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  4. A proton is accelerating in a cyclotron where the applied magnetic field is 2 T. If the potential gap is effectively 100 kV then how much revolutions the proton has to make between the dees to acquire a kinetic energy of 20 MeV ?

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Q. A proton is accelerating in a cyclotron where the applied magnetic field is $2\, T$. If the potential gap is effectively $100 \,kV$ then how much revolutions the proton has to make between the "dees" to acquire a kinetic energy of $20\, MeV ?$

Moving Charges and Magnetism

Solution:

Energy increased in each revolution $=2 \times 100 \times 10^{3} \,eV$
$=2 \times 10^{5} \,eV$
Now for energy $E=2 \times 10^{7} \,eV$
Number of revolution $=\frac{2 \times 10^{7} \,eV }{2 \times 10^{5} \,eV }=100$