How is the drift speed of a charge carrier in a conductor directly proportional to the electric field at the location of the charge carrier?

Question

I doubt if it is an empirical relation because it is not possible to measure physically, the drift speed of electrons in a conductor. Is it a fundamental assumption that we make? if so, what is the reason for this assumption? Or can it be proved mathematically?

Answer 1

I doubt if it is an empirical relation because it is not possible to measure physically, the drift speed of electrons in a conductor.* However, it can be demonstrated for coloured ions.