Cyclotron accelerating protons to 20 MeV with potential gap 100 kV

[bhargavdjoshi]

Homework Statement

A Cyclotron is accelerating proton, where the applied magnetic field is 2 T, the potential gap is 100 KV, then how much turn are required for a kinetic energy of 20 MeV....

(a) 300
(b) 200
(c) 150
(d) 100

 

[Gear300]

20MeV is around when relativistic effects take place. The voltage alternates periodically. After one turn (or half a turn--semicircle...I'm not sure) the proton gains a kinetic energy of qV, V being the potential gap. Using that value, find out how many turns it takes to total 20MeV.