A magnet induces circular electric currents in a metal plate that moves through its magnetic field. See the diagram on the right. The diagram shows a metal plate (C) moving to the right under a stationary magnet. The magnetic field () from the North pole of the magnet passes through the plate downwards. Since the plate is moving, the magnetic flux through an area of ​​the plate varies. In the sector of the plate that moves under the leading side of the magnet (left side) the magnetic field through a point on the plate increases as it approaches the magnet, . By Faraday's law of induction, this generates a circular electric field on the plate in a counterclockwise direction around the magnetic field lines. This field induces a counterclockwise flow of electric current (), in the sheet. This is Foucault current. In the part of the sheet under the trailing edge of the magnet (right side) the magnetic field through a given point on the sheet decreases as it moves away from the magnet, < 0}}, inducing a second clockwise eddy current in the sheet.

Another equivalent way of understanding current is to see that the free charge carriers (electrons) in the metal sheet move with the sheet to the right, so the magnetic field exerts a lateral force on them due to the Lorentz force. Since the velocity of the charges is to the right and the magnetic field is directed downward, from the right-hand rule the Lorentz force on the positive charges is toward the back of the diagram (to the left when looking in the direction of motion v). This causes a current toward the back under the magnet, which flows through parts of the sheet outside the magnetic field, clockwise to the right and counterclockwise to the left, to the front of the magnet again. The moving charge carriers in the metal, the electrons, actually have a negative charge, so their movement is in the opposite direction to the conventional current shown.

The magnetic field of the magnet, acting on the electrons moving laterally under the magnet, then exerts a Lorentz force directed backwards, opposite to the speed of the metal sheet. The electrons, in collisions with the atoms of the metal network, transfer this force to the sheet, exerting a drag force on the sheet proportional to its speed. The kinetic energy consumed by overcoming this drag force is dissipated as heat by currents flowing through the resistance of the metal, so the metal heats up under the magnet.

Due to Ampere's circuit law, each of the circular currents in the sheet creates an opposing magnetic field (). Another way to understand the drag force is to see that due to Lenz's law the counterfields oppose the change of magnetic field through the sheet. At the leading edge of the magnet (left side) by the right hand rule the counter current creates a magnetic field pointing upward, opposing the field of the magnet, causing a repulsive force between the blade and the leading edge of the magnet. Conversely, at the trailing edge (right side), the clockwise current causes a magnetic field that points downward, in the same direction as the magnet's field, creating an attractive force between the sheet and the trailing edge of the magnet. Both forces oppose the movement of the blade.

Electrical

Eddy currents are used to enhance the effect in motion-to-electricity converters such as electrical generators and dynamic microphones. They can also be used to induce a magnetic field in aluminum cans, allowing them to be easily separated from other recyclable items. Superconductors allow perfect, lossless conduction, creating eddy currents equal and opposite to the external magnetic field, thus allowing magnetic levitation. For the same reason, the magnetic fields within a superconducting medium will be exactly zero, regardless of the external field applied.

One of the practical applications of eddy currents is that used in electricity consumption meters, where the disc cuts lines of force, as it rotates, driven by the field of a magnet. The currents, which are produced in the disc, generate a force opposite to the one that drives it. This eddy current braking allows the counters to be calibrated, modifying the position of the magnet. This same device is used to adjust the end speed of the turntables and dampen the measuring instruments.

Some tachometers have a magnet that rotates at the speed being measured against a moving metal disk. The electromagnetic actions, due to Foucault currents, activate it in the direction of rotation of the magnet. Thanks to a return spring, it is possible to immobilize the disc in a balanced position, which is a function of the speed of the magnet.

Eddy currents are still used in non-destructive testing to detect surface discontinuities and measure electrical conductivity in non-magnetic metals.

Living mechanics electrotechnics

Eddy currents are used to brake at the end of some roller coasters. This mechanism has no mechanical wear and produces precise braking force. Typically, heavy copper plates extending from the carriage are moved between pairs of very powerful permanent magnets. The electrical resistance between the plates generates a drag effect analogous to friction, which dissipates the kinetic energy of the car.

Although the loss of useful energy is almost always undesirable, it sometimes has some practical applications. One of them is in some trains and heavy vehicles, such as coaches and trucks, whose brakes are activated by inducing Foucault currents (electric retarder). During braking, the cardan shaft is exposed to the magnetic field of an electromagnet, which generates eddy currents in the wheel cores and rims. Eddy currents encounter resistance as they flow through the metal, and dissipate energy as heat, causing the wheels to slow down. The faster the wheels rotate, the stronger the effect will be, resulting in that as the train slows down, so will the braking force, achieving smooth braking proportional to the speed of the wheels.

If an aluminum disc, which rotates freely, is placed in front of a magnet, the magnetic field produced by the magnet significantly reduces the rotation speed of the disc, that is, it produces a braking torque proportional to the speed of the disc. This braking effect is also due to eddy currents, and is applied in numerous measuring devices, such as watthourimeters or electric energy meters.

It should be noted that this braking action only manifests itself in planes perpendicular to the induction lines, since the circuits embrace most of the flow, experiencing the maximum effect of the variations when it is perpendicular.

Contenido

Las corrientes de Foucault son la causa principal del efecto pelicular en conductores que transportan corriente alterna.

energy losses

Eddy currents, as already mentioned, have the effect of transforming part of the energy into heat. This heat produced in the metal mass is only used in high-frequency electric furnaces, so, in general, it represents a loss of energy. To study these losses, a sheet of length, width and thickness is considered, subjected to a variable field of value:.

where ω is the pulsation and B is the maximum induction.

In this circumstance the flow through the surface of said loop is:.

Where S is the surface that the flow crosses, whose value is.

Therefore it is possible to write the previous equation in the form:.

On the other hand, it is known that the induced emf in the loop is:

Deriving it, we have:

If a differential turn is taken in the sheet, its resistance will be.

and neglecting 2x compared to 2b, we will write:.

The power in the loop will be,.

E being the effective voltage, whose value depending on the maximum, E, is.

Therefore the power lost will be:.

And the total power lost as a result of eddy currents:.

If we now replace ω with , we obtain.

or, what is the same:.

where , is the volume of the load.

From all of the above, it can be deduced that the losses in watts per cubic meter due to eddy currents will be:

Given the harmful nature of eddy currents, for the reasons already noted, it is necessary to take the following precautions:

• - all metal masses subjected to induction variations must be rolled and placed in parallel packages. In this way, the travel of eddy currents generated in planes perpendicular to the flows is avoided;

• - the rivets and screws that join the sheets must not close conductive circuits that embrace variable flow;

• - the metal supports of the coils must be cut by means of an incision parallel to the induction lines, or use non-conductive substances.

If we repeat the example of the pendulum, modifying the structure of the copper plates, that is, the piece is split vertically with numerous cuts, it will be possible to verify that the braking of the pendulum has decreased significantly. This does not mean that the currents have disappeared, but rather that due to the limitation of the band where it performs, limited by the cuts made, they are greatly diminished.

To reduce the development of eddy currents, the system of constructing iron cores instead of solid ones is used, using overlapping sheets or sheets with a thickness of 0.2 to 0.6 mm, isolated from each other with varnish or paper. The sheets are made with a high resistivity silicon steel, so that the intensity of the induced current decreases and the losses thus reach an admissible value. This construction does not produce a decrease in the magnetic flux, since it is always arranged according to the plane that the lines of force run through.

The quality of these sheets in terms of losses due to hysteresis and eddy currents is characterized by the power in watts (W), dissipated per kilo of sheet subjected to an alternative induction of one tesla "Tesla (unit)"), at a rate of 50 magnetization cycles per second.

The following table gives the values ​​of the specific losses in W/kg, for various qualities of magnetic plates that exist on the market.

In the iron cores used in high-frequency coils, the classic arrangement in sheets, which has been seen before, is no longer sufficient, therefore, these cores are built with special iron, of compressed powder and agglomerated with insulating varnish, in such a way that each grain of iron is isolated from its closest ones, this being the only way to reduce the losses in the iron, until an acceptable value is achieved.

• - Inductive sensor.

• - Transformer.

• - Tesla coil.

• - Ferrite "Ferrite (ferromagnetic ceramic)").

• - Film effect.

• - Stoll, R. L. (1974). The Analysis of Eddy Currents. Oxford University Press.

• - Krawczyk, Andrzej; J. A. Tegopoulos. Numerical Modeling of Eddy Currents.

• - A video demonstration of eddy currents.

• - Eddy current separators for non-magnetic materials - machines used in the recycling sector.

• - Videos of eddy current separators.

• - A conductivity meter using the eddy current method Archived July 6, 2018 at the Wayback Machine.

A magnet induces circular electric currents in a metal plate that moves through its magnetic field. See the diagram on the right. The diagram shows a metal plate (C) moving to the right under a stationary magnet. The magnetic field () from the North pole of the magnet passes through the plate downwards. Since the plate is moving, the magnetic flux through an area of ​​the plate varies. In the sector of the plate that moves under the leading side of the magnet (left side) the magnetic field through a point on the plate increases as it approaches the magnet, . By Faraday's law of induction, this generates a circular electric field on the plate in a counterclockwise direction around the magnetic field lines. This field induces a counterclockwise flow of electric current (), in the sheet. This is Foucault current. In the part of the sheet under the trailing edge of the magnet (right side) the magnetic field through a given point on the sheet decreases as it moves away from the magnet, < 0}}, inducing a second clockwise eddy current in the sheet.

Another equivalent way of understanding current is to see that the free charge carriers (electrons) in the metal sheet move with the sheet to the right, so the magnetic field exerts a lateral force on them due to the Lorentz force. Since the velocity of the charges is to the right and the magnetic field is directed downward, from the right-hand rule the Lorentz force on the positive charges is toward the back of the diagram (to the left when looking in the direction of motion v). This causes a current toward the back under the magnet, which flows through parts of the sheet outside the magnetic field, clockwise to the right and counterclockwise to the left, to the front of the magnet again. The moving charge carriers in the metal, the electrons, actually have a negative charge, so their movement is in the opposite direction to the conventional current shown.

The magnetic field of the magnet, acting on the electrons moving laterally under the magnet, then exerts a Lorentz force directed backwards, opposite to the speed of the metal sheet. The electrons, in collisions with the atoms of the metal network, transfer this force to the sheet, exerting a drag force on the sheet proportional to its speed. The kinetic energy consumed by overcoming this drag force is dissipated as heat by currents flowing through the resistance of the metal, so the metal heats up under the magnet.

Due to Ampere's circuit law, each of the circular currents in the sheet creates an opposing magnetic field (). Another way to understand the drag force is to see that due to Lenz's law the counterfields oppose the change of magnetic field through the sheet. At the leading edge of the magnet (left side) by the right hand rule the counter current creates a magnetic field pointing upward, opposing the field of the magnet, causing a repulsive force between the blade and the leading edge of the magnet. Conversely, at the trailing edge (right side), the clockwise current causes a magnetic field that points downward, in the same direction as the magnet's field, creating an attractive force between the sheet and the trailing edge of the magnet. Both forces oppose the movement of the blade.

Electrical

Eddy currents are used to enhance the effect in motion-to-electricity converters such as electrical generators and dynamic microphones. They can also be used to induce a magnetic field in aluminum cans, allowing them to be easily separated from other recyclable items. Superconductors allow perfect, lossless conduction, creating eddy currents equal and opposite to the external magnetic field, thus allowing magnetic levitation. For the same reason, the magnetic fields within a superconducting medium will be exactly zero, regardless of the external field applied.

One of the practical applications of eddy currents is that used in electricity consumption meters, where the disc cuts lines of force, as it rotates, driven by the field of a magnet. The currents, which are produced in the disc, generate a force opposite to the one that drives it. This eddy current braking allows the counters to be calibrated, modifying the position of the magnet. This same device is used to adjust the end speed of the turntables and dampen the measuring instruments.

Some tachometers have a magnet that rotates at the speed being measured against a moving metal disk. The electromagnetic actions, due to Foucault currents, activate it in the direction of rotation of the magnet. Thanks to a return spring, it is possible to immobilize the disc in a balanced position, which is a function of the speed of the magnet.

Eddy currents are still used in non-destructive testing to detect surface discontinuities and measure electrical conductivity in non-magnetic metals.

Living mechanics electrotechnics

Eddy currents are used to brake at the end of some roller coasters. This mechanism has no mechanical wear and produces precise braking force. Typically, heavy copper plates extending from the carriage are moved between pairs of very powerful permanent magnets. The electrical resistance between the plates generates a drag effect analogous to friction, which dissipates the kinetic energy of the car.

Although the loss of useful energy is almost always undesirable, it sometimes has some practical applications. One of them is in some trains and heavy vehicles, such as coaches and trucks, whose brakes are activated by inducing Foucault currents (electric retarder). During braking, the cardan shaft is exposed to the magnetic field of an electromagnet, which generates eddy currents in the wheel cores and rims. Eddy currents encounter resistance as they flow through the metal, and dissipate energy as heat, causing the wheels to slow down. The faster the wheels rotate, the stronger the effect will be, resulting in that as the train slows down, so will the braking force, achieving smooth braking proportional to the speed of the wheels.

If an aluminum disc, which rotates freely, is placed in front of a magnet, the magnetic field produced by the magnet significantly reduces the rotation speed of the disc, that is, it produces a braking torque proportional to the speed of the disc. This braking effect is also due to eddy currents, and is applied in numerous measuring devices, such as watthourimeters or electric energy meters.

It should be noted that this braking action only manifests itself in planes perpendicular to the induction lines, since the circuits embrace most of the flow, experiencing the maximum effect of the variations when it is perpendicular.

Contenido

Las corrientes de Foucault son la causa principal del efecto pelicular en conductores que transportan corriente alterna.

energy losses

Eddy currents, as already mentioned, have the effect of transforming part of the energy into heat. This heat produced in the metal mass is only used in high-frequency electric furnaces, so, in general, it represents a loss of energy. To study these losses, a sheet of length, width and thickness is considered, subjected to a variable field of value:.

where ω is the pulsation and B is the maximum induction.

In this circumstance the flow through the surface of said loop is:.

Where S is the surface that the flow crosses, whose value is.

Therefore it is possible to write the previous equation in the form:.

On the other hand, it is known that the induced emf in the loop is:

Deriving it, we have:

If a differential turn is taken in the sheet, its resistance will be.

and neglecting 2x compared to 2b, we will write:.

The power in the loop will be,.

E being the effective voltage, whose value depending on the maximum, E, is.

Therefore the power lost will be:.

And the total power lost as a result of eddy currents:.

If we now replace ω with , we obtain.

or, what is the same:.

where , is the volume of the load.

From all of the above, it can be deduced that the losses in watts per cubic meter due to eddy currents will be:

Given the harmful nature of eddy currents, for the reasons already noted, it is necessary to take the following precautions:

• - all metal masses subjected to induction variations must be rolled and placed in parallel packages. In this way, the travel of eddy currents generated in planes perpendicular to the flows is avoided;

• - the rivets and screws that join the sheets must not close conductive circuits that embrace variable flow;

• - the metal supports of the coils must be cut by means of an incision parallel to the induction lines, or use non-conductive substances.

If we repeat the example of the pendulum, modifying the structure of the copper plates, that is, the piece is split vertically with numerous cuts, it will be possible to verify that the braking of the pendulum has decreased significantly. This does not mean that the currents have disappeared, but rather that due to the limitation of the band where it performs, limited by the cuts made, they are greatly diminished.

To reduce the development of eddy currents, the system of constructing iron cores instead of solid ones is used, using overlapping sheets or sheets with a thickness of 0.2 to 0.6 mm, isolated from each other with varnish or paper. The sheets are made with a high resistivity silicon steel, so that the intensity of the induced current decreases and the losses thus reach an admissible value. This construction does not produce a decrease in the magnetic flux, since it is always arranged according to the plane that the lines of force run through.

The quality of these sheets in terms of losses due to hysteresis and eddy currents is characterized by the power in watts (W), dissipated per kilo of sheet subjected to an alternative induction of one tesla "Tesla (unit)"), at a rate of 50 magnetization cycles per second.

The following table gives the values ​​of the specific losses in W/kg, for various qualities of magnetic plates that exist on the market.

In the iron cores used in high-frequency coils, the classic arrangement in sheets, which has been seen before, is no longer sufficient, therefore, these cores are built with special iron, of compressed powder and agglomerated with insulating varnish, in such a way that each grain of iron is isolated from its closest ones, this being the only way to reduce the losses in the iron, until an acceptable value is achieved.

• - Inductive sensor.

• - Transformer.

• - Tesla coil.

• - Ferrite "Ferrite (ferromagnetic ceramic)").

• - Film effect.

• - Stoll, R. L. (1974). The Analysis of Eddy Currents. Oxford University Press.

• - Krawczyk, Andrzej; J. A. Tegopoulos. Numerical Modeling of Eddy Currents.

• - A video demonstration of eddy currents.

• - Eddy current separators for non-magnetic materials - machines used in the recycling sector.

• - Videos of eddy current separators.

• - A conductivity meter using the eddy current method Archived July 6, 2018 at the Wayback Machine.