Radius of curvature of charged particle in magnetic field
=========================================================

When a charged particle enters a magnetic field, it experiences an :doc:`electromagnetic
force <laws.electricity.vector.lorentz_force_via_electromagnetic_field>` upon itself.
In the absence of the electric field, the particle starts moving in a circular orbit. The
radius of curvature of the particle's orbit is determined by the mass, speed, and charge
of the particle as well as by the magnetic flux density.

**Conditions:**

#. The particle's speed and the magnetic field are perpendicular to each other.
#. The magnetic field is uniform.
#. The electric field is zero.

**Links:**

#. `Physics LibreTexts, formula 11.4.2 <https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/11%3A_Magnetic_Forces_and_Fields/11.04%3A_Motion_of_a_Charged_Particle_in_a_Magnetic_Field>`__.

.. py:currentmodule:: symplyphysics.laws.electricity.radius_of_curvature_of_charged_particle_in_magnetic_field

.. py:data:: radius_of_curvature

    :attr:`~symplyphysics.symbols.basic.radius_of_curvature` of the particle's orbit.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: mass

    :attr:`~symplyphysics.symbols.basic.mass` of the particle.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: speed

    :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the particle.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: charge

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

Symbol:
    :code:`q`

Latex:
    :math:`q`

Dimension:
    :code:`charge`


.. 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:: law

    :code:`r = m * v / (q * B)`


    Latex:
        .. math::
            r = \frac{m v}{q B}