Wave impedance from permeability and permittivity
=================================================

The impedance of a wave is a value determined by the ratio of the transverse component
of the electric field to the transverse component of the magnetic field of a traveling
wave.

**Notation:**

#. :math:`Z_0` (:code:`Z_0`) is :attr:`~symplyphysics.quantities.vacuum_impedance`.

**Conditions:**

#. The dielectric medium is ideal, i.e. its conductivity :math:`sigma = 0`.

**Links:**

#. `Wikipedia, derivable from last formula in paragraph <https://en.wikipedia.org/wiki/Wave_impedance#Definition>`__.

..
    TODO: rename file

.. py:currentmodule:: symplyphysics.laws.electricity.characteristic_resistance_of_medium

.. py:data:: wave_impedance

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

Symbol:
    :code:`eta`

Latex:
    :math:`\eta`

Dimension:
    :code:`impedance`


.. py:data:: relative_permittivity

    :attr:`~symplyphysics.symbols.electrodynamics.relative_permittivity` of the medium.

Symbol:
    :code:`epsilon_r`

Latex:
    :math:`\varepsilon_\text{r}`

Dimension:
    :code:`dimensionless`


.. py:data:: relative_permeability

    :attr:`~symplyphysics.symbols.electrodynamics.relative_permeability` of the medium.

Symbol:
    :code:`mu_r`

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

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`eta = Z_0 * sqrt(mu_r / epsilon_r)`


    Latex:
        .. math::
            \eta = Z_0 \sqrt{\frac{\mu_\text{r}}{\varepsilon_\text{r}}}