Cyclotron accelerating protons to 20 MeV with potential gap 100 kV

AI Thread Summary
A cyclotron is used to accelerate protons to achieve a kinetic energy of 20 MeV with a potential gap of 100 kV and an applied magnetic field of 2 T. The energy gained per turn is determined by the equation qV, where q is the charge of the proton and V is the potential gap. To calculate the number of turns required to reach 20 MeV, the total energy must be divided by the energy gained per turn. The discussion highlights that relativistic effects become significant around 20 MeV, indicating a need for careful consideration in calculations. Ultimately, the solution involves determining the correct number of turns based on these parameters.
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Homework Statement


A Cyclotron is accelerating proton, where the applied magnetic field is 2 T, the potential gap is 100 KV, then how much turn are required for a kinetic energy of 20 MeV...

(a) 300
(b) 200
(c) 150
(d) 100
 
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20MeV is around when relativistic effects take place. The voltage alternates periodically. After one turn (or half a turn--semicircle...I'm not sure) the proton gains a kinetic energy of qV, V being the potential gap. Using that value, find out how many turns it takes to total 20MeV.
 

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