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Consider a proton cyclotron with a radius 3 meters, a magnetic field B=0.6 T and a...

Consider a proton cyclotron with a radius 3 meters, a magnetic field B=0.6 T and a voltage source with an amplitude V = 10 kV.

What is the maximum energy in joules the protons can reach?

To reach the same energy using a single DC potential, how many volts would be required?

How long would it take for a proton starting at rest to reach this energy? (hint how much work is done on the proton in each full orbit?) What fraction of the speed of light (c) does this proton reach? Do the calculation using the energy-based mass unit for the proton m= 938 MeV/c^2, without invoking joules or kilograms or the numerical value of c

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