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

For a moving charged particle of mass m and charge e, moving perpendicularly to the direction of magnetic field B, the magnetic field will make it move in a circular motion. If the velocity of the particle is v, then `qvB = (mv^(2))/r ` [r is the radius of circular path]
` rArr " " v/r = (eB)/m`
`rArr" " omega = v/r`
Here, `omega` is the angular frequency of rotation of the particle and its dimensions can be calculated as below:
` omega = ([LT^(-1)])/([L]) = [T^(-1)]`
The time period of revolution of charged particle is given by:
`T = (2 pim)/(eB)`
` :. ` The frequency of revolution is
` v = 1/T = (eB)/(2 pi m) `
It also has the dimension of `[T^(-1)]` .
It also has the dimension of `[T^(-1)]`.
It is not possible to construct dimensionless
quantities using the quantities given in the question.