Maximum electric field strength of main wave in rectangular waveguide
=====================================================================

A rectangular waveguide is a rectangular metal waveguide capable of supporting waves
propagating along it. The main wave is a transverse electric wave with the first index
equal to :math:`1` and the second index equal to :math:`0`.

**Notes:**

#. *Horizontal* dimension refers to the dimension of the cross section of the waveguide
   that is orthogonal to its central axis. See image for reference.

.. image:: https://www.electronics-notes.com/images/waveguide-rectangular-te-modes-01.svg
    :width: 400px
    :align: center

**Notation:**

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

**Conditions:**

#. The wave propagating in the waveguide must be the main wave.
#. The waveguide must be rectangular.

..
    TODO: find link

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.waveguides.maximum_electric_field_intensity_of_main_wave_in_rectangular_waveguide

.. py:data:: maximum_electric_field_strength

    Maximum :attr:`~symplyphysics.symbols.electrodynamics.electric_field_strength` in the waveguide.

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`voltage/length`


.. py:data:: relative_permittivity

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

Symbol:
    :code:`epsilon_r`

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

Dimension:
    :code:`dimensionless`


.. py:data:: width

    Horizontal dimension of the waveguide. See :attr:`~symplyphysics.symbols.classical_mechanics.length`.

Symbol:
    :code:`a`

Latex:
    :math:`a`

Dimension:
    :code:`length`


.. py:data:: wavelength

    :attr:`~symplyphysics.symbols.classical_mechanics.wavelength` of the signal.

Symbol:
    :code:`lambda`

Latex:
    :math:`\lambda`

Dimension:
    :code:`length`


.. py:data:: magnetic_field_strength

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

Symbol:
    :code:`H`

Latex:
    :math:`H`

Dimension:
    :code:`current/length`


.. py:data:: law

    :code:`E = 2 * Z_0 * a * H / (lambda * sqrt(epsilon_r))`


    Latex:
        .. math::
            E = \frac{2 Z_0 a H}{\lambda \sqrt{\varepsilon_\text{r}}}