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  4. A cyclotron is accelerating proton, where the applied magnetic field is 2 T and the potential gap is 100 textkeV . To acquire kinetic energy of 20 textMeV , the number of turns, the proton has to move between the dees is

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Q. A cyclotron is accelerating proton, where the applied magnetic field is $2 \, T$ and the potential gap is $100 \, \text{keV}$ . To acquire kinetic energy of $20 \, \text{MeV}$ , the number of turns, the proton has to move between the dees is

NTA AbhyasNTA Abhyas 2022

Solution:

Energy gained in one movement across the gap is $100 \, \text{keV}$
Therefore the energy gained in one turn is $200 \, \text{keV}$
$N=\frac{20 \, M e V}{200 \, \text{keV}}=\frac{20 \times 1 0^{6}}{200 \times 1 0^{3}}=100$