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# Hall effect

The Hall effect refers to the potential difference (voltage) on opposite sides of a thin sheet of conducting or semiconducting material in the form of a 'Hall bar' or a van der Pauw element through which an electric current is flowing, created by a magnetic field applied perpendicular to the Hall element. The ratio of the voltage created to the amount of current is known as the Hall resistance, and is a characteristic of the material in the element. Dr. Edwin Hall discovered this effect in 1879.

## Analysis

The Hall effect comes about due to the nature of the current flow in the conductor. Current consists of many small charge-carrying "particles" (typically electrons) which see a force due to the magnetic field. Some of these charge elements end up forced to the sides of the conductors, where they create a pool of net charge. This is only notable in larger conductors where the separation between the two sides is large enough.

One important feature of the Hall effect is that it differentiates between positive charges moving in one direction and negative charges moving in the opposite. The Hall effect offered the first real proof that electric currents in metals are carried by moving electrons, not by protons. Interestingly enough, the Hall effect also showed that in some substances (especially semiconductors), it is more appropriate to think of the current as positive "holes" moving rather than negative electrons.

By measuring the Hall voltage across the element, one can determine the strength of the magnetic field applied. This can be expressed as $V_H = \frac{IB}{den}$ where VH is the voltage across the width of the plate, I is the current across the plate length, B is the magnetic field, d is the depth of the plate, e is the electron charge, and n is the bulk density of the carrier electrons.

So called Hall effect sensors are readily available from a number of different manufacturers, and may be used in various sensors such as fluid flow sensors, power sensors , and pressure sensors.

In the presence of large magnetic field strength and low temperature, one can observe the quantum Hall effect, which is the quantization of the Hall resistance.

In ferromagnetic materials, the Hall resistivity also shows an anomalous contribution, known as the Anomalous Hall Effect, proportional to the magnetization of the material. Although a well-recognised phenomena, there is still debate about its origins.

Chemicals