Instantaneous energy of magnetic field
======================================

There is an oscillatory circuit with alternating current. Then the energy of the magnetic field in
the inductor will depend on the inductance, the maximum value of the current, the angular frequency
of the current, the time and the initial phase.

**Conditions:**

#. The current depends on time sinusoidally:

   .. math::

       I(t) = I_\text{max} \cos(\omega t + \varphi)

.. py:currentmodule:: symplyphysics.laws.electricity.instantaneous_energy_of_magnetic_field

.. py:data:: energy

    :attr:`~symplyphysics.symbols.basic.energy` stored in the coil.

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`energy`


.. py:data:: inductance

    :attr:`~symplyphysics.symbols.electrodynamics.inductance` of the coil.

Symbol:
    :code:`L`

Latex:
    :math:`L`

Dimension:
    :code:`inductance`


.. py:data:: current_amplitude

    :attr:`~symplyphysics.symbols.electrodynamics.current` amplitude.

Symbol:
    :code:`I_max`

Latex:
    :math:`I_\text{max}`

Dimension:
    :code:`current`


.. py:data:: angular_frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_frequency` of the current.

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:: initial_phase

    Initial :attr:`~symplyphysics.symbols.classical_mechanics.phase_shift` of the oscillations.

Symbol:
    :code:`phi`

Latex:
    :math:`\varphi`

Dimension:
    :code:`angle`


.. py:data:: law

    :code:`E = L * I_max^2 / 2 * cos(w * t + phi)^2`


    Latex:
        .. math::
            E = \frac{L I_\text{max}^{2}}{2} \cos^{2}{\left(\omega t + \varphi \right)}