If you ask a person who is familiar with physics at the level of only basic knowledge about what the Hall effect is and where it is applied, there is no answer. Surprisingly, in the realities of the modern world this happens quite often. In fact, the Hall effect is used in many electrical devices. For example, the once popular computer disk drives for floppy disks determined the initial position of the engine using Hall generators. The corresponding sensors “migrated” to the circuitry of modern CD drives (both CD and DVD). In addition, applications include not only various measuring instruments, but even electric energy generators based on the conversion of heat into a stream of charged particles under the influence of a magnetic field (MHD).
Edwin Herbert Hall in 1879, conducting experiments with a conductive plate, discovered a seemingly causeless phenomenon of the appearance of potential (voltage) due to the interaction of electric current and magnetic field. But first things first.
Let's do a little thought experiment: take a metal plate and pass an electric current through it. Next, we place it in an external magnetic field so that the field strength lines are oriented perpendicular to the plane of the conductive plate. As a result, a potential difference arises on the faces (across the direction of the current) . This is the Hall effect. The reason for his appearance is the well-known power of Lorentz.
There is a way to determine the magnitude of the arising voltage (sometimes called the Hall potential). The general expression takes the form:
Uh = Eh * H,
where H is the thickness of the plate; Eh is the external field strength.
Since the potential arises due to the redistribution of charge carriers in the conductor, it is limited (the process does not continue indefinitely). The transverse movement of charges will stop at the moment when the value of the Lorentz force (F = q * v * B) equals the counteraction q * Eh (q is the charge).
Since the current density J is equal to the product of the concentration of charges, their velocity and unit value q, i.e.
J = n * q * v,
respectively,
v = J / (q * n).
From here follows (having connected the formula with tension):
Eh = B * (J / (q * n)).
Combine all of the above and determine the potential of the hall through the value of the charge:
Uh = (J * B * H) / n * q).
The Hall effect allows us to assert that sometimes in metals not hole but electron conductivity is observed. For example, these are cadmium, beryllium and zinc. Studying the Hall effect in semiconductors, no one doubted that charge carriers were “holes”. However, as already indicated, this applies to metals. It was believed that during the distribution of charges (the formation of the Hall potential), the general vector will be formed by electrons (negative sign). However, it turned out that not electrons create the current in the field. In practice, this property is used to determine the density of charge carriers in a semiconducting material.
The quantum Hall effect (1982) is no less known. It is one of the properties of the conductivity of a two-dimensional electron gas (particles can only move freely in two directions) under conditions of ultra-low temperatures and high external magnetic fields. When studying this effect, the existence of "fragmentation" was discovered. It seemed that the charge is formed not by single carriers (1 + 1 + 1), but by constituent parts (1 + 1 + 0.5). However, it turned out that no laws were violated. In accordance with the Pauli Principle, a kind of vortex is created around each electron in a magnetic field from the quanta of the stream itself. With increasing field intensity, a situation arises when the correspondence “one electron = one vortex” ceases to be fulfilled. Each particle has several quanta of magnetic flux. These new particles are precisely the reason for the fractional result with the Hall effect.