When electrons (or holes) move in a conducting plate that is immersed in a magnetic field, they experience a Lorentz force

(in MKS),where q is the charge,E is the electric field, v is the velocity,and B is the magnetic field.Note that the second term is transverse to velocity and to the magnetic field. Therefore, if sensing electrodes are placed across the transverse dimension of the plate, a voltage, called the Hall voltage, will appear.

Ignoring scattering, and for an ideal plate geometry, the Hall voltage can be written in terms of the current as

where I is the current (in amps), B is the magnitude of the magnetic field (in tesla) component transverse to the current, the carriers have charge q (in Coulombs), n is the number density of charge carriers (in ),t is the thickness of the plate (in meters), and

is the Hall coefficient, measured in

We may also write an expression for the Hall voltage in terms of the impressed potential V (in volts) that drives the current,

where is is the mobility (in ) of the carriers, and the plate has width w and length l.From these considerations, we see that a Hall sensor or sample in a Hall measurement should have low carrier density, but the carriers should have high mobility. For maximum the plate will have and deviations from this condition will require geometrical corrections to these simple formulas. Also, the area of the contacts must be minimal. Since semiconductors have much smaller carrier concentrations than metals, they are preferred for Hall sensors.

To a rough approximation,

where is the resistivity of the plate (measured in Ohm-meters). In this formula, is actually the Hall mobility, so measuring the Hall voltage is a way of measuring mobility in a material.