Current density via number density and drift velocity
=====================================================

Current density is the amount of charge per unit time that flows through a unit area of a chosen
cross section. The current density vector is defined as a vector whose magnitude is the electric
current per cross-sectional area at a given point in space, its direction being that of the motion
of the positive charges at this point.

**Conditions:**

#. Charge carriers carry the the same amount of charge.

**Links:**

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

.. py:currentmodule:: symplyphysics.laws.condensed_matter.current_density_via_number_density_and_drift_velocity

.. 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:: number_density

    :attr:`~symplyphysics.symbols.basic.number_density`, or number of charge carriers per unit volume.

Symbol:
    :code:`n`

Latex:
    :math:`n`

Dimension:
    :code:`1/volume`


.. py:data:: drift_velocity

    :attr:`~symplyphysics.symbols.chemistry.drift_velocity` of charge carriers.

Symbol:
    :code:`u`

Latex:
    :math:`u`

Dimension:
    :code:`velocity`


.. py:data:: charge

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

Symbol:
    :code:`q`

Latex:
    :math:`q`

Dimension:
    :code:`charge`


.. py:data:: law

    :code:`j = q * n * u`


    Latex:
        .. math::
            j = q n u