What is the Hall Effect?

If you ask a person familiar with physics at the level of only basic knowledge of what the Hall effect is and where it is applied, you can not get an answer. Surprisingly, this is happening quite often in the realities of the modern world. In fact, the Hall effect is used in many electrical devices. For example, the once popular computer floppy disk drives determined the initial position of the engine with the help of Hall generators. The corresponding sensors "migrated" to the schemes of modern drives for CDs (both CD and DVD). In addition, the fields of application include not only various measuring instruments, but even electric energy generators based on the conversion of heat into a flux of charged particles under the action of a magnetic field (MHD).

Edwin Herbert Hall in 1879, conducting experiments with a conducting plate, discovered an uncaused, at first glance, phenomenon of the appearance of a potential (voltage), in the interaction of an electric current and a magnetic field. But first things first.

Let's do a little thought experiment: take a metal plate and let it flow electric current. Next, we place it in an external magnetic field in such a way that the lines of field strength are oriented perpendicular to the plane of the conductive plate. As a result, a potential difference appears on the faces (across the direction of the current) . This is the Hall effect. The reason for his appearance is the famous Lorentz force.

There is a way to determine the value of the resulting voltage (sometimes called the Hall potential). The general expression takes the form:

Uh = Eh * H,

Where H is the plate thickness; Eh is the external field strength.

Since the potential arises from the redistribution of charge carriers in a conductor, it is limited (the process does not continue indefinitely). The transverse displacement of charges stops at the moment when the Lorentz force (F = q * v * B) is equalized with the counteraction q * Eh (q is the charge).

Since the current density J is equal to the product of the concentration of charges, their speed and unit value q, that is,

J = n * q * v,

respectively,

V = J / (q * n).

This implies (by relating the formula to the strength):

Eh = B * (J / (q * n)).

Combine all of the above and determine the Hall potential through the value of the charge:

Uh = (J * B * H) / n * q).

The Hall effect allows us to state that sometimes in metals, not electronic, but hole conductivity is observed. For example, this is cadmium, beryllium and zinc. Studying the Hall effect in semiconductors, no one doubted that charge carriers are "holes". However, as already indicated, this applies to metals. It was believed that in the distribution of charges (formation of the Hall potential), the common vector will be formed by electrons (negative sign). However, it turned out that electrons are not created in the field at all. In practice, this property is used to determine the density of charge carriers in a semiconducting material.

No less known is the quantum Hall effect (1982). It is one of the properties of the conductivity of a two-dimensional electron gas (particles can move freely only in two directions) under conditions of ultralow temperatures and high external magnetic fields. When studying this effect, the existence of "fractionality" was discovered. One gets the impression that the charge is formed not by individual carriers (1 + 1 + 1), but by constituent parts (1 + 1 + 0.5). However, it turned out that no laws are violated. In accordance with the Pauli Principle, around each electron in a magnetic field a peculiar vortex is created from the quanta of the flux itself. With increasing intensity of the field, a situation arises where the correspondence "one electron = one vortex" ceases to be satisfied. Each particle has several magnetic flux quanta . These new particles are precisely the cause of the fractional result with the Hall effect.