A cyclotron designed to accelerate protons has an outer radius of 0.830 m. The p

Question

A cyclotron designed to accelerate protons has an outer radius of 0.830 m. The protons are emitted nearly at rest from a source at the center and are accelerated through 600 V each time they cross the gap between the does. The does are between the poles of an electromagnet where the field is 0.890 T. Find the cyclotron frequency for the protons in this cyclotron. Find the speed at which protons exit the cyclotron. Find their maximum kinetic energy. Your response differs from the correct answer by more than 10%. Double check your calculations. Ev How many revolutions does a proton make in the cyclotron? Revolutions For what time interval does one proton accelerate? s

Explanation / Answer

r = 0.83 m , V =600 V, B =0.89 T

(a) Centripetal force = magnetic force

mv^2/r = qvB

mv/r = qB

v/r = w

mw =qB

mass of proton m = 1.67*10^-27 kg, q =1.6*10^-19 C

(1.67*10^-27*w^2) = (1.67*10^-19*0.89)

w=9434 rad/s

(b) v =rw

v = 0.83*9434 =7830.2 m/s

(c) K =(1/2)mv^2

K =0.5*1.67*10^-27*7830.2*7830.2/(1.6*10^-19)

K =0.32 eV

(d) f = w/2pi

f= 9434/(2*3.14) = 1502 revolutions

(e) T =1/f

T = (1/1502) = 6.66*10^-4 s

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