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In electromagnetism, an eddy current (also called Foucault's current) is a loop of electric current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magnetic field. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. They can be induced within nearby stationary conductors by a time-varying magnetic field created by an AC electromagnet or transformer, for example, or by relative motion between a magnet and a nearby conductor. The magnitude of the current in a given loop is proportional to the strength of the magnetic field, the area of the loop, and the rate of change of flux, and inversely proportional to the resistivity of the material. When graphed, these circular currents within a piece of metal look vaguely like eddies or whirlpools in a liquid.
By Lenz's law, an eddy current creates a magnetic field that opposes the change in the magnetic field that created it, and thus eddy currents react back on the source of the magnetic field. For example, a nearby conductive surface will exert a drag force on a moving magnet that opposes its motion, due to eddy currents induced in the surface by the moving magnetic field. This effect is employed in eddy current brakes which are used to stop rotating power tools quickly when they are turned off. The current flowing through the resistance of the conductor also dissipates energy as heat in the material. Thus eddy currents are a cause of energy loss in alternating current (AC) , , and generators, and other AC machinery, requiring special construction such as laminated core or to minimize them. Eddy currents are also used to heat objects in induction heating furnaces and equipment, and to detect cracks and flaws in metal parts using eddy-current testing instruments.
In 1834, Emil Lenz stated Lenz's law, which says that the direction of induced current flow in an object will be such that its magnetic field will oppose the change of magnetic flux that caused the current flow. Eddy currents produce a secondary field that cancels a part of the external field and causes some of the external flux to avoid the conductor.
French physicist Léon Foucault (1819–1868) is credited with having discovered eddy currents. In September 1855, he discovered that the force required for the rotation of a copper disc becomes greater when it is made to rotate with its rim between the poles of a magnet, the disc at the same time becoming heated by the eddy current induced in the metal. The first use of eddy current for non-destructive testing occurred in 1879 when David E. Hughes used the principles to conduct Metallurgy sorting tests.
Since the metal is moving, the magnetic flux through a given area of the sheet is changing. In particular, the part of the sheet moving toward the edge of the magnet (the left side) experiences an increase in magnetic flux density . This change in magnetic flux, in turn, induces a circular electromotive force (EMF) in the sheet, in accordance with Faraday's law of induction, exerting a force on the electrons in the sheet, causing a counterclockwise circular current in the sheet. This is an eddy current. Similarly, the part of the sheet moving away from the edge of the magnet (the right side) experiences a decrease in magnetic flux density , inducing a second eddy current, this time in a clockwise direction. Since the electrons have a negative charge, they move in the opposite direction to the conventional current shown by the arrows.
Another equivalent way to understand the origin of eddy currents is to see that the free () in the metal sheet are moving with the sheet to the right, so the magnetic field exerts a sideways Lorentz force on them given by . Since the charge of the electrons is negative, by the right hand rule the force is to the right looking in the direction of motion of the sheet. So there is a flow of electrons toward the viewer under the magnet. This divides into two parts, flowing right and left around the magnet outside the magnetic field back to the far side of the magnet in two circular eddies. Since the electrons have a negative charge, the direction of conventional current arrows shown is in the opposite direction, toward the left under the magnet.
The electrons collide with the metal lattice atoms, exerting a drag force on the sheet proportional to its velocity. The kinetic energy used to overcome this drag is dissipated as heat by the currents flowing through the metal, so the metal gets warm under the magnet. As described by Ampère's circuital law, each of the circular currents in the sheet induces its own magnetic field (marked in blue arrows in the diagram).
Another way to understand the drag is to observe that in accordance with Lenz's law, the induced electromotive force must oppose the change in magnetic flux through the sheet. At the leading edge of the magnet (left side), the anti-clockwise current creates a magnetic field pointing up (as can be shown using the right hand rule), opposing the magnet's field. This causes a repulsive force to develop between the sheet and the leading edge of the magnet. In contrast, at the trailing edge (right side), the clockwise current causes a magnetic field pointed down, in the same direction as the magnet's field, resulting in an attractive force between the sheet and the trailing edge of the magnet. In both cases, the resulting force is not in the direction of motion of the sheet.
Self-induced eddy currents are responsible for the skin effect in conductors. The latter can be used for non-destructive testing of materials for geometry features, like micro-cracks. A similar effect is the proximity effect, which is caused by externally induced eddy currents.
An object or part of an object experiences steady field intensity and direction where there is still relative motion of the field and the object (for example in the center of the field in the diagram), or unsteady fields where the currents cannot circulate due to the geometry of the conductor. In these situations charges collect on or within the object and these charges then produce static electric potentials that oppose any further current. Currents may be initially associated with the creation of static potentials, but these may be transitory and small.
Eddy currents generate resistive losses that transform some forms of energy, such as kinetic energy, into heat. This Joule heating reduces efficiency of iron-core and electric motors and other devices that use changing magnetic fields. Eddy currents are minimized in these devices by selecting magnetic core materials that have low electrical conductivity (e.g., ferrites or iron powder mixed with resin) or by using thin sheets of magnetic material, known as laminations. Electrons cannot cross the insulating gap between the laminations and so are unable to circulate on wide arcs. Charges gather at the lamination boundaries, in a process analogous to the Hall effect, producing electric fields that oppose any further accumulation of charge and hence suppressing the eddy currents. The shorter the distance between adjacent laminations (i.e., the greater the number of laminations per unit area, perpendicular to the applied field), the greater the suppression of eddy currents.
The conversion of input energy to heat is not always undesirable, however, as there are some practical applications. One is in the brakes of some trains known as eddy current brakes. During braking, the metal wheels are exposed to a magnetic field from an electromagnet, generating eddy currents in the wheels. This eddy current is formed by the movement of the wheels. So, by Lenz's law, the magnetic field formed by the eddy current will oppose its cause. Thus the wheel will face a force opposing the initial movement of the wheel. The faster the wheels are spinning, the stronger the effect, meaning that as the train slows the braking force is reduced, producing a smooth stopping motion.
Induction heating makes use of eddy currents to provide heating of metal objects.
This equation is valid only under the so-called quasi-static conditions, where the frequency of magnetisation does not result in the skin effect; that is, the electromagnetic wave fully penetrates the material.
The penetration depth for a good conductor can be calculated from the following equation: where is the penetration depth (m), is the frequency (Hz), is the magnetic permeability of the material (H/m), and is the electrical conductivity of the material (S/m).
Taking the curl on both sides of this equation and then using a common vector calculus identity for the curl of the curl results in
From Gauss's law for magnetism, , so
Using Ohm's law, , which relates current density to electric field in terms of a material's conductivity , and assuming isotropic homogeneous conductivity, the equation can be written as
Using the differential form of Faraday's law, , this gives
By definition, , where is the magnetization of the material and is the vacuum permeability. The diffusion equation therefore is
With a very strong handheld magnet, such as those made from neodymium, one can easily observe a very similar effect by rapidly sweeping the magnet over a coin with only a small separation. Depending on the strength of the magnet, identity of the coin, and separation between the magnet and coin, one may induce the coin to be pushed slightly ahead of the magnet – even if the coin contains no magnetic elements, such as the US penny. Another example involves dropping a strong magnet down a tube of copperArchived at Ghostarchive and the Wayback Machine: – the magnet falls at a dramatically slow pace.
In a perfect conductor with no resistance, surface eddy currents exactly cancel the field inside the conductor, so no magnetic field penetrates the conductor. Since no energy is lost in resistance, eddy currents created when a magnet is brought near the conductor persist even after the magnet is stationary, and can exactly balance the force of gravity, allowing magnetic levitation. Superconductors also exhibit a separate inherently quantum mechanical phenomenon called the Meissner effect in which any magnetic field lines present in the material when it becomes superconducting are expelled, thus the magnetic field in a superconductor is always zero.
Using with electronic switching comparable to electronic speed control it is possible to generate electromagnetic fields moving in an arbitrary direction. As described in the section above about eddy current brakes, a non-ferromagnetic conductor surface tends to rest within this moving field. When however this field is moving, a vehicle can be levitated and propelled. This is comparable to a maglev but is not bound to a rail. Hendo Hoverboards - World's first REAL hoverboard
A Ferraris acceleration sensor, also called a Ferraris sensor, is a contactless sensor that uses eddy currents to measure relative acceleration.Bernhard Hiller. "Ferraris Acceleration Sensor - Principle and Field of Application in Servo Drives" . Jian Wang, Paul Vanherck, Jan Swevers, Hendrik Van Brussel. "Speed Observer Based on Sensor Fusion Combining Ferraris Sensor and Linear Position Encoder Signals". J. Fassnacht and P. Mutschler. "Benefits and limits of using an acceleration sensor in actively damping high frequent mechanical oscillations". 2001. .
Similarly, in magnetic materials of finite conductivity, eddy currents cause the confinement of the majority of the magnetic fields to only a couple of the surface of the material. This effect limits the flux linkage in and having .
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