A cyclotron's oscillator frequency is `10MHz`. What should be the operating magnetic field fro accelerating protons? If the radius of its dees is `60cm`, what is the kinetic energy (in `MeV`) of the proton beam produced by the acceleration?
`(e-1.60xx10^-19C,m_p=1.67xx10^-27kg, 1MeV=1.6xx10^-13J)`

Explanation

The oscillator frequency should be same as proton.s cyclotron frequency.
Using Eqs. (4.5) and (4.6 (a)) we have
`B=2pimv//q=1.67xx10^(-27)xx10^(7)//(1.6xx10^(-19))=0.66T`
Final velocity of protons is
`v=rxx2piv=0.6mxx6.3xx10^(7)=3.78xx10^(7)m//s`