A proton circulates in a cyclotron, beginning approximately at rest at the cente

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 270 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 10 passes through the gap? (c) Let r10 be the radius of its circular path in the dee that it enters as it completes those 10 passes, and let r11 be its next radius, as it enters a dee the next time. By what percentage does the radius increase when it changes from r10 to r11? (r11 - r10) / r10%)

Explanation / Answer

Assuming that there is a synchronous magnetic field to keep it in a circular orbit, the energy gained on each passage through 270V is
A)E = qV = 1.602 x 10^-19 x 270 = 4.3254 x 10^-17 J or 270 eV.
b)After 10 passes
10 x 270 = 2700 keV

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