Lawrence force and galvanomagnetic effects

Forces applied to moving charged particles

If an electrically charged particle moves in a surrounding magnetic field, then the internal magnetic field of that moving particle and the surrounding field interact, generating a force applied to the particle. This force tends to change the direction of motion of the particle. A single moving particle with an electric charge causes the appearance Bio-Savara magnetic field.

Although the Bio-Savart field, strictly speaking, is only generated by an infinitely long wire in which many charged particles move, the cross-section of the magnetic field around the trajectory of an individual particle passing through that particle has the same circular configuration.

However, the Bio-Savart field is constant in both space and time, and the field of an individual particle measured at a given point in space changes as the particle moves.

Lorentz's law defines the force acting on a moving electrically charged particle in a magnetic field:

F=kQB (dx/dt),

where B — the electric charge of the particle; B is the induction of the external magnetic field in which the particle moves; dx/dt — velocity of particles; F — the resulting force on the particle; k — constant of proportionality.

The magnetic field surrounding the electron's trajectory is directed clockwise when viewed from the region the electron is approaching. Under the conditions of the electron's motion, its magnetic field is directed against the external field, weakening it in the lower part of the region shown, and coincides with the external field, strengthening it in the upper part.

Both factors result in a downward force applied to the electron. Along a straight line coinciding with the direction of the external field, the electron's magnetic field is directed at right angles to the external field. With such a mutually perpendicular direction of the fields, their interaction does not generate any forces.

In short, if a negatively charged particle moves from left to right in a plane and the external magnetic field is directed by the observer at the depth of the scheme, then the Lorentz force applied to the particle is directed from top to bottom.

Forces acting on a negatively charged particle whose trajectory is directed perpendicular to the force vector of the external magnetic field

Lawrence's Powers

A wire moving in space crosses the lines of force of the magnetic field existing in this space, as a result of which a certain mechanical coercive field acts on the electrons inside the wire.

The movement of electrons through a magnetic field occurs along with the wire.This movement may be restricted by the action of any forces which impede the movement of the conductor; however, in the direction of travel of the wire, the electrons are not affected by electrical resistance.

Between the two ends of such a wire, a Lorentz voltage is generated, which is proportional to the speed of movement and the magnetic induction. Lorentz forces move electrons along the wire in one direction, resulting in more electrons accumulating at one end of the wire than at the other.

The voltage generated by this separation of charges tends to bring the electrons back to a uniform distribution and eventually equilibrium is established while maintaining a certain voltage proportional to the speed of the wire. If you create conditions where current can flow in the wire, then a voltage will be established in the circuit that is opposite to the original Lorentz voltage.

The photo shows an experimental setup to demonstrate the Lorentz force. Left image: what it looks like Right: Lorentz force effect. An electron flies from the right end to the left. The magnetic force crosses the flight path and deflects the electron beam downwards.

Since an electric current is an ordered movement of charges, the effect of a magnetic field on a current-carrying conductor is the result of its action on individual moving charges.

The main application of the Lorentz force is in electrical machines (generators and motors).

The force acting on a current-carrying conductor in a magnetic field is equal to the vector sum of the Lorentz forces acting on each charge carrier. This force is called Ampere's force, i.e.Ampere force is equal to the sum of all Lorentz forces acting on a current-carrying conductor. Look: Ampere's Law

Galvanomagnetic effects

Various consequences of the action of Lorentz forces, causing a deviation of the trajectory of negatively charged particles - electrons, while moving through solids, are called galvanomagnetic effects.

When an electric current flows in a solid wire placed in a magnetic field, the electrons carrying that current are deflected in a direction perpendicular to both the direction of the current and the direction of the magnetic field. The faster the electrons move, the more they are deflected.

As a result of the deflection of the electrons, gradients of electric potential are established in directions perpendicular to the direction of the current. Due to the fact that the faster moving electrons are deflected more than the slower moving ones, thermal gradients arise, also perpendicular to the direction of the current.

Thus, galvanomagnetic effects include electrical and thermal phenomena.

Given that electrons can move under the influence of forcing electric, thermal and chemical fields, galvanomagnetic effects are classified both by the type of forcing field and by the nature of the resulting phenomena - thermal or electrical.

The term "galvanomagnetic" refers only to certain phenomena observed in solids, where the only kind of particles capable of moving in any appreciable amount are electrons, functioning either as "free agents" or as agents for the formation of so-called holes .Therefore, galvanomagnetic phenomena are also classified depending on the type of carrier involved in them — free electrons or holes.

One of the manifestations of heat energy is the continuous movement of a part of the electrons of any solid substance along randomly directed trajectories and at random speeds. If these motions have completely random characteristics, then the sum of all the individual motions of the electrons is zero, and it is impossible to detect any consequences of the deviations of individual particles under the influence of Lorentz forces.

If there is an electric current, it is carried by a certain number of charged particles or carriers moving in the same or the same direction.

In solids, the electric current arises as a result of the superposition of some general unidirectional motion on the original random motion of electrons. In this case, the electron activity is partly a random response to the effect of thermal energy and partly a unidirectional response to the effect that generates an electric current.

A beam of electrons moving in a circular orbit in a constant magnetic field. The purple light showing the path of an electron in this tube is created by the collision of electrons with gas molecules.

Although any movement of electrons responds to the action of Lorentz forces, only those movements that contribute to the transfer of current are reflected in galvanomagnetic phenomena.

So, galvanomagnetic phenomena are one of the consequences of placing a solid body in a magnetic field and adding unidirectional motion to the motion of its electrons, which under the initial conditions was random in nature. One of the results of this combination of conditions is the appearance of population gradients of the carrier particles in a direction perpendicular to their unidirectional motion.

Lorentz forces tend to move all carriers to one side of the wire. Since the carriers are charged particles, such gradients of their population also create gradients of electric potential that balance the Lorentz forces and can themselves excite an electric current.

In the presence of such a current, a three-component equilibrium is established between Lorentz forces, galvanomagnetic voltages and resistive voltages.

The random movement of electrons is supported by thermal energy, which is determined by the temperature of a substance. The energy needed to keep the particles moving in one direction must come from another source. This latter cannot be formed inside the substance itself, if it is in an equilibrium state, the energy must come from the environment.

Thus, galvanomagnetic conversion is related to electrical phenomena that are a consequence of the appearance of carrier population gradients; such gradients are established in solids when they are placed in a magnetic field and subjected to various influences from the external environment, causing a general unidirectional movement of carriers whose movement in the initial conditions is random.

Classification of galvanomagnetic effects

Six main galvanomagnetic effects are known:

1.Hall effects — the appearance of gradients of the electric potential as a result of the deviation of the carriers during their movement under the influence of the forcing electric field. In this case, holes and electrons simultaneously or individually move in opposite directions and therefore deviate in the same direction.

Look - Hall sensor applications

2. Nerst effects — the appearance of electric potential gradients as a result of the deflection of the carriers during their movement under the influence of a forced thermal field, while the holes and electrons simultaneously or separately move in the same direction and therefore deviate in opposite directions.

3. Photoelectromagnetic and mechanoelectromagnetic effects — the appearance of gradients of the electric potential as a result of the deviation of the carriers during their movement under the influence of the forcing chemical field (gradients of the population of particles). In this case, the holes and electrons formed in pairs move together in the same direction and therefore deviate in opposite directions.

4. The effects of Ettingshausen and Riga — Leduc — the appearance of thermal gradients as a result of carrier deflection, when hot carriers are deflected to a greater extent than cold ones. If the thermal gradients occur in connection with the Hall effects, then this phenomenon is called the Ettingshausen effect, if they occur in connection with the Nernst effect, then the phenomenon is called the Rigi-Leduc effect.

5. Increase in electrical resistance as a result of deflection of carriers during their movement under the influence of a driving electric field. Here, at the same time, there is a decrease in the effective cross-sectional area of ​​the conductor due to the shift of the carriers to one side of it and a decrease in the distance traveled by the carriers in the direction of the current due to the extension of their path due to moving along a curved path instead of a straight one.

6. Increase in thermal resistance as a result of changing conditions similar to the above.

Hall effect sensor

The main combined effects occur in two cases:

• when conditions are created for the flow of electric current under the influence of potential gradients resulting from the above phenomena;
• when conditions are created for the formation of a heat flow under the influence of thermal gradients resulting from the above phenomena.

In addition, combined effects are known, in which one of the galvanomagnetic effects is combined with one or more non-galvanomagnetic effects.

1. Thermal effects:

• carrier mobility changes due to temperature changes;
• electron and hole mobilities change to varying degrees depending on temperature;
• carrier population changes due to temperature changes;
• the electron and hole populations change to varying degrees due to changes in temperature.

2. Effects of anisotropy. The anisotropic characteristics of crystalline substances alter the results of the phenomenon that would be observed with isotropic characteristics.

3. Thermoelectric effects:

• thermal gradients due to the separation of warm and cold media generate thermoelectric effects;
• thermoelectric effects are enhanced as a result of carrier bias, the chemical potential per unit volume of the substance changes due to a change in the carrier population (Nerst effects).

4. Ferromagnetic effects. Carrier mobility in ferromagnetic substances depends on the absolute strength and direction of the magnetic field (as in the Gaussian effect).

5. Effect of dimensions. If the body has large dimensions compared to the electron trajectories, then the properties of the substance throughout the volume of the body have a predominant effect on the electron activity. If the dimensions of the body are small compared to the electron trajectories, then surface effects may predominate.

6. The influence of strong fields. Galvanomagnetic phenomena depend on how long the carriers travel along their cyclotron trajectory. In strong magnetic fields, the carriers can travel a considerable distance along this path. The total number of different possible galvanomagnetic effects is more than two hundred, but in fact each of them can be obtained by combining the phenomena listed above.

See also: Electricity and magnetism, basic definitions, types of moving charged particles