An alternating electric field, of frequency ν, is applied across the dees (radius = R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by

Question

Dr. Abubacker · Accepted Answer

[Solution from source] The dee voltage frequency must equal the cyclotron frequency ν = eB/(2πm), so B = 2πmν/e. At the dee radius R, v = eBR/m = 2πνR, so K = ½mv² = ½m(2πνR)² = 2π²mν²R². B = mν/e misses the 2π factor between ν and angular frequency. Answer (4).

Q. An alternating electric field, of frequency ν, is applied across the dees (radius = R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by

Explanation

Reviewed by Dr. Abubacker

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