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 **i**x+**j**y+**k**z and the magnetic dipole moment **m**
vector is **k**m. 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 mμ_{o}/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.

- "Using computer algebra to investigate the motion of an electric charge in magnetic and electric dipole fields," George McGuire, Am. J. Phys. 71(8), 809 (2003), DOI: 10.1119/1.1579496
- "Radiationbelts," J.A.Van Allen, in Encyclopedia of Physics VCH,2nd ed., p.1010. (1990)

The Charged Particle Motion Near a Magnetic Dipole Java model was developed by Wolfgang Christian using the Easy Java Simulations (EJS) modeling and authoring tool created by Francisco Esquembere in Murcia, Spain. It was later converted from Java to JavaScript by Wolfgang Christian and Robert Hanson using the SwingJS system developed by Hanson and his students at St. Olaf College.

Updated 10 August 2020.