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Dipoles are the simplest magnetic objects in physics. Nonetheless, they can cause some surprisingly complex behavior for a charged particle moving nearby.
A charged particle moving according to the Lorentz force about a magnetostatic dipole provides an example of complex behavior that can come about even in simple physical systems. In the case illustrated here, the charged particle spirals along magnetic field lines but reflects in a magnetic "mirror" at "high latitudes" in the field.
This Demonstration allows the specification of the initial conditions of the charged particle, the magnetic field parameter, and the duration of motion. The resulting trajectory is shown as a blue curve. The current velocity direction is shown as a short green line segment and the field direction at the current trajectory point is shown by a red segment. The particle trajectory spirals around the field direction.
A sphere and magnetic pole are provided at the middle of the visualization only for conceptual purposes. A magnetic dipole need not have a finite dimension, and the example shown here does not affect the simulation. The sphere is provided for a visual frame of reference. Such a reference is useful in visualizing the motion of a charged particle in the Earth’s magnetic field.