In a non-relativistic cyclotron, a particle gains the same kinetic energy ΔK at every gap crossing. If rₙ is the orbit radius immediately after the nth equal energy gain, how does rₙ depend on n?
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In a non-relativistic cyclotron, a particle gains the same kinetic energy ΔK at every gap crossing. If rₙ is the orbit radius immediately after the nth equal energy gain, how does rₙ depend on n?

G1 Physics · Accepted Answer

Kₙ=nΔK and r=p/(qB)=√(2mKₙ)/(qB), so rₙ∝√n.