The Hall effect is the appearance of a voltage transverse to a current flowing through a conductor or semiconductor when a magnetic field is applied perpendicular to the current. The voltage is proportional to both the current and the magnetic field, which makes the effect the basis of practical magnetic-field sensors. Edwin Hall discovered it in 1879 at Johns Hopkins, eighteen years before the electron itself was identified — the measurement was a tour de force for the apparatus of the time.
The mechanism is the Lorentz force. Charge carriers moving through a conductor at velocity in a magnetic field experience a force . The force pushes carriers to one side of the conductor, and they accumulate there until the electrostatic field they create balances the magnetic force. The resulting potential difference across the conductor — measured transverse to the current — is the Hall voltage:
where is the current, is the magnetic field perpendicular to the current, is the carrier density, is the carrier charge, and is the thickness of the sample. Semiconductors give large Hall voltages because is small, which is why the effect is most useful in semiconductor-based sensors.
The Hall effect is the standard sensing principle inside a Magnetometer — pass a known current through a semiconductor, measure the transverse voltage, and infer the magnetic field. Magnetometers are in turn used as one of the three sensors inside an IMU, where they provide the absolute reference to magnetic north that anchors orientation estimates.