Cyclotron Motion
A particle moving perpendicular to a constant
magnetic field undergoes uniform circular motion at constant speed, v.
Thus, the magnetic force due to the external
field produces a centripetal
acceleration.
Fmag = qvB = mac
Fmag =
m(v2/r)
Since cyclotron motion occurs when particle
is traveling perpendicular to field:
qvB = mv2/r
rcyc = mv/qB
rcyc = mv/qB
From this expression it is possible to obtain
the charge to mass ratio, which is the topic of Friday’s lab:
q/m
= v/rcyc B
rcyc = mv/qB
In practical applications, B can be set to an appropriate value. The particle speed can be controlled by use
of a known ∆V, to accelerate the particle.
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