User talk:Rocketmagnet/HallEffectScratch

Explanation
The Hall effect comes about due to the nature of the current flow in a conductor. Current consists of the movement of many small charge-carrying "particles" (typically, but not always, electrons). Normally, the electrons flow in the straightest possible line. However, if a magnetic field is present which is perpendicular to the flow of electrons, then the electrons will experience a force which is perpendicular to both the flow of electrons and the magnetic field. This force pushes the electrons to one side of the flow. This force is known as the Lorentz Force.

, when a magnetic field is present that is not parallel to their motion. When such a magnetic field is absent, the charges follow an approximately straight, 'line of sight' path. However, when a perpendicular magnetic field is applied, their path is curved so that moving charges accumulate on one face of the material. This leaves equal and opposite charges exposed on the other face, where there is a dearth of mobile charges. The result is an asymmetric distribution of charge density across the hall element that is perpendicular to both the 'line of sight' path and the applied magnetic field. The separation of charge establishes an electric field that opposes the migration of further charge, so a steady electrical potential builds up for as long as the current is flowing.

For a simple metal where there is only one type of charge carrier (electrons) the Hall voltage VH is given by

$$V_H = \frac{-IB/d}{ne}. $$

The Hall coefficient is defined as

$$R_H=\frac{V_H}{IB/d}=-\frac{1}{ne},$$

where I is the current across the plate length, B is the magnetic flux density, d is the depth of the plate, e is the electron charge, and n is the bulk density of the carrier electrons.

As a result, the Hall effect is very useful as a means to measure both the carrier density and the magnetic field.