Electric flux through closed surface in linear material
=======================================================

The :ref:`Gauss's law <Electric flux through closed surface via total charge>` 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:**

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

**Links:**

#. `Wikipedia — Gauss's law <https://en.wikipedia.org/wiki/Gauss%27s_law#Equation_for_linear_materials>`__.

.. py:currentmodule:: symplyphysics.laws.electricity.electric_flux_through_closed_surface_in_linear_material

.. py:data:: electric_flux

    :attr:`~symplyphysics.symbols.electrodynamics.electric_flux` through a closed surface :math:`S`.

Symbol:
    :code:`Phi_E`

Latex:
    :math:`\Phi_{\vec E}`

Dimension:
    :code:`length*voltage`


.. py:data:: total_free_charge

    Total free :attr:`~symplyphysics.symbols.electrodynamics.charge` contained in the volume bound by :math:`S`.

Symbol:
    :code:`q_free`

Latex:
    :math:`q_\text{free}`

Dimension:
    :code:`charge`


.. py:data:: absolute_permittivity

    :attr:`~symplyphysics.symbols.electrodynamics.absolute_permittivity` of the medium in the volume bound by :math:`S`.

Symbol:
    :code:`epsilon`

Latex:
    :math:`\varepsilon`

Dimension:
    :code:`capacitance/length`


.. py:data:: law

    :code:`Phi_E = q_free / epsilon`


    Latex:
        .. math::
            \Phi_{\vec E} = \frac{q_\text{free}}{\varepsilon}