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 
.
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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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