Hall effect

Consider a strip carrying current through a magnetic field directed perpendicular to the strip. The magnetic part of the Lorentz force deflects moving charge carriers toward one side. Charge then accumulates on opposite edges, setting up a transverse electric field. The growing electric force eventually balances the sideways magnetic force, leaving a measurable potential difference across the material: the Hall voltage. Reversing the magnetic field or current reverses the voltage polarity.

In a simple model with one dominant carrier type, a rectangular sample of thickness t carrying current I in a perpendicular field B has Hall voltage magnitude V_H = R_H I B / t, where R_H is the Hall coefficient. For a single carrier population of charge q and volume density n, R_H = 1/(nq), with its sign dependent on the charge convention and carrier type. Thus, with the geometry, current, and field known, a Hall measurement can estimate carrier density. Conversely, if the material's carrier response is calibrated, the voltage can be used to measure magnetic field. Real materials may have multiple carrier bands, complex geometry, or temperature-dependent coefficients, so the simple one-carrier expression is an approximation rather than a universal formula.

The sign of the Hall voltage, interpreted with the chosen orientation of current and magnetic field, indicates the sign of the dominant mobile charge carriers in the basic one-carrier case. This made the effect particularly useful in semiconductor physics, where conduction may be dominated by negatively charged electrons or by positively behaving holes. The interpretation requires care: actual semiconductor samples can contain both carrier types, and their relative contributions can affect the measured Hall coefficient.

Edwin Herbert Hall reported the effect in 1879 while investigating the action of a magnetic field on current in a metal strip. The classical effect produces a transverse voltage that varies with magnetic field under ordinary conditions. In two-dimensional electron systems at low temperatures and strong fields, the Hall resistance can instead show quantized plateaus: this is the quantum Hall effect, a distinct quantum phenomenon built on the same basic transverse measurement. Klaus von Klitzing's discovery of the integer quantum Hall effect was recognized with the 1985 Nobel Prize in Physics.

Hall sensors and probes convert the transverse voltage into a practical magnetic-field measurement; they are used in laboratory instruments and electronic sensing systems. In materials research, Hall measurements can identify the dominant carrier sign and estimate carrier density and mobility when paired with electrical-resistance measurements. Measurements can be small and sensitive to contact placement, sample uniformity, temperature gradients, and unwanted thermoelectric voltages. Researchers therefore control the geometry and often reverse the current or magnetic field to separate the Hall signal from offsets.