Verify that the cyclotron frequency

Question:

Verify that the cyclotron frequency ꞷ = eB/m has the correct dimensions of [T]-1.

Solution:

The path traced by the particle in a cyclotron is a circular path in which magnetic force acts as a centripetal force

mv2/R = evB

eB/m = v/R = ꞷ

B = F/ev = [MLT-2]/[AT][LT-1] = [MA-1T-2] [ꞷ] = [eB/m] = [v/R] = [T]-1

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