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Verify that the cyclotron frequency omeg...

Verify that the cyclotron frequency `omega=(eB)/m` has the correct dimensions of `[T]^(-1)`.

Text Solution

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When charge particle enter perpendicular magnetic field it provides the centripetal force for revolution. So,
`(mv^(2))/R=qvB`
`therefore(mv)/R=qB`
but `v/R=omegaandq=e`
`omega=(eB)/m=v/R`
`therefore[omega]=[(eB)/m]=([v])/([R])`
= `(M^(0)L^(1)T^(-1))/L^(1)`
= `M^(0)L^(0)T^(-1)=[T^(-1)]`
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Knowledge Check

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