Power carried by main wave of 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`.

..
    TODO find link

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

.. py:data:: power

    :attr:`~symplyphysics.symbols.basic.power` transmitted by the waveguide.

Symbol:
    :code:`P`

Latex:
    :math:`P`

Dimension:
    :code:`power`


.. py:data:: width

    Width, or first dimension of the cross section. See :attr:`~symplyphysics.symbols.classical_mechanics.length`.

Symbol:
    :code:`a`

Latex:
    :math:`a`

Dimension:
    :code:`length`


.. py:data:: height

    Height, or second dimension of the cross section. See :attr:`~symplyphysics.symbols.classical_mechanics.length`.

Symbol:
    :code:`b`

Latex:
    :math:`b`

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:: material_resistance

    :attr:`~symplyphysics.symbols.electrodynamics.electrical_resistance` of the medium filling the waveguide.

Symbol:
    :code:`R`

Latex:
    :math:`R`

Dimension:
    :code:`impedance`


.. py:data:: electric_field_strength

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

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`voltage/length`


.. py:data:: law

    :code:`P = a * b * sqrt(1 - (lambda / (2 * a))^2) * E^2 / (4 * R)`


    Latex:
        .. math::
            P = \frac{a b \sqrt{1 - \left(\frac{\lambda}{2 a}\right)^{2}} E^{2}}{4 R}