The Charged Particle Motion Near a Magnetic Dipole shows the motion of an electric charge in a magnetic dipole field. The motion arises from the cross product of the charge's velocity with the magnetic field. The numerical solution is produced using the Lorentz force law
where the magnetic dipole field B is
In Cartesian coordinates, the charged particle position r vector is ix+jy+kz and the magnetic dipole moment m vector is km. If we assume that a dipole located at the origin is oriented along the z-axis, the Cartesian magnetic field components are
These components can now be used to compute the force
This model uses solves Newton's second law for a particle using units such that mμo/4π=1.
Although this simulation is not to scale, the Charged Particle Motion Near a Magnetic Dipole model shows the magnetic mirroring that gives rise to the Van Allen radiation belts. Electrons and protons high in the Earth's atmosphere spiral along the magnetic field lines toward the poles where the magnetic field increases and the drift velocity changes direction there by trapping the particles.
Updated 10 August 2020.