Charged Particle Motion in Earth's Magnetosphere
Charged Particle Motion in a Uniform Magnetic Field
A particle with charge moving with velocity in a uniform magnetic field experiences a force:
The force on the particle is perpendicular to both the velocity and magnetic field and thus does no work on the particle.
If the velocity is perpendicular to the magnetic field, the particle moves in a circle of radius with centripetal acceleration . Equating the magnetic force to the particle mass times the centripetal acceleration, we can show that the radius of gyration (or gyroradius) of the particle is equal to .
Click the question marks to see the formulation:
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For a given gyroradius, the corresponding frequency of gyration (or gyrofrequency), expressed in radians per second, is .
Click the question marks to see the expression:
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If a component of the particle's velocity ( ) is parallel to the magnetic field, then is replaced by in the preceding two equations, while the component carries the particle along the magnetic field, creating a helical trajectory.
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