Question

Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]^–1.

Answer 1

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]`