Problem 8 The cyclotron (see figure) is a device used to accelerate elementary p
ID: 779112 • Letter: P
Question
Problem 8 The 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 metal dees.) The electric field changes direction each half cycle, owing to an AC voltage V Vo sin(2 ft), so that the particles are increased in speed at each passage through the gap ap If the radius of the cyclotron is 1.430 10 m, and the magnetic field strength 4.940x10 T, what is the maximum kinetic energy of accelerated protons in ev? (The charge of a proton i 1 6000-19 C and the mass is1 670 0-27 kg. I electron volt is 1.600-10-19) ev Submit Answer Tries 0/ Due Monday March 26 11:59 am (EDTExplanation / Answer
From force balance
Fc = Fm
mV^2/r = q*V*B
V = q*B*r/m
Now max kinetic energy is given by:
KE = 0.5*m*V^2
KE = 0.5*m*(qBr/m)^2
KE = (qBr)^2/2m
Using given values:
KE = (1.6*10^-19*4.94*10^-1*1.43*10^-1)^2/(2*1.67*10^-27)
KE = 3.82*10^-14 J = (3.82*10^-14)/(1.6*10^-19) eV
KE = 238750 eV
KE = 2.388*10^5 eV