A charged particle of charge e and mass m is moving in an electric field `vecE` and magnetic field `vecB`. Constant dimensionless quantities and quantities of dimention `[T]^-1`.

Explanation

No dimensionless quantity can be constructed using given quantities.
For a charge particle moving perpendicular to the magnetic field, the magnetic lorentz Forces provides necessary centripetal force for revolution.
`(mv^(2))/(R)=qvB`
On simplifying the terms, we have
`therefore(qB)/(m)=(v)/(R)=omega`
Finding the dimensional formula of angular frequency
`therefore[omega]=[(qB)/(m)]=[(v)/(R)]=[T]^(-1)`
This is the required expression.