Current density from mobility
=============================

The current density can be calculated from the concentration and mobilities of holes and
electrons and the electric field.

**Notation:**

#. :math:`e` (:code:`e`) is :attr:`~symplyphysics.quantities.elementary_charge`.

**Links:**

#. `Wikipedia, last formula <https://en.wikipedia.org/wiki/Electron_mobility#Relation_to_current_density>`__.

.. py:currentmodule:: symplyphysics.laws.condensed_matter.current_density_from_mobility

.. py:data:: current_density

    :attr:`~symplyphysics.symbols.electrodynamics.current_density` of charge carriers.

Symbol:
    :code:`j`

Latex:
    :math:`j`

Dimension:
    :code:`current/area`


.. py:data:: electrons_concentration

    Concentration (:attr:`~symplyphysics.symbols.basic.number_density`) of electrons.

Symbol:
    :code:`n_e`

Latex:
    :math:`n_\text{e}`

Dimension:
    :code:`1/volume`


.. py:data:: holes_concentration

    Concentration (:attr:`~symplyphysics.symbols.basic.number_density`) of holes.

Symbol:
    :code:`n_h`

Latex:
    :math:`n_\text{h}`

Dimension:
    :code:`1/volume`


.. py:data:: electrons_mobility

    :attr:`~symplyphysics.symbols.chemistry.mobility` of electrons.

Symbol:
    :code:`mu_e`

Latex:
    :math:`\mu_\text{e}`

Dimension:
    :code:`area/(time*voltage)`


.. py:data:: holes_mobility

    :attr:`~symplyphysics.symbols.chemistry.mobility` of holes.

Symbol:
    :code:`mu_h`

Latex:
    :math:`\mu_\text{h}`

Dimension:
    :code:`area/(time*voltage)`


.. py:data:: electric_field_strength

    :attr:`~symplyphysics.symbols.electrodynamics.electric_field_strength`.

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`voltage/length`


.. py:data:: law

    :code:`j = e * (-n_e * mu_e + n_h * mu_h) * E`


    Latex:
        .. math::
            j = e \left(- n_\text{e} \mu_\text{e} + n_\text{h} \mu_\text{h}\right) E