A cyclotron (see figure below) designed to accelerate protons has an outer radiu

Question

A cyclotron (see figure below) designed to accelerate protons has an outer radius of 0.333 m. The protons are emitted nearly at rest from a source at the center and are accelerated through 662 V each time they cross the gap between the dees. The dees are between the poles of an electromagnet where the field is 0.776 T.

(a) Find the cyclotron frequency for the protons in this cyclotron.

(b) Find the speed at which protons exit the cyclotron.


(c) Find their maximum kinetic energy.


(d) How many revolutions does a proton make in the cyclotron?



(e) For what time interval does the proton accelerate?

Explanation / Answer

given potentila difference delV =  662V outer radius is R = 0.333m. magnetic field B = 0.776T mass of the proton is m = 1.67*19-27kg charge of the proton is q = 1.6*10-19C a) the cyclotron frequency is       w = qB/m            =0.7434730538922156 *10^6--------- b) the speed at which protons exit the cyclotron is      v = BqR/m        =24757652.6946 --------- c) maximum kinetic energy is    KEmax = 1/2*mv2                = 5.1180601e-13 ----------- 5.1180601e-13 d) the number of revolutions is    n = R2B2q/2mv       =1.29 =1 ---------- e) the time interval is t = n(2pi/w)                                 =0.00000844687 ---------

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