All Problems

Motion of Charged Particles in Electric and Magnetic Fields

Problem 3.396

The cyclotron's oscillator frequency is equal to \(v=10 \mathrm{MHz}\). Find the effective accelerating voltage applied across the dees of that cyclotron if the distance between the neighbouring trajectories of protons is not less than \(\Delta r=1.0 \mathrm{~cm},\) with the trajectory radius being equal to \(r=0.5 \mathrm{~m}\).

Reveal Answer
V2π2v2mrΔr/e=0.10MVV \geqslant 2 \pi^{2} v^{2} m r \Delta r / e=0.10 \mathrm{MV}