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(8%) Problem ii: A cyclotron accelerates charged particles of mass m as shown in

ID: 1866098 • Letter: #

Question

(8%) Problem ii: A cyclotron accelerates charged particles of mass m as shown in the figure. The magnetic field B contains the particles within the machine while the electric field in the gap accelerates the particles. Since the particles pass through the electric field in both directions, the frequency of the AC source must match the frequency of the particle motion. Dees Otheexpertta.com 50% Part (a) Find the frequency/of theaccelerating voltage needed for a proton interns of the variables given in hep 50% Part (b) Calculate the frequency, in megahertz, of the accelerating voltage needed for a proton in a , 35-T field. blem.

Explanation / Answer

a) we know, radius of orbit of charge particle, r = m*v/(B*q)

we know, time period of charged particle, T = 2*pi*r/v

= 2*pi*(m*v/(B*q))/v

= 2*pi*m/(B*q)

so, frequency, f = 1/T

= B*q/(2*pi*m)

b) we know

for proton, q = 1.6*10^-19 C

m = 1.67*10^-27 kg

so, f = 1.35*1.6*10^-19/(2*pi*1.67*10^-27)

= 2.06*10^7 Hz