21. Electrodynamics (Cyclotron)
The cyclotron frequency is the frequency of a charged particle moving perpendicular to the direction of a constant magnetic field B. Since the motion of a charged particle in the cyclotron is circular (because of a uniform magnetic field), we can calculate the cyclotron frequency by using the fact that the centripetal force equals to the magnetic Lorentz force.
where is the velocity of the charged particle, and is the magnitude of the magnetic field in the cyclotron. , are the mass and electric charge of a particle, respectively. The above equation yields where is the period of the charged particle. Since the relationship between the period and frequency is Thus, Now, let's look at the particles, Mass: Electric charge: Therefore, their cyclotron frequencies in the same magnetic field,