The Hall effect occurs when a magnetic field is applied to an electrical current in a conductor, resulting in a voltage being generated perpendicular to the direction of the current. The magnetic field produces a force on the charge carriers in the conductor (usually electrons) perpendicular to their direction of travel. This causes them to accumulate on one side of the conductor. This separation of electric charge produces an electric field and so a voltage. There is an analogous quantum mechanical effect, known as the Quantum Hall effect.
The effect was first identified by the physicist Edwin Herbet Hall in 1879. The Hall effect has uses such as Hall probes, which allow one to measure large magnetic fields (around 1 Tesla) and can also be used to find the drift velocity of electrons in conductors.
Suppose a current I is flowing through a square wire and the wire is in a uniform magnetic field B that points out through the top of the wire. The current I can be written as I = neAvd, where n is the number density of charge carriers (how many there are per unit volume), e is the elementary charge, A is the cross sectional area of the wire and vd is the drift velocity of the charge carriers. the force due to the magnetic field is FM = eBvd or:
When the charge carriers separate, they produce an electric field, the force of which on a carrier is FE = VHe/W, with VH being the Hall voltage and W the width of the wire. At equilibrium, these two forces are equal and opposite, so the Hall voltage is:
For most metals, this voltage is negative, indicating that the charge flowing through a metal is negative (electrons). However, some metals such as aluminium, zinc and cadmium, the Hall voltage is positive, suggesting positive charge is flowing. These are known as "holes" and have important consequences in semiconductors.