Lorentz force via electromagnetic field
=======================================

The **Lorentz force law** states that a charged particle moving in an electromagnetic
field experiences a force that depends on the values of the electric field and the
magnetic field.

**Notation:**

#. :math:`\left[ \vec a, \vec b \right]` (:code:`cross(a, b)`) is the cross product between
   :math:`\vec a` and :math:`\vec b`.

**Notes:**

#. This law is valid even in the relativistic case.
#. This law works only in principle because a real particle would generate its own
   electromagnetic field that would interact with the external one which would alter
   the electromagnetic force it experiences.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Lorentz_force>`__.

.. py:currentmodule:: symplyphysics.laws.electricity.vector.lorentz_force_via_electromagnetic_field

.. py:data:: lorentz_force

    Vector of the Lorentz :attr:`~symplyphysics.symbols.classical_mechanics.force` exerted on the charged particle.

Symbol:
    :code:`F`

Latex:
    :math:`{\vec F}`

Dimension:
    :code:`force`


.. py:data:: charge

    Value of the electric :attr:`~symplyphysics.symbols.electrodynamics.charge` of the test particle.

Symbol:
    :code:`q`

Latex:
    :math:`q`

Dimension:
    :code:`charge`


.. py:data:: electric_field

    Vector of the electric field. See :attr:`~symplyphysics.symbols.electrodynamics.electric_field_strength`.

Symbol:
    :code:`E`

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

Dimension:
    :code:`voltage/length`


.. py:data:: velocity

    Vector of the particle's velocity. See :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v`

Latex:
    :math:`{\vec v}`

Dimension:
    :code:`velocity`


.. py:data:: magnetic_flux_density

    Vector of the :attr:`~symplyphysics.symbols.electrodynamics.magnetic_flux_density`.

Symbol:
    :code:`B`

Latex:
    :math:`{\vec B}`

Dimension:
    :code:`magnetic_density`


.. py:data:: law

    :code:`F = q * (E + cross(v, B))`


    Latex:
        .. math::
            {\vec F} = q \left({\vec E} + \left[ {\vec v}, {\vec B} \right]\right)