Short circuit inductance of microstrip line
===========================================

To create a short circuit based on a microstrip line, a metallized hole can be made in
the line. Such an opening will have a certain inductance, which can be calculated.

**Notation:**

#. :math:`\mu_0` (:code:`mu_0`) is :attr:`~symplyphysics.quantities.vacuum_permeability`.

..
    TODO: add link

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.transmission_lines.microstrip_lines.short_circuit_inductance_of_microstrip_line

.. py:data:: inductance

    :attr:`~symplyphysics.symbols.electrodynamics.inductance` of a metallized hole in a microstrip line.

Symbol:
    :code:`L`

Latex:
    :math:`L`

Dimension:
    :code:`inductance`


.. py:data:: substrate_thickness

    :attr:`~symplyphysics.symbols.classical_mechanics.thickness` of the substrate of the microstrip line.

Symbol:
    :code:`h`

Latex:
    :math:`h`

Dimension:
    :code:`length`


.. py:data:: radius

    :attr:`~symplyphysics.symbols.classical_mechanics.radius` of the metallized hole.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`L = mu_0 / (2 * pi) * (h * log((h + sqrt(r^2 + h^2)) / r) + 1.5 * (r - sqrt(r^2 + h^2)))`


    Latex:
        .. math::
            L = \frac{\mu_0}{2 \pi} \left(h \log \left( \frac{h + \sqrt{r^{2} + h^{2}}}{r} \right) + 1.5 \left(r - \sqrt{r^{2} + h^{2}}\right)\right)


    ..
        TODO: check if `1.5` isn't really `3/2`