Solution:
Given: Linear speed of proton v = 3 x 10^8 m/s, current i = 12 mA,
Circumference = 7500 m, and Proton charge q = 1.609 x 10^-19 C
Radius of collider R = Circumference/2pi = 7500/(2x3.142) = 1193.66 m
Angular speed proton ω = v/R = 3 x 10^8/1193.66 = 2.5133 x 10^5 rad/s
Period T = 2pi/angular speed = 2pi/(2.5133 x 10^5) = 25 x 10^-6 sec
Current through beam i = total charge Q/time for one loop T
Total charge Q = i x T = 12 x 10^-3 x 25 x 10^-6 = 3 x 10^-7 C
Number of protons in beam = total charge/charge per proton
= 3 x 10^-7/1.609 x 10^-19 = 1.8645 x 10^12 protons
= 1.8645 Trillion protons
I hope this answers your question and helps.
Shailesh Kadakia, Expert Math and Physics tutor
Former Professor, University of Pittsburgh PA
