Electric flux through closed surface via total charge
=====================================================

Known as **Gauss's law**, it states that the electric flux through any closed surface :math:`S` is equal to
the total charge within volume :math:`V` enclosed by that surface, and in the SI units, divided by the
vacuum permittivity. The closed surface is also referred to as **Gaussian surface**.

**Conditions:**

#. :math:`S = \partial V`, i.e. surface :math:`S` encloses volume :math:`V`. In other words, the surface
   must be closed.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Gauss%27s_law#Equation_involving_the_E_field>`__.

.. py:currentmodule:: symplyphysics.laws.electricity.electric_flux_through_closed_surface_via_total_charge

.. py:data:: total_electric_flux

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

Symbol:
    :code:`Phi_E`

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

Dimension:
    :code:`length*voltage`


.. py:data:: total_charge

    Total :attr:`~symplyphysics.symbols.electrodynamics.charge` inside volume :math:`V`.

Symbol:
    :code:`q`

Latex:
    :math:`q`

Dimension:
    :code:`charge`


.. py:data:: law

    :code:`Phi_E = q / epsilon_0`


    Latex:
        .. math::
            \Phi_\mathbf{E} = \frac{q}{\varepsilon_0}