Question

A cyclotron oscillator frequency is `10MHz`. What should be the operating magnetic field for accelerating protons? If the radius of its dees is `60cm`, what is the kinetic energy of the proton beam produced by the acceleration in `MeV`?
`(e=1*6xx10^(-19)C, m_p=1*67xx10^(-27)kg, 1MeV=1*6xx10^(-13)J)`

Answer 1

`B=(2pivm)/(q)`
`=2xx22/7xx((10xx10^6)xx(1*67xx10^(-27)))/(1*6xx10^(-19))=0*66T`
`K_(max.)=(B^2q^2r_0^2)/(2m)`
`=((0*66)^2xx(1*6xx10^(-19))^2xx(0*60)^2)/(2xx1*67xx10^(-27))J`
`=((0*66)^2xx(1*6xx10^(-19))^2xx(0*60)^2)/(2xx(1*67xx10^(-27))xx1*6xx10^(-13))MeV`
`=7*5MeV`