Electromotive force induced in rotating coil
============================================

Suppose a coil is being rotated around the axis that lies in the coil's cross section
(see `Figure <https://www.schoolphysics.co.uk/age16-19/Electricity%20and%20magnetism/Electromagnetic%20induction/text/Induced_emf_in_a_rotating_coil/index.html>`__)
in a magnetic field under the conditions described below. Then an electromotive will
be induced in the contour of the coil. Its amplitude depends on the number of turns in
the coil, the magnetic flux density, the angular frequency of the coil's rotation and
the area of the coil's contour.

**Notes:**

#. The angle :math:`\varphi` between the normal to the coil's contour and the magnetic flux
   density is :math:`\varphi \propto \cos(\omega t)`. See `Figure <https://thefactfactor.com/wp-content/uploads/2020/03/Self-Induction-17.png>`__. 

**Conditions:**

#. The magnetic field is uniform.
#. The angular velocity of the coil's rotation is orthogonal to the magnetic field.
#. The area of the coil's contour is constant.
#. The angular speed of the coil's rotation constant.

.. py:currentmodule:: symplyphysics.laws.electricity.electromotive_force_induced_in_uniformly_rotating_coil

.. py:data:: electromotive_force

    :attr:`~symplyphysics.symbols.electrodynamics.electromotive_force` induced in the coil.

Symbol:
    :code:`E`

Latex:
    :math:`\mathcal{E}`

Dimension:
    :code:`voltage`


.. py:data:: coil_turn_count

    Number of turns in the coil. See :attr:`~symplyphysics.symbols.basic.positive_number`.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: magnetic_flux_density

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

Symbol:
    :code:`B`

Latex:
    :math:`B`

Dimension:
    :code:`magnetic_density`


.. py:data:: contour_area

    Cross-sectional :attr:`~symplyphysics.symbols.classical_mechanics.area` of the contour enclosed by the coil.

Symbol:
    :code:`A`

Latex:
    :math:`A`

Dimension:
    :code:`area`


.. py:data:: angular_frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_frequency` of the coil's rotation.

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time`.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: law

    :code:`E = -N * B * A * w * sin(w * t)`


    Latex:
        .. math::
            \mathcal{E} = - N B A \omega \sin{\left(\omega t \right)}