5 Problem 16 A cyclotron accelerates charged particles of ma

(5%) Problem 16: 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 AC voltage Dees ©theexpertta.com 50% Part (a) Find the frequency fof the accelerating voltage needed for a proton in terms of the variables given in the problem Grade Summary Deductions Potential 0% 100% 78 9HOME Submissions Attempts remaining: 7 % per attempt) detailed view 1|2|3| 0 ENID BACKSPACE DEL CLEAR Submit Hint I give up! Hints: 0% deduction per hint. Hints remaining: Feedback: 0%-deduction per feedback. 50% Part (b) Calculate the frequency, in megahertz, of the accelerating voltage needed for a proton in a 1.35-T field

Solution

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

Time period, T = 2*pi*r/v

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

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

but we know, f = 1/T

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

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

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

= 2.06*10^7 Hz

= 20.6 Mhz