Electric flux through closed surface in linear material

The Gauss’s law can be written for linear materials, featuring free charges, i.e. such charges that are not bound to any nucleus and can move freely, as opposed to bound charges that occur due to the material’s polarization.

Conditions:

1. The material is linear, homogeneous, isotropic, and nondispersive.

Links:

1. Wikipedia — Gauss’s law.

electric_flux

electric_flux through a closed surface \(S\).

Symbol:

Phi_E

Latex:

\(\Phi_{\vec E}\)

Dimension:

length*voltage

total_free_charge

Total free charge contained in the volume bound by \(S\).

Symbol:

q_free

Latex:

\(q_\text{free}\)

Dimension:

charge

absolute_permittivity

absolute_permittivity of the medium in the volume bound by \(S\).

Symbol:

epsilon

Latex:

\(\varepsilon\)

Dimension:

capacitance/length

law

Phi_E = q_free / epsilon

Latex:

\[\Phi_{\vec E} = \frac{q_\text{free}}{\varepsilon}\]