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$(A)$ In a cyclotron, a particle gains energy equal to $qV$ every time it crosses the gap between the two "dees".Since there are two gaps per revoluti

Vedclass · Accepted Answer

$100$

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$(A)$ In a cyclotron, a particle gains energy equal to $qV$ every time it crosses the gap between the two "dees".Since there are two gaps per revolution, the energy gained per revolution is $\Delta E = 2qV$.Given: Potential difference $V = 100 \,kV = 10^5 \,V$.Energy gained per revolution $= 2 	imes e 	imes 10^5 \,V = 2 	imes 10^5 \,eV$.Target kinetic energy $E = 20 \,MeV = 20 	imes 10^6 \,eV = 2 	imes 10^7 \,eV$.Number of revolutions $n = \frac{E}{\Delta E} = \frac{2 	imes 10^7 \,eV}{2 	imes 10^5 \,eV} = 100$.

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

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