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Charged Particle Motion in Earth's Magnetosphere

Charged Particle Motion in a Uniform Magnetic Field

A particle with charge q moving with velocity vector v in a uniform magnetic field vector B experiences a force:

F = qv cross B

The force on the particle is perpendicular to both the velocity and magnetic field and thus does no work on the particle.

Vector diagram of force, velocity, magnetic field for moving charged particle

If the velocity is perpendicular to the magnetic field, the particle moves in a circle of radius r with centripetal acceleration v squared over r. Equating the magnetic force to the particle mass m times the centripetal acceleration, we can show that the radius of gyration (or gyroradius) of the particle is equal to mv over qB.

Click the question marks to see the formulation:

Animation courtesy the COMET and HAO programs at UCAR/NCAR.

For a given gyroradius, the corresponding frequency of gyration (or gyrofrequency), expressed in radians per second, is qB over m.

Click the question marks to see the expression:

Animation courtesy the COMET and HAO programs at UCAR/NCAR.

If a component of the particle's velocity ( v parallel ) is parallel to the magnetic field, then v is replaced by v perpendicular in the preceding two equations, while the v parallel component carries the particle along the magnetic field, creating a helical trajectory.

Animation courtesy the COMET and HAO programs at UCAR/NCAR.

Last modified May 13, 2005 by Randy Russell.

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