The cyclotron formula gives the radius r of a particle's orbit in a cyclotron, and can be derived by equating
For relativistic motion in cgs, this gives
where p is the momentum, v is the speed, c is the speed of light, and
is the magnetic field. Solving for r gives
In MKS,
giving
The radius of a cyclotron orbit for nonrelativistic motion is obtained by plugging in p = mv to the relativistic formula, where m is the mass of the particle. In cgs, this gives
and the angular frequency is
In MKS,
and
(1)
For relativistic motion in cgs, this gives
(2)
where p is the momentum, v is the speed, c is the speed of light, and
is the magnetic field. Solving for r gives(3)
In MKS,
(4)
giving
(5)
The radius of a cyclotron orbit for nonrelativistic motion is obtained by plugging in p = mv to the relativistic formula, where m is the mass of the particle. In cgs, this gives
(6)
and the angular frequency is
(7)
In MKS,
(8)
and
(9)
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