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.

The quantities provided are charge, electric field and magnetic field. Using these three we can never eliminate the units to unity. Hence, there is no such constructible dimensionless quantity.

[T]^-1 is the dimension of frequency.

The time period of a cyclotron is,

Hence the frequency is going to be,

This is the [T]^-1 quantity.