The Hall effect is the production of a voltage difference across an electrical conductor transverse to an electric current and a magnetic field.In 1879, Edwin Hall, a student at Johns Hopkins University, experimented with thin gold foil. He noticed that the magnetic field not only bends the current but also creates a transverse potential difference. It turned out that the sign of the voltage depends on the sign of the charge carriers: in metals it is one way, and in semiconductors the opposite. Thus was born the method for determining the type of conductivity.
Edwin Hall discovered the effect in 1879, inspired by Maxwell's idea that the magnetic field should act on the conductor, not on the current directly. He used gold foil and a strong magnet, measuring the tiny voltage with a galvanometer. Subsequent research led to the discovery of the quantum Hall effect by Klaus von Klitzing in 1980.
Used for measuring magnetic fields, contactless current sensing, and in magnetoresistive sensors. In semiconductors, it is used for material characterization: by measuring R_H and conductivity, one finds mobility and carrier concentration. Limits: the weak-field condition where trajectories are nearly straight; in strong fields quantum effects appear.
Hall sensors are used in cars (ignition), phones (flip cover with a magnet), and for contactless magnetic field measurement.
The Hall effect revealed that in some semiconductors, current is carried by positive 'holes' rather than electrons — this was a surprise in the 20th century. And the quantum Hall effect, discovered a century later, provided a standard for electrical resistance.
| σ_H | variable | Hall conductivity — electrical conductivity siemens |
| ν | variable | Filling factor (integer or fractional) — filling factor |
| e | variable | Elementary charge — electric charge coulomb |
| h | variable | Planck constant — planck constant joule second |



















