Charged Particles Moving in a Magnetic Field
B is the magnetic field directed away from us.
Positively charged particles are red.
Negatively charged particles are blue.
arrow shows the velocity of the particle.
arc is the trajectory of the particle.
In this demonstration particles are entering the region of the
magnetic field with their velocoties 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 = q V B ,
where q is the magnitude of the charge of the particle,
V its velocity, and B is the magnetic field.
This force can be also considered as the centripetal force
Fc = m V2 / R ,
where m is the particle's mass and R is the radius of
the circular tragectory.
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
R = m V / q B .