Divergence of electric displacement field is volumetric charge density
======================================================================

The divergence of the electric induction field (also known as the electric displacement field) is
equal to the volumetric charge density at all points in space. Another form of this law states
that there exist electric charges.

**Links:**

#. `Wikipedia, first line in table <https://en.wikipedia.org/wiki/Maxwell%27s_equations#Macroscopic_formulation>`__.
#. `Physics LibreTexts, formula 15.2.3 <https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electricity_and_Magnetism_(Tatum)/15%3A_Maxwell's_Equations/15.02%3A_Maxwell's_First_Equation>`__.

..
    TODO: rename file

.. py:currentmodule:: symplyphysics.laws.electricity.maxwell_equations.charge_density_from_electric_induction_divergence

.. py:data:: position_vector

    Position vector of a point in space. See :attr:`~symplyphysics.symbols.classical_mechanics.distance_to_origin`.

Symbol:
    :code:`r`

Latex:
    :math:`{\vec r}`

Dimension:
    :code:`length`


.. py:data:: electric_displacement

    Vector field of the :attr:`~symplyphysics.symbols.electrodynamics.electric_displacement` as a function of the
    :attr:`~position_vector`.

Symbol:
    :code:`D(r)`

Latex:
    :math:`{\vec D} \left( {\vec r} \right)`

Dimension:
    :code:`charge/area`


.. py:data:: volumetric_charge_density

    Scalar field of the :attr:`~symplyphysics.symbols.electrodynamics.volumetric_charge_density` as a function of the
    :attr:`~position_vector`.

Symbol:
    :code:`rho(r)`

Latex:
    :math:`\rho{\left({\vec r} \right)}`

Dimension:
    :code:`charge/volume`


.. py:data:: law

    :code:`div(D(r)) = rho(r)`


    Latex:
        .. math::
            \text{div} \, {\vec D} \left( {\vec r} \right) = \rho{\left({\vec r} \right)}