In a cyclotron, why is the orbital frequency of a circulating non-relativistic ion independent of its orbital radius?
Answer and explanation
Correct answer: D. f = qB / (2pi*m)
- Step 1: Equating magnetic force to centripetal force: qvB = mv^2 / r gives v = qBr / m. Step 2. Orbital period T = 2pir / v = 2pim / (qB). Cyclotron frequency f = 1/T = qB / (2pim), independent of r and v. Answer: f = qB / (2pim). Why not the others:* At relativistic speeds, ion mass increases (gammam), causing particles to fall out of phase with constant RF drive.
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