In a cyclotron the frequency of alternating current is 12 MHz and the radii of its dee is `0.53m`. What should be the operating magnetic field to accelerate protons ? Given mass of proton `=1.67xx10^(-27)` kg and charge `=+1.6xx10^(-19)C`.

Explanation

condition of resonance,
`(1)/(2pi)((q)/(m))B=n_(0) or, B=(2pi n_(0)m)/(q)`
Here, `n_(0)=12MHz=12xx10^(6) Hz=12xx10^(6)s^(-1)`
So, `B=(2xx3.14xx (12xx16^(6))xx(1.67xx10^(-27)))/(1.6xx10^(-19))`
`=0.79Wb*m^(-2)`