Eddy current
In electromagnetism, an eddy 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 inductors, transformers, electric motors and generators, and other AC machinery, requiring special construction such as laminated magnetic cores or ferrite cores 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.
Origin of term
The term eddy current comes from analogous currents seen in water in fluid dynamics, causing localised areas of turbulence known as eddies giving rise to persistent vortices. Somewhat analogously, eddy currents can take time to build up and can persist for very long times in conductors due to their inductance.History
The first person to observe eddy currents was François Arago, the President of the Council of Ministers of the 2nd French Republic during the brief period from 10 May to 24 June 1848, who was also a mathematician, physicist and astronomer. In 1824 he observed what has been called rotatory magnetism, and that most conductive bodies could be magnetized; these discoveries were completed and explained by Michael Faraday.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 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 metallurgical sorting tests.
Theory
A magnet induces circular electric currents in a metal sheet moving through its magnetic field. The accompanying diagram shows a metal sheet moving to the right with velocity under a stationary magnet. The magnetic field from the magnet's north pole passes down through the metal sheet.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 experiences an increase in magnetic flux density. This change in magnetic flux, in turn, induces a circular electromotive force 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 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 charge carriers 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.
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, the anti-clockwise current creates a magnetic field pointing up, 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, 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.
Properties
Eddy currents in conductors of non-zero resistivity generate heat as well as electromagnetic forces. The heat can be used for induction heating. The electromagnetic forces can be used for levitation, creating movement, or to give a strong braking effect. Eddy currents can also have undesirable effects, for instance power loss in transformers. In this application, they are minimized with thin plates, by lamination of conductors or other details of conductor shape.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, 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 transformers 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 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, 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.
Power dissipation of eddy currents
Under certain assumptions the power lost due to eddy currents per unit mass for a thin sheet or wire can be calculated from the following equation:where
- is the power lost per unit mass,
- is the peak magnetic field,
- is the thickness of the sheet or diameter of the wire,
- is the frequency,
- is a constant equal to 1 for a thin sheet and 2 for a thin wire,
- is the resistivity of the material, and
- is the density of the material.