Charged Particles Moving in a Magnetic Field
is the magnetic field directed away from us (indicated by x
Positively charged particles are red
Negatively charged particles are blue
The green arrow
velocity of the particle.
The gray arc
is the trajectory
of the particle.
In this demonstration particles are entering the region of the magnetic field with
their velocities being perpendicular to the magnetic field lines. In such a situation
the magnetic force serves to move the particles in a circular path. According to
the "right hand rule" the magnetic force acting on the particle always
remains perpendicular to its velocity.
The magnitude of the magnetic force is F = qvB⊥, where q
is the magnitude of the charge of the particle, v its velocity, and B⊥
is the magnitude of the perpendicular magnetic field.
This force can be also considered as the centripetal force Fc = mv2/R,
where m is the particle's mass and R is the radius of the circular
Making two above expressions equal to each other and solving the resulting equation
for R we can easily find that the radius R of the circular path is
proportional to the velocity of the particle.
R = mv/qB⊥
© Copyright © 1997, Sergey Kiselev and Tanya Yanovsky-Kiselev
All rights reserved.
Last modified: June 20, 1997