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

Verify that the cyclotron frequency \omega = e\frac{B}{}m has the correct dimensions of [T]^{-1}.

Answers (1)

In the device cyclotron, a circular path is followed by the accelerating particle duet eh magnetic field acting as a centripetal force.

\frac{mv^{2}}{R}=evB

On simplifying the terms, we have

\therefore \frac{eB}{m}=\frac{v}{R}=\omega

We know that 

B = \frac{F}{eV}=\frac{[MLT^{2}]}{[AT][LT^{-1}]}=[MA^{-1}T^{-2}]

And then dimensional formula of the angular frequency

 [\omega]= \left [\frac{eB}{m} \right ]=\left [\frac{v}{R} \right ]

[\omega ]=\frac{[AT][MA^{-1}T^{-2}]}{[M]}=[T^{-1}]

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infoexpert24

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