Cyclotron frequency |
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An electron in a cyclotron moves in a series of half circles of increasing radius in a perpendicular, uniform, magnetic field. The velocity of the electron in the magnetic field can be found by equating the centripetal force and the force on the moving charge in the magnetic field. The time for one half circle, T1/2, is given by.... ... independent of the radius of the path r. |
| Because the time to complete one half cycle does not depend on the radius of the path, a square wave voltage of fixed frequency will accelerate the electron repeatedly across the gap between the D's of the cyclotron. The required angular frequency w is just 2p/T.=.Be/m. |