A cyclotron (figure) designed to accelerate protons has an outer radius of 0.315 m. The protons are emitted nearly at rest from a source at the center and are accelerated through 566 V each time they cross the gap between the dees. The dees are between the poles of an electromagnet where the field is 0.784 T.
The black dashed curved lines represent the path the particles take.
After being accelerated, the particles exit here: North pole of magnet.
(a) Find the cyclotron frequency for the protons in this cyclotron: 7.51e7 rad/s.
(b) Find the speed at which protons exit the cyclotron: 3.97 m/s.
(c) Find their maximum kinetic energy: 4.52 eV.
(d) How many revolutions does a proton make in the cyclotron? 3 revolutions.
(e) For what time interval does the proton accelerate? 1.06e-8 s.