Please do all steps to the question and have legiable handwritting. A cyclotron

Question

Please do all steps to the question and have legiable handwritting.

A cyclotron designed to accelerate protons has an outer radius of 0.850 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 dees. The dees are between the poles of an electromagnet where the field is 0.390 T. (a) Find the cyclotron frequency for the protons in this cyclotron. rad/s (b) Find the speed at which protons exit the cyclotron. m/s (c) Find their maximum kinetic energy. eV (d) How many revolutions does a proton make in the cyclotron? revolutions (e) For what time interval does one proton accelerate? s

Explanation / Answer

r =0.85 m , B =0.39 T , V =600 V , proton mass =1.67*10^-27 kg

charge of proton e =1.6*10^-19C

(a) F =qvB =mv^2/r

qB = m(v/r)

v =rw, w =2pi*f

qB = mw

w = (1.6*10^-19*0.39)/(1.67*10^-27)

w = 3.7*10^7 rad/s

(b) v = rw

v =(0.85*5.95*10^6)

v = 5.06*10^6 m/s

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

K = (0.5*1.67*10^-27*5.06*5.06*10^12)/(1.6*10^-19)

K = 133618.8 eV

(d) w =2pi*f

f = 5.95*10^6Hz

cyclotron makes 5.95*10^6 revolutions in one second.

(e) T =1/f

T = 1/(5.95*10^6)

T = 1.68*10^-7 s

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