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Question
Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]–1.
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Solution
In cyclotron, charge particle describes the circular path where the magnetic force acts as centripetal force.
`(mv^2)/R = ev B`
On simplifying the terms, we have
∴ `(eB)/m = v/R = ω`
We know that `B = F/(ev) = ([MLT^-2])/([AT][LT^-1]) = [MA^-1T^-2]`
And then dimensional formula of angular frequency
∴ [ω] = `[(eB)/m] = [v/R]`
[ω] = `([AT][MA^-1T^-2])/([M]) - [T^-1]`
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