Electromotive force induced in rotating rod
===========================================

Let a rod rotate in a uniform magnetic field. The plane of rotation is perpendicular
to the magnetic field lines. The axis of rotation passes through one of the ends of
the rod. A wire is connected at both ends of the rod so that it makes a contour.
Then the electromotive force induced at the ends of the rod depends on the magnitude
of the magnetic flux density, the rotation frequency and the length of the rod.

**Links:**

#. `Example 13.4.2 <https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/13%3A_Electromagnetic_Induction/13.04%3A_Motional_Emf>`__.

**Conditions:**

#. The angular velocity of the rod is parallel to the magnetic field. This means that
   the rod is rotating in a plane perpendicular to the magnetic field.
#. The magnetic field is uniform.
#. The angular velocity of the rod is constant.

.. py:currentmodule:: symplyphysics.laws.electricity.electromotive_force_induced_in_rotating_rod

.. py:data:: electromotive_force

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

Symbol:
    :code:`E`

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

Dimension:
    :code:`voltage`


.. py:data:: magnetic_flux_density

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

Symbol:
    :code:`B`

Latex:
    :math:`B`

Dimension:
    :code:`magnetic_density`


.. py:data:: angular_frequency

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

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: length

    :attr:`~symplyphysics.symbols.classical_mechanics.length` of the rod.

Symbol:
    :code:`l`

Latex:
    :math:`l`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`E = B * w * l^2 / 2`


    Latex:
        .. math::
            \mathcal{E} = \frac{B \omega l^{2}}{2}