Problem 8 he cyclotron (see figure) is a device used to accelerate elementary pa
ID: 2031103 • Letter: P
Question
Problem 8 he cyclotron (see figure) is a device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B The particles are accelerated to higher speeds each time they pass through the gap between the metal 'dees," where there is an electric field E. (There is no electric field inside the hollow metail dees ) The clectric fickd changes direction each half -cycle, owing to an AC voltage V- Vo sin2nfo.so that the particles are increased in speod at each passage through the gap 0 T.what is the masimum kinetic energy of accelerated protons in ev? If the radius of the cyelotron is 7.930x10 m, and the magnetic field strength 4.750x The charge of a proton is 1,600x 10C and the mass is 1 8070107 kg. I ectron vult is 1,600x 1019 ev An Tries OW 12 minutesExplanation / Answer
we know,
maximum radius of the orbit of charged particle,
r_max = m*v_max/(B*q)
v_max = B*q*r_max/m
= 4.75*10^-1*1.6*10^-19*7.93*10^-1/(1.67*10^-27)
= 3.609*10^7 m/s
maximum kinetic energy, KE_max = (1/2)*m*v_max^2
= (1/2)*1.67*10^-27*(3.609*10^7)^2
= 1.088*10^-12 J
= 1.088*10^-12/(1.6*10^-19) eV
= 6.80*10^6 eV <<<<<-------Answer