H}^{_\mathrm{G}}</math>
| <math>\mathbf{M}^{_\mathrm{I}} = \chi^{_\mathrm{I}}_\mathrm{m}\mathbf{H}^{_\mathrm{I}}</math>
|-
| <math>\mathbf{B}^{_\mathrm{G}} = \mu^{_\mathrm{G}}\mathbf{H}^{_\mathrm{G}}</math>
| <math>\mathbf{B}^{_\mathrm{I}} = \mu^{_\mathrm{I}}\mathbf{H}^{_\mathrm{I}}</math>
|-
| <math>\mu^{_\mathrm{G}} = 1+4\pi\chi^{_\mathrm{G}}_\mathrm{m}</math>
| <math>\mu^{_\mathrm{I}}/\mu_0 = 1+\chi^{_\mathrm{I}}_\mathrm{m}</math>
|}
where
* {{math|'''B'''}} and {{math|'''H'''}} are the [[magnetic field]]s;
* {{math|'''M'''}} is [[magnetization]];
* <math>\mu</math> is [[magnetic permeability]];
* <math>\mu_0</math> is the [[permeability of vacuum]] (used in the SI system, but meaningless in Gaussian units); and
* <math>\chi_\mathrm{m}</math> is the [[magnetic susceptibility]].

The quantities <math>\mu^{_\mathrm{G}}</math> and <math>\mu^{_\mathrm{I}}/\mu_0</math> are both dimensionless, and they have the same numeric value. By contrast, the [[magnetic susceptibility]] <math>\chi_\mathrm{m}^{_\mathrm{G}}</math> and <math>\chi_\mathrm{m}^{_\mathrm{I}}</math> are both unitless, but has {{em|different numeric values}} in the two systems for the same material:
<math display="block">4\pi \chi_\mathrm{m}^{_\mathrm{G}} = \chi_\mathrm{m}^{_\mathrm{I}}</math>