Question

A proton circulates in a cyclotron, beginning approximately at rest at the center. Whenever it passes through the gap between dees, the electric potential difference between the dees is 160 V. (a) By how much does its kinetic energy increase with each passage through the gap? (b) What is its kinetic energy as it completes 132 passes through the gap? (c) Let r 132 be the radius of the proton's circular path as it completes those 132 passes and enters a dee, and let r 133be its next radius, as it enters a dee the next time. By what percentage does the radius increase when it changes from r 132 to r 133? That is, what is percentage increase = (r 133 - r 132)/r 132*100%?

Answer 1

(a) We Know from the energy conservation
Kinetic energy = potential energy
Kinetic energy = charge*potential = (1.6*10^-19)*160
Kinetic energy = 256*10^-19 J
Hence kinetic energy will increase in each pass by 256*10^-19 J
(b) After 132 passes
Kinetic energy will be (K₁₃₂) = 132*256*10^-19 = 33.792*10^-16 J
(c) We know that
K₁₃₃ = 133*(256*10^-19 ) = 34.048*10^-19 J

Now R after 132 passes


Percentage increase =


= 0.378 %