Diode constant of cylindrical diode
===================================

In a cylindrical diode, the cathode is located in the center, and the anode is located
around it in the form of a cylinder. The radius of the anode is usually much larger than
the radius of the cathode. The diode constant depends on the radii and on the area of
the anode.

**Notation:**

#. :math:`\varepsilon_0` (:code:`epsilon_0`) is :attr:`~symplyphysics.quantities.vacuum_permittivity`.
#. :math:`e` (:code:`e`) is :attr:`~symplyphysics.quantities.elementary_charge`.
#. :math:`m_\text{e}` (:code:`m_e`) is :attr:`~symplyphysics.quantities.electron_rest_mass`.

..
    TODO: find link

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

.. py:data:: diode_constant

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

Symbol:
    :code:`g`

Latex:
    :math:`g`

Dimension:
    :code:`current/voltage**(3/2)`


.. py:data:: anode_area

    :attr:`~symplyphysics.symbols.classical_mechanics.area` of the anode.

Symbol:
    :code:`A_a`

Latex:
    :math:`A_\text{a}`

Dimension:
    :code:`area`


.. py:data:: anode_radius

    :attr:`~symplyphysics.symbols.classical_mechanics.radius` of the anode.

Symbol:
    :code:`r_a`

Latex:
    :math:`r_\text{a}`

Dimension:
    :code:`length`


.. py:data:: cathode_radius

    :attr:`~symplyphysics.symbols.classical_mechanics.radius` of the cathode.

Symbol:
    :code:`r_c`

Latex:
    :math:`r_\text{c}`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`g = 4 * epsilon_0 / 9 * sqrt(2 * e / m_e) * A_a / (r_a^2 * (1 - r_c / r_a)^2)`


    Latex:
        .. math::
            g = \frac{\frac{4 \varepsilon_0}{9} \sqrt{\frac{2 e}{m_\text{e}}} A_\text{a}}{r_\text{a}^{2} \left(1 - \frac{r_\text{c}}{r_\text{a}}\right)^{2}}