THE CYCLOTRON IS A DEVICE USED TO ACCELERATE ELEMENTARY PARTICLES SUCH AS TO spe

Question

THE CYCLOTRON IS A DEVICE USED TO ACCELERATE ELEMENTARY PARTICLES SUCH AS TO speeds. Particles starting at point A travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass in the gap between the metal "dees", where there is an electric field E (there is no electric field within the hollow metal dees). The electric field changes direction each half-cycle due to an AC voltage V = V0 sin 2Pi ft, so that the particles are increased in speed each passage through the gap. If a proton starts at rest at point A. the magnetic field strength is B = 0.85 T, the radius of the cyclotron is r = 0.95 m, and the gap between the dees is very small, what is the shortest possible time in which the proton can reach its maximum possible kinetic energy?

Explanation / Answer

   In cyclotron , when the proton is circulates in the dees , The magnetic force acting on the proton is equal to centripetal force acting on the proton mathematically, magnetic force cting on the proton : F = Q V B where Q is the charge on the proton             V be the velocity of the proton             B is the applied mangnetic field     lly,         centripetal force actingon the proton is :             F = M R W2      where R is th eradious of th e cyclotron            M is the   mass of the proton            W is the angualr frquency          thus,     Q VB = M RW2           As V = RW               W = B Q/ M thus, Time period or time taken for maximum kinetic energy attain is :        T = 2 /W         T = 2 M / BQ       where M = 1.67 x10-27 Kg                 B = 0.85 T                  Q = + 1.6x10-19 C     thus, T = 2(3.14) (1.67x10-27)/ (0.85)(1.6x10-19)               = [10.4876 / 1.36] x                  = 7.711x 10-8 sec                    or              time : T = 0.711ns           As V = RW               W = B Q/ M thus, Time period or time taken for maximum kinetic energy attain is :        T = 2 /W         T = 2 M / BQ       where M = 1.67 x10-27 Kg                 B = 0.85 T                  Q = + 1.6x10-19 C     thus, T = 2(3.14) (1.67x10-27)/ (0.85)(1.6x10-19)               = [10.4876 / 1.36] x                  = 7.711x 10-8 sec                    or              time : T = 0.711ns

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