The operating frequency of a cyclotron remains practically constant even though the…
PHYSICS · Single correct · AP · Physics C: Electricity and Magnetism · Magnetic Fields and Electromagnetism · Magnetic Fields and Electromagnetism
Problem
The operating frequency of a cyclotron remains practically constant even though the radius of the particle’s path keeps increasing. Which one of the following statements best explains this observation in the non-relativistic limit?
(a) The cyclotron’s radio-frequency oscillator fixes the time period; the particle merely adjusts its motion to stay in step, so the operating frequency is inherently constant.
(b) The radius increases in direct proportion to the speed so that the ratio v/r (and hence the angular frequency qB/m) remains constant for a given B.
(c) As the particle’s speed rises, the magnetic force acting on it becomes smaller, compensating for the larger path and keeping the period unchanged.
(d) Inside each dee, the electric field exactly cancels the magnetic field, producing uniform circular motion with a fixed period.