The Hall Effect
The Hall Effect is a very useful method for finding the drift velocity or mean free time between collisions for the carriers in a conductor.
The experiment involves placing a sample of the solid at the intersection of crossed electric and magnetic.
If a small rectangular piece of semiconductor is placed in crossed electric and magnetic fields the force on the charge carriers moving under the influence of the applied field is
F = qv x B
This produces a separation of carriers and induces an electric field Ey and a Hall voltage VH perpendicular to Bz and jx . At equilibrium the force due to the internal field balances the Lorentz force on the carriers
where the current density
The current flows in the x-direction, while the induced E-field is in the y-direction and the B-field is in the z-direction. Here y is the thickness of the sample in the y-direction.
The Hall coefficient RH is defined by
where N is the carrier density and e the charge on the carriers and
In the Hall experiment we measure VH, z, Ix and Bz and calculate RH and hence N.