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  • A charged particle of charge e and mass m is moving in an electric field E, and magnetic field B. Construct dimensionless quantities and quantities of dimension [T]^-1

A charged particle of charge e and mass m is moving in an electric field E, and magnetic field B. Construct dimensionless quantities and quantities of dimension [T]^{-1 }

Answers (1)

When a charged particle is moving in both electric and magnetic field, the physical quantities can no  help to construct dimensional quantity.

The necessary centripetal force is provided by the magnetic Lorentz forces when a charged particle is moving perpendicular to the magnetic field.

 

\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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