Foucault currents (or eddy currents) are currents of an inductive nature that appear in massive conductors in an alternating magnetic field. Closed circuits of eddy currents appear deep in the conductor itself. The electrical resistance of a massive conductor is small, therefore, Foucault currents can reach large values. The strength of eddy currents depends on the shape and properties of the conductor material, the direction of the alternating magnetic field, and the speed at which the magnetic flux changes. The distribution of Foucault currents in a conductor can be very complex.
The amount of heat that is released per $1 s$ by Foucault currents is proportional to the square of the frequency of change of the magnetic field.
According to Lenz's law, Foucault's currents choose such directions in order to influence the cause that causes them. This means that if a conductor moves in a magnetic field, then it should experience strong braking, which is caused by the interaction of Foucault currents and the magnetic field.
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Let us give an example of the emergence of Foucault's shackles. Let us make a copper disk with a diameter of $5 cm$ and a thickness of $6 mm$ fall in a narrow gap between the poles of an electromagnet. If the magnetic field is turned off, the disk falls quickly. Let's turn on the electromagnet. The field should be large (about $0.5T$). The fall of the disk will become slow and will resemble movement in a very viscous medium.
The essence of the phenomenon
Eddy or Foucauldian currents are those that flow due to the influence of an alternating magnetic field. In this case, it is not the field itself that changes, but the conductive position of this field. That is, if a conductive movement of a static field occurs, then energy will still be generated in it.
Foucaults arise where an alternating magnetic field changes and in fact they are no different from energy flowing through wires or secondary electrical transformer windings.
Definition from the textbook
Meaning
The faster a conducting body moves in a field, the stronger the Foucault currents will be. The frequency of alternating current and its amplitude, when increasing, also contribute to their increase. When a conducting body is exposed to an electromagnet with alternating current, eddy currents increase with increasing frequency of the current and its amplitude. The direction of rotation of the “vortex” is determined by a similar magnetic flux parameter. If the latter increases, that is, the rate of change is positive (dФ / dt > 0), the eddy currents rotate clockwise.
When the magnetic flux decreases (dФ / dt < 0), the direction of rotation changes to the opposite. The “vortex” of charges in the body chooses such a plane of rotation to provide maximum resistance to the force that causes them (Lenz’s rule). This plane makes a right angle with the lines of force of the inducing field.
In this case, the eddy currents themselves generate a magnetic field directed against the external (inducing) magnetic field that causes them. This is the mechanism of interaction of Foucault currents with an inductor, which caused the disk to rotate in Arago’s experiment.
Properties of eddy currents
It is worth noting that eddy energy is no different from inductive wire energy. The direction and strength of Foucault depends on the metal conductor element, on the direction in which the alternating magnetic flux goes, what properties the metal has and how the magnetic flux changes. At the same time, the current distribution is very complex.
In conductive objects with large volumes, currents are large, which causes a significant increase in body temperature.
The current energy is capable of creating heat in the conductor for induction furnace and metal melting. Like other induction varieties, Foucaults interact with the primary magnetic field and inhibit inductive movement.
Heating as one of the properties
Beneficial and harmful effects
Foucault currents have beneficial and harmful effects. They heat and melt metals in the vacuum and damper areas, but at the same time, energy losses occur in the areas of transformer cores and generators due to the large amount of heat generated.
Beneficial effect of induction currents
Application
Eddy currents have found application in electromagnetic induction. They are used to brake rotating massive parts. Thanks to magnetic induction braking, they are also used to calm the moving parts of electrical measuring instruments, in particular to create a counteracting torque and slow down the moving part of electric meters.
They are also used in a magnetic brake disc on an electric meter. In some cases they are used in technological operations that are impossible without the use of high frequencies. For example, when pumping air from vacuum devices and gas cylinders. In addition, they are needed to completely degas the fittings in a high-frequency generator.
Application in conductors
Ways to reduce stray currents
To reduce stray fuch currents, it is necessary to increase the resistance along the current path as much as possible by filling the circulation system with distilled water and installing insulating pipeline hoses at the heat exchanger and valve.
It is worth noting that their presence in electric machines is undesirable due to the heating of the cores and the creation of energy loss, since, according to Lennz’s law, they demagnetize these devices. Several methods are used to reduce their harmful effects.
Thus, machine cores are made of steel and insulated from each other using varnish film, scale and other materials. Thanks to this, they do not spread. In addition, the cross-sectional design on each individual conductor reduces the current flow.
Some devices use coils of annealed iron wire as cores. In this case, the stripes on them run parallel to those lines that are located on the magnetic flux.
Note! Vortex energy is limited by insulating gaskets, that is, the bundles consist of individual cores isolated from each other.
Eddy currents,
Foucault currents, closed electric currents in a massive conductor that arise when the magnetic flux penetrating it changes.
Voltage currents are induced currents (see Electromagnetic induction
) and are formed in a conducting body either due to a change in time of the magnetic field in which the body is located (
Fig. 1
), or due to the movement of the body in a magnetic field, leading to a change in the magnetic flux through body or any part of it (
Fig. 2
). The faster the magnetic flux changes, the greater the magnitude of the current.
Unlike electric current in wires, which flows along precisely defined paths, volts are closed directly in the conducting mass, forming vortex-like circuits. These current circuits interact with the magnetic flux that generated them. According to Lenz's rule
, the magnetic field of a wind turbine is directed in such a way as to counteract the change in the magnetic flux that induces these wind waves.
Voltage leads to uneven distribution of magnetic flux over the cross section of the magnetic circuit
.
This is explained by the fact that in the center of the cross-section of the magnetic circuit, the magnetizing force of the magnetic circuit, directed towards the main flow, is greatest, since this part of the cross-section is covered by the largest number of circuits of the magnetic circuit. This “displacement” of the flux from the middle of the cross-section of the magnetic circuit is expressed all the more sharply the higher the frequency of the alternating current and the greater the magnetic permeability
of the ferromagnet.
At high frequencies, the flow passes only in a thin surface layer of the core. This causes a decrease in the apparent (averaged over the cross section) magnetic permeability. The phenomenon of displacement of a magnetic flux changing with a high frequency from a ferromagnet is similar to the electrical skin effect
and is called the magnetic skin effect.
In accordance with the Joule-Lenz law
V. t. heat the conductors in which they originated. Therefore, volts lead to energy losses (losses per volt) in magnetic circuits (in the cores of transformers and alternating current coils, in the magnetic circuits of machines).
To reduce energy losses on high-voltage circuits (and harmful heating of magnetic circuits) and reduce the effect of “displacement” of magnetic flux from ferromagnets, the magnetic circuits of machines and alternating current devices are made not from a solid piece of ferromagnetic material (electrical steel), but from separate plates isolated from each other friend (for example, with a special varnish). This division into plates located perpendicular to the direction of the power supply limits the possible contours of the power supply paths ( Fig. 3
), which greatly reduces the magnitude of these currents.
At very high frequencies, the use of ferromagnets for magnetic circuits is impractical; in these cases, they are made from magnetodielectrics
, in which electrical currents practically do not arise due to the very high resistance of these materials.
When a conducting body moves in a magnetic field, the induced currents cause a noticeable mechanical interaction between the body and the field. This principle is based, for example, on the braking of the moving system in electric energy meters, in which an aluminum disk rotates in the field of a permanent magnet ( Fig. 2
). In alternating current machines with a rotating field, a solid metal rotor is entrained by the field due to the electric current generated in it. The interaction of the electric current with an alternating magnetic field underlies various types of pumps for pumping molten metal.
The same group of mechanical effects caused by electrical energy includes the expulsion of nonferromagnetic metal bodies from the field of an alternating current coil.
Voltage currents also arise in the conductor itself, through which alternating current flows, which leads to an uneven distribution of the current over the cross-section of the conductor. At moments when the current in the conductor increases, inductive currents are directed at the surface of the conductor along the primary electric current, and at the axis of the conductor - towards the current ( Fig. 4
). As a result, the current inside the conductor will decrease, and at the surface it will increase. High-frequency currents practically flow in a thin layer near the surface of the conductor, but there is no current inside the conductor. This phenomenon is called the electrical skin effect. To reduce energy losses per volt, large-section wires for alternating current are made from separate cores, insulated from each other.
Voltage heaters are used for melting and surface hardening of metals, and their force action is used in vibration dampers of moving parts of instruments and apparatus, in induction brakes (in which a massive metal disk rotates in the field of electromagnets), etc.
Lit.:
Neiman L. R., Kalantarov P. L., Theoretical foundations of electrical engineering, 5th ed., M., 1959.
Table of contents
Possible problems
Vortex species conduct energy and dissipate it, releasing Joule heat. This energy from the rotor of an asynchronous propulsion system is prepared from furromagnets and contributes to heating of the cores.
To combat this phenomenon, the cores are made of thin steel, covered with insulation and installed across the plates. If the plates are thin, they have low bulk density. Thanks to ferrites and substances with high magnetoresistance, the cores are made solid. Directing them weakens the energy inside the wire.
As a result, it is uneven. This is the phenomenon of skin effect or surface effect due to which the inner conductor is useless and conductor tubes are used in circuits where there is high frequency.
Note! The skin effect is used to heat the surface metal for metal hardening. In this case, hardening can be carried out at any depth.
Foucault currents are inductive currents that arise in large solid conductors. Denoted by the letter f. They have the property of heating conductors. As a result, they are more often used in induction-type furnaces. It is important to note that they are capable of generating a magnetic field. This is the mechanism of their work. In some cases they are useful, in others they are undesirable. In any case, they are used in many devices.
Characteristics
Self-induced eddy currents are responsible for the skin effect in conductors. [1] The latter can be used for non-destructive testing of materials for geometric characteristics such as microcracks. [2] A similar effect is the proximity effect caused by external eddy currents. [3]
(left)
eddy currents
(I'm red)
inside the solid iron core of the transformer.
(correct)
Making a thin lamination rod parallel to the field
(B, green)
with insulation between them reduces eddy currents. Although the field and currents are shown in the same direction, they actually reverse the direction of the alternating current in the transformer winding.
Induction heating uses eddy currents to heat metal objects.
Eddy current power dissipation
Under certain assumptions (homogeneous material, uniform magnetic field, no skin effect, etc.), the power loss due to eddy currents per unit mass for a thin sheet or wire can be calculated using the following equation: [4]
P
- power loss per unit mass (W / kg),
B
p - maximum magnetic field (T),
d
sheet thickness or wire diameter (m),
w
- frequency (Hz),
k
- constant equal to 1 for a thin sheet and 2 for a thin wire, ρ is the resistivity of the material (Ohm m), and
D
is the density of the material (kg/m3).
This equation is valid only under so-called quasi-static conditions, when the magnetizing frequency does not lead to a skin effect; that is, the electromagnetic wave completely penetrates the material.
Skin effect
In very rapidly changing fields, the magnetic field does not penetrate completely into the material. This skin effect
invalidates the above equation.
However, in any case, increasing the frequency of the same field will always increase the eddy currents, even if the field penetration is uneven. [ quote needed
]
The penetration depth for a good conductor can be calculated using the following equation: [5]
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where δ is the penetration depth (m), w
is the frequency (Hz), μ is the magnetic permeability of the material (H/m), and σ is the electrical conductivity of the material (S/m).
Diffusion equation
The derivation of a useful equation for modeling the effect of eddy currents in a material begins with the differential magnetostatic form of Ampere's Law, [6] providing an expression for the magnetizing field H
ambient current density
J
:
Taking curl on either side of this equation and then using the general identity of vector calculus for curl curl leads to
Using Ohm's Law, J
= σ
E
, which relates the current density
J
to the electric field
E
in terms of the material conductivity σ and assuming isotropic uniform conductivity, the equation can be written as
Using the differential form of Faraday's Law, ∇ × E
= −∂
B
/∂
t
, this gives
From Wikipedia - the free encyclopedia
Eddy currents were first discovered by the French scientist D. F. Arago (1786-1853) in 1824 in a copper disk located on an axis under a rotating magnetic needle. Due to eddy currents, the disk began to rotate. This phenomenon, called the Arago phenomenon, was explained several years later by M. Faraday from the standpoint of the law of electromagnetic induction discovered by him: a rotating magnetic field induces eddy currents in the copper disk, which interact with the magnetic needle. Eddy currents were studied in detail by the French physicist Foucault (1819-1868) and named after him. Foucault also discovered the phenomenon of heating metal bodies rotated in a magnetic field by eddy currents.
Foucault currents arise under the influence of time-varying
(alternating) magnetic field [4] and
in physical nature are no different from induction currents arising in wires and secondary windings of electrical transformers
.
Since the electrical resistance of a massive [5] conductor can be small, the strength of the inductive electric current caused by Foucault currents can reach extremely large values. In accordance with Lenz's rule, Foucault currents in the volume of a conductor choose such a path as to counteract to the greatest extent the cause that causes their flow. Therefore, in particular, good conductors moving in a strong magnetic field experience strong inhibition due to the interaction of Foucault currents with an external magnetic field. This effect is used to dampen the moving parts of galvanometers, seismographs and other instruments without using friction, as well as in some designs of railway braking systems.
Source
Eddy currents: physical meaning, losses, field, application
In turn, eddy currents induce their own magnetic fluxes that are closed in the conductor, which, in accordance with Lenz’s rule, prevent the change in the magnetic flux of the device or device, thereby weakening it.
Let us consider the process of formation of eddy currents in a metal core placed in the magnetic field of a coil through which alternating current flows. An alternating magnetic flux is formed around the coil, crossing the core.
An EMF will also be induced in the core, causing so-called eddy currents in it, which heat the core. Since the core resistance is insignificant, the induced induction currents can be quite large, which will lead to strong heating of the core.
The first research in the field of studying eddy currents was carried out in 1824 by the French physicist D.F. Arago, who discovered their presence in a copper disk located on an axis under a revolving magnetic needle.
Under the influence of eddy currents, the disk turned around.
The first detailed studies of eddy currents were carried out by the French researcher Foucault, and they subsequently received their name from him.
Methods for reducing eddy currents
The power spent on heating electrical devices of the electromagnetic type significantly reduces their efficiency. Therefore, in order to reduce the magnitude of eddy currents, the resistance of the magnetic circuit is increased.
For this purpose, the cores are not made solid, but are assembled from separate thin plates (0.1-0.5 mm thick), covered with a layer of insulating material.
Also, during the manufacture of the core, special additives are introduced into the raw material to increase its resistance.
Practical application of Foucault currents
In some cases, eddy currents are used for useful purposes. For example, the creation of a magnetic brake device for an electric meter disk. As the disk turns around, it crosses the magnetic lines of the magnet; eddy currents are formed in the thickness of the disk, which create their own magnetic fluxes that prevent the rotation of the disk and cause it to slow down.
Eddy currents have a beneficial effect during induction melting of metals.
To do this, a crucible with metal is placed in a magnetic field, which, under its influence, induces eddy currents that melt the metal, while the crucible remains cold.
Brief Definition
Eddy currents are currents that flow in conductors under the influence of an alternating magnetic field. The field does not necessarily have to change; a body can move in a magnetic field, but a current will still begin to flow in it.
It is impossible to find the real trajectory of current movement to take them into account; the current flows where it finds the path with the least resistance. Eddy currents always flow in a closed loop. The main conditions for its occurrence are the presence of an object in an alternating magnetic field or its movement relative to the field.
History of discovery
In 1824, scientist D.F. Arago conducted an experiment. He mounted a copper disk on one axis and placed a magnetic needle above it. When the magnetic needle rotated, the disk began to move. This is how the phenomenon of eddy currents was observed for the first time. The disk began to rotate due to the fact that, due to the flow of currents, a magnetic field appeared, which interacted with the arrow. This was then called the Arago phenomenon.
A couple of years later, M. Faraday, who discovered the law of electromagnetic induction, explained this phenomenon in this way: a moving magnetic field induces a current in the disk (as in a closed circuit) and it interacts with the field of the arrow.
Why is the second name Foucault's currents?
Because the physicist Foucault studied the phenomenon of eddy currents in detail. During his research, he made a great discovery. It consisted in the fact that bodies heat up under the influence of eddy currents. We've sorted out the theory, now we'll talk about where Foucault currents are used and which ones cause problems.
The video below provides a more detailed definition of this phenomenon:
Damage from eddy currents
If you have looked at the design of a 50 Hz network transformer, you probably noticed that its core is made of thin sheets, although it may seem that it would be easier to make a solid cast structure.
The fact is that this is how they fight eddy currents. Foucault established the heating of bodies in which they flow. Since the operation of a transformer is based on the principles of interaction of alternating magnetic fields, eddy currents are inevitable.
Any heating of bodies is the release of energy in the form of heat. In this case, core losses will occur. Why is this dangerous? In an electrical installation, strong heating leads to the destruction of the insulation of the windings and failure of the machine. Eddy currents depend on the magnetic properties of the core.
How to reduce losses
Energy losses in the magnetic circuit are not beneficial, so how to deal with them? To reduce their size, the core is made from thin plates of electrical steel - these are unique preventive measures to reduce parasitic currents. Such losses are described by a formula that can be used to calculate:
As you know: the smaller the cross-section of the conductor, the greater its resistance, and the greater its resistance, the less the current. The plates are isolated from each other with scale or a layer of varnish. The cores of large transformers are tightened with an insulated pin. This reduces core losses, i.e. These are the main ways to reduce Foucault currents.
What are the consequences of this phenomenon? The magnetic field that arises due to the flow of Foucault currents weakens the field that caused them to arise. That is, eddy currents reduce the strength of electromagnets. The same applies to the design of parts of electric motors and generators: rotor and stator.
How to determine in a transformer
Finding out where the eddy currents are located in a transformer is not difficult. As a rule, they are located in transformer cores. When they close in the cores, they heat them and create energy. Since they appear in planes that are perpendicular to the magnetic flux according to the characteristic, a transformer reduction of the cores occurs.
Note! Insulated steel plates are used to measure them.
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Definition in transformer
Toki Fuko
Foucault currents or eddy currents
are called currents of inductive nature that arise in massive conductors located in an alternating magnetic field.
Closed circuits of eddy currents originate deep in the conductor itself. The electrical resistance value of a massive conductor is a rather small value; accordingly, Foucault currents can acquire large values. The shape and properties of the conductor material, the direction of the alternating magnetic field and the rate of change of the magnetic flux are quantities on which the strength of eddy currents depends. The distribution of Foucault currents in a conductor can be extremely complex. The amount of heat that is emitted per 1 s of Foucault currents is proportional to the square of the frequency of change of the magnetic field. Based on Lenz's law, it can be stated that Foucault currents flow in such directions as to eliminate the cause that causes them through their influence. Thus, if a conductor is in motion in the region of a magnetic field, then it should be subject to strong inhibition caused by the interaction of Foucault currents and the magnetic field.
Foucault's currents in human economic activity
The simplest example of the manifestation of Foucault currents in everyday life is their effect on the magnetic circuit of a winding transformer. Due to the influence of induced currents, low-frequency vibration appears (the transformer hums), which contributes to strong heating. In this case, energy is wasted and the efficiency of the installation decreases. To prevent significant losses, transformer cores are not made in one piece, but are assembled from thin strips of electrical steel with low electrical conductivity. The strips are insulated between each other with electrical varnish or a layer of scale. The advent of ferrite elements made it possible to manufacture small-sized magnetic cores in one piece. The effect of eddy currents is used throughout industry and mechanical engineering. Magnetic levitation trains use Foucault currents for braking, and high-precision instruments have a pointer damping system based on the action of eddy currents. Induction furnaces are widely used in metallurgy, having a whole range of advantages over similar installations. In an induction furnace, the heated metal can be placed in an airless space, ensuring its complete degassing. Induction melting of ferrous metals has also become widespread in metallurgy due to the high efficiency of installations.
Use of Foucault currents
The heat emitted by Foucault currents is used in heating processes. Thus, metal smelting using Foucault currents is more profitable than smelting using other heating methods. An induction furnace using this method is a coil through which a high-frequency and high-power current flows. A conductive body is located inside the coil, in which high-intensity eddy currents arise that heat the substance to the point of melting. This is how metals are melted under vacuum conditions, making it possible to obtain materials of high purity. When using Foucault currents for the purpose of degassing, the internal metal elements of vacuum structures are heated.
Foucault's currents are not always useful.
Such energy, for example, in the rotor of an asynchronous motor, usually made of ferromagnets, heats up the cores, which worsens their characteristics. To avoid this phenomenon, cores are produced in the form of thin plates, which are separated by thin layers of insulator. The plates are installed in such a way that the Foucault currents are directed across them. In the case of small thickness of the plates, eddy currents have a small volume density. With the advent of ferrites and substances with high magnetoresistance, it became possible to manufacture solid cores.
Approximate formulas that can describe the skin effect in a homogeneous cylindrical conductor:
Application in practice
Now about the useful areas of application of Foucault currents. A huge contribution was made to metallurgy with the invention of induction steelmaking furnaces. They are designed in such a way that a molten mass of metal is placed inside a coil through which a high-frequency current flows. Its magnetic field induces large currents within the metal until it completely melts.
Author's note!
The development of induction furnaces has significantly improved the environmental friendliness of metal production and changed the understanding of smelting methods. I work at a metallurgical plant, where ten years ago they launched a new high-tech workshop with such installations, and a few years after the development of the new equipment, the classic open-hearth furnace was closed. This indicates the productivity of this method of heating metals. Eddy currents are also used to surface harden metal.
Visual application in practice:
In addition to metallurgy, they are used in the production of electric vacuum devices. The problem is the complete removal of gases before sealing the flask. Using Foucault currents, the electrodes of the lamp are heated to high temperatures, thus deactivating the gas.
In everyday life, you can come across kitchen induction stoves on which food is prepared, thanks to the use of this phenomenon. As you can see, eddy currents have their pros and cons.
Foucault's currents are both beneficial and harmful. In some cases, their influence entails non-electrical problems. For example, a pipeline laid near cable lines rots faster without any apparent third-party reasons. At the same time, induction heating devices have shown themselves to be quite good, especially since you can assemble such a device for household use yourself. We hope you now know what Foucault eddy currents are, as well as what applications they have found in production and in everyday life.
