Charge density in diode
=======================

The simplest device implementing a cathode current control method is a diode device. It
contains a vacuum chamber, a thermionic cathode, a mesh electrode and an anode.

**Notation:**

#. :math:`\varepsilon_0` (:code:`epsilon_0`) is :attr:`~symplyphysics.quantities.vacuum_permittivity`.

..
    TODO: find link

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.diodes.space_charge_density_in_diode_device

.. py:data:: charge_density

    :attr:`~symplyphysics.symbols.electrodynamics.volumetric_charge_density` in the diode.

Symbol:
    :code:`rho`

Latex:
    :math:`\rho`

Dimension:
    :code:`charge/volume`


.. py:data:: grid_voltage

    :attr:`~symplyphysics.symbols.electrodynamics.voltage` on the grid.

Symbol:
    :code:`V`

Latex:
    :math:`V`

Dimension:
    :code:`voltage`


.. py:data:: distance

    :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance` between the grid and the cathode.

Symbol:
    :code:`d`

Latex:
    :math:`d`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`rho = 4 * epsilon_0 / 9 * V / d^2`


    Latex:
        .. math::
            \rho = \frac{\frac{4 \varepsilon_0}{9} V}{d^{2}}