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| {{About|the electrical phenomenon|the [[Ted McKeever]] comic|Eddy Current (comics)}}
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| {{Electromagnetism|cTopic=Electrodynamics}}
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| '''Eddy currents''' (also called '''Foucault currents'''<ref>http://books.google.com/books?id=6w5TAAAAMAAJ&q=foucault+currents&dq=foucault+currents&hl=en&ei=AFKbTLm0G47KjAf7uYnyCQ&sa=X&oi=book_result&ct=result&resnum=5&ved=0CDYQ6AEwBDgK</ref>) are [[electric current]]s induced within [[conductor (material)|conductor]]s by a changing [[magnetic field]] in the conductor. These circulating [[Eddy (fluid dynamics)|eddies]] of current have [[inductance]] and thus induce magnetic fields. These fields can cause repulsion, attraction,<ref name=laithwaite>linear Electric Machines- A Personal View
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| ERIC R. LAITHWAITE</ref> propulsion, drag, and heating effects. The stronger the applied magnetic field, the greater the [[electrical conductivity]] of the conductor, and the faster the field changes, the greater the currents that are developed and the greater the fields produced.
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| The term ''eddy current'' comes from analogous currents seen in [[water]] when dragging an [[oar]] breadthwise: localised areas of turbulence known as ''eddies'' give rise to persistent vortices. Somewhat analogously, eddy currents can take time to build up and can persist for very short times in conductors due to their inductance.
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| 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 [[Eddy current brake|braking]] effect. Eddy currents can also have undesirable effects, for instance power loss in [[transformer]]s. In this application, they are minimized with thin plates, by [[Electrical steel#Lamination coatings|lamination]] of conductors or other details of conductor shape.
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| Self-induced eddy currents are responsible for the [[skin effect]] in conductors.<ref>Israel D. Vagner, B.I. Lembrikov, Peter Rudolf Wyder, Electrodynamics of Magnetoactive Media, Springer, 2003, ISBN 3540436944, page 73, Retrieved online on 7 Jan. 2014 at http://books.google.com/books?id=E8caSplsF28C&pg=PA73</ref> The latter can be used for non-destructive testing of materials for geometry features, like micro-cracks.<ref>http://books.google.com/books?id=ZvscLzOlkNgC&pg=PA570</ref> A similar effect is the [[proximity effect (electromagnetism)|proximity effect]], which is caused by externally-induced eddy currents.<ref>http://books.google.com/books?id=mMJxcWqm_1oC&pg=PA80</ref>
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| ==History==
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| The first person to observe current eddies was [[François Arago]] (1786–1853), the 25th Prime Minister of France, 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]] (1791–1867).
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| In 1834, [[Heinrich 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 magnetic field 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.
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| 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 metallurgical sorting tests.<ref>[http://ndt-review.blogspot.com/2010/12/eddy-current-method-short-research.html Short research about the history of eddy current]</ref>
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| ==Explanation==
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| [[File:Wikipedia Eddy Currents.png|thumb|200px|As the circular plate moves down through a small region of constant magnetic field directed into the page, eddy currents are induced in the plate. The direction of those currents is given by [[Lenz's law]], i.e. so that the plate's movement is hindered.]]
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| When a conductor moves through an inhomogeneous field generated by a source, [[electromotive force]]s (EMFs) can be generated around loops within the conductor. These EMFs acting on the [[resistivity]] of the material generate a current around the loop, in accordance with [[Faraday's law of induction]]. These currents dissipate energy, and create a magnetic field that tends to oppose changes in the current- they have inductance.
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| Eddy currents are created when a conductor experiences changes in the magnetic field. If either the conductor is moving through a steady magnetic field, or the magnetic field is changing around a stationary conductor, eddy currents will occur in the conductor. Both effects are present when a conductor moves through a varying magnetic field, as is the case at the top and bottom edges of the magnetized region shown in the diagram. Eddy currents will be generated wherever a conducting object experiences a change in the intensity or direction of the magnetic field at any point within it, and not just at the boundaries.
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| The swirling current set up in the conductor is due to electrons experiencing a [[Lorentz force]] that is perpendicular to their motion. Hence, they veer to their right, or left, depending on the direction of the applied field and whether the strength of the field is increasing or declining. The resistivity of the conductor acts to damp the amplitude of the eddy currents, as well as straighten their paths. [[Lenz's law]] states that the current swirls in such a way as to create an induced magnetic field that opposes the phenomenon that created it. In the case of a varying applied field, the induced field will always be in the opposite direction to that applied. The same will be true when a varying external field is increasing in strength. However, when a varying field is falling in strength, the induced field will be in the same direction as that originally applied, in order to oppose the decline.
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| 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.
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| [[File:Lamination eddy currents.svg|thumb|Lamination of conductors parallel to the field lines reduce eddy currents]]
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| 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 [[transformer]]s 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., [[Ferrite (magnet)|ferrites]]) 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.
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| 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 brake]]s. During braking, the metal wheels are exposed to a magnetic field from an electromagnet, generating eddy currents in the wheels. The eddy currents meet resistance as charges flow through the metal, thus dissipating energy as heat, and this acts to slow the wheels down. 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.
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| ===Power dissipation of eddy currents===
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| Under certain assumptions (uniform material, uniform magnetic field, no [[skin effect]], etc.) the power lost due to eddy currents per unit mass for a thin sheet or wire can be calculated from the following equation:<ref>F. Fiorillo, Measurement and characterisation of magnetic materials, Elsevier Academic Press, 2004, ISBN 0-12-257251-3, page. 31</ref>
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| :<math>P = \frac{\pi^2 B_\text{p}^{\,2} d^2 f^2 }{6k \rho D},</math>
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| where
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| : ''P'' is the power lost per unit mass (W/kg),
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| : ''B''<sub>p</sub> is the peak magnetic field (T),
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| : ''d'' is the thickness of the sheet or diameter of the wire (m),
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| : ''f'' is the frequency (Hz),
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| : ''k'' is a constant equal to 1 for a thin sheet and 2 for a thin wire,
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| : ρ is the [[resistivity]] of the material (Ω m), and
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| : ''D'' is the [[density]] of the material (kg/m<sup>3</sup>).
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| 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.
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| === Skin effect ===
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| {{main|Skin effect}}
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| In very fast-changing fields, the magnetic field does not penetrate completely into the interior of the material. This ''skin effect'' renders the above equation invalid. However, in any case increased frequency of the same value of field will always increase eddy currents, even with non-uniform field penetration.{{cn|date=September 2012}} | |
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| The penetration depth can be calculated from the following equation:<ref>{{cite book|last=Wangsness|first=Roald|title=Electromagnetic Fields|edition=2nd|pages=387–8}}</ref>
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| :<math>\delta = \frac{1}{\sqrt{\pi f \mu \sigma}},</math>
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| where δ is the penetration depth (m), ''f'' 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).
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| ===Diffusion equation===
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| The derivation of a useful equation for modelling the effect of eddy currents in a material starts with the differential, magnetostatic form of [[Ampère's circuital law|Ampère's Law]],<ref name="bertotti">G. ''Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers'', San Diego: Academic Press, 1998.</ref> providing an expression for the [[magnetizing field]] '''H''' surrounding a current density '''J''':
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| :<math>\nabla \times \mathbf{H} = \mathbf{J}.</math>
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| Taking the [[curl (mathematics)|curl]] on both sides of this equation and then using a common vector calculus identity for the [[Vector calculus identities#Curl of the curl|curl of the curl]] results in
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| :<math>{\color{white}-}\nabla \left( \nabla \cdot \mathbf{H} \right) - \nabla^2\mathbf{H} = \nabla \times \mathbf{J}.</math>
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| From [[Gauss's law for magnetism]], {{nowrap|∇ · '''H''' {{=}} 0}}, so
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| :<math>-\nabla^2\mathbf{H}=\nabla\times\mathbf{J}.</math>
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| Using [[Ohm's law]], '''J''' {{=}} σ'''E''', which relates current density '''J''' to electric field '''E''' in terms of a material's conductivity σ, and assuming isotropic homogeneous conductivity, the equation can be written as
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| :<math>-\nabla^2\mathbf{H}=\sigma\nabla\times\boldsymbol{E}.</math>
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| Using the differential form of [[Faraday's law]], {{nowrap|∇ × '''E''' {{=}} −∂'''B'''/∂''t''}}, this gives
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| :<math>{\color{white}-}\nabla^2\mathbf{H} = \sigma \frac{\partial \mathbf{B}}{\partial t}.</math>
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| By definition, {{nowrap|'''B''' {{=}} μ<sub>0</sub>('''H''' + '''M''')}}, where '''M''' is the [[magnetization]] of the material and μ<sub>0</sub> is the [[vacuum permeability]]. The diffusion equation therefore is
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| :<math>{\color{white}-}\nabla^2\mathbf{H} = \mu_0 \sigma \left( \frac{\partial \mathbf{M} }{\partial t}+\frac{\partial \mathbf{H}}{\partial t} \right).</math>
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| ==Applications==
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| ===Electromagnetic braking===
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| {{Main|Eddy current brake}}
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| [[File:Eddy currents en.png|thumb|upright=1.2|Braking forces resulting from eddy currents in a metal plate moving through an external magnetic field]]
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| Eddy currents are used for braking; since there is no contact with a brake shoe or drum, there is no mechanical wear. However, an eddy current brake cannot provide a "holding" torque and so may be used in combination with mechanical brakes, for example, on overhead cranes. Another application is on some roller coasters, where heavy [[copper]] plates extending from the car are moved between pairs of very strong permanent magnets. [[Electrical resistance]] within the plates causes a dragging effect analogous to friction, which dissipates the kinetic energy of the car. The same technique is used in electromagnetic brakes in railroad cars and to quickly stop the blades in power tools such as circular saws. Using electromagnets, the strength of the magnetic field can be adjusted and so the magnitude of braking effect changed.
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| ===Repulsive effects and levitation===
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| {{main|electrodynamic suspension}}
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| [[File:Linear motor field.gif|thumb|A cross section through a linear motor placed above a thick aluminium slab. As the [[linear induction motor]]'s field pattern sweeps to the left, eddy currents are left behind in the metal and this causes the field lines to lean.]]
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| In a varying magnetic field the induced currents exhibit diamagnetic-like repulsion effects. A conductive object will experience a repulsion force. This can lift objects against gravity, though with continual power input to replace the energy dissipated by the eddy currents. An example application is separation of [[aluminum can]]s from other metals in an [[eddy current separator]]). Ferrous metals cling to the magnet, and aluminum (and other non-ferrous conductors) are forced away from the magnet; this can separate a waste stream into ferrous and non-ferrous scrap metal. | |
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| 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 (United States coin)|penny]]. Another example involves dropping a strong magnet down a tube of copper<ref>http://www.youtube.com/watch?v=nrw-i5Ku0mI</ref> – the magnet falls at a dramatically slow pace.
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| Perfect conductors allow lossless conduction that allows eddy currents to form on the surface of the conductor that exactly cancel any changes in the magnetic field applied to the object after the material's resistance went to zero, thus allowing [[magnetic levitation]]. [[Superconductor]]s are a subclass of perfect conductors in that they also exhibit the [[Meissner Effect]], an inherently quantum mechanical phenomenon that is responsible for expelling any magnetic field lines present during the superconducting transition, thus making the magnetic field zero in the bulk of the superconductor.
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| ===Attractive effects===
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| In some geometries the overall force of eddy currents can be attractive, for example, where the flux lines are past 90 degrees to a surface, the induced currents in a nearby conductor cause a force that pushes a conductor towards an electromagnet.<ref name=laithwaite/>
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| ===Identification of metals===
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| In coin operated [[vending machine]]s, eddy currents are used to detect counterfeit coins, or [[slug (coin)|slug]]s. The coin rolls past a stationary magnet, and eddy currents slow its speed. The strength of the eddy currents, and thus the retardation, depends on the conductivity of the coin's metal. Slugs are slowed to a different degree than genuine coins, and this is used to send them into the rejection slot.
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| ===Vibration and position Sensing===
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| Eddy currents are used in certain types of [[proximity sensors]] to observe the vibration and position of rotating shafts within their bearings. This technology was originally pioneered in the 1930s by researchers at [[General Electric]] using vacuum tube circuitry. In the late 1950s, solid-state versions were developed by [[Donald E. Bently]] at [[Bently Nevada]] Corporation. These sensors are extremely sensitive to very small displacements making them well suited to observe the minute vibrations (on the order of several thousandths of an inch) in modern [[turbomachinery]]. A typical proximity sensor used for vibration monitoring has a scale factor of 200 mV/mil. Widespread use of such sensors in turbomachinery has led to development of industry standards that prescribe their use and application. Examples of such standards are [[American Petroleum Institute]] (API) Standard 670 and [[International Organization for Standardization|ISO]] 7919.
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| ===Structural testing===
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| Eddy current techniques are commonly used for the [[nondestructive testing|nondestructive examination]] (NDE) and condition monitoring of a large variety of metallic structures, including [[heat exchanger]] tubes, aircraft fuselage, and aircraft structural components..
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| ===Side effects===
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| Eddy currents are the root cause of the [[skin effect]] in conductors carrying AC current.
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| [[File:EI-transformer core interleaved.svg|thumb|Lamination of magnetic cores in transformers greatly improves the efficiency by minimising eddy currents]]
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| Similarly, in magnetic materials of finite conductivity eddy currents cause the confinement of the majority of the magnetic fields to only a couple [[skin depth]]s of the surface of the material. This effect limits the [[flux linkage]] in [[inductor]]s and [[transformer]]s having [[magnetic core]]s.
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| ===Other applications===
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| *[[Metal detector]]s
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| *Conductivity meters for non-magnetic metals<ref>[http://zappitec.com/?p=p&l=e Conductivity meter for non-magnetic metals]</ref> <ref>[http://www.foerstergroup.de/SIGMATEST.171+M5c50842c46a.0.html Portable non-destructive conductivity gauge]</ref>
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| *[[Adjustable-speed drive#Eddy current drives|Eddy current adjustable-speed drives]]
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| *[[Eddy-current testing]]
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| *[[Electricity meter|Electric meters]] (Electromechanical Induction Meters)
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| *[[Induction heating]]
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| *[[Proximity sensor]] (Displacement sensors)
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| *[[Vending machine]]s (detection of coins)
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| *Coating Thickness Measurements <ref>[http://www.helmut-fischer.com/Product_Group_overview_1.asp?PSG=0120&wg=11&CountryID=91&LanguageID=2 Hand-Held Instruments – eddy current test method ]</ref>
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| *Sheet Resistance Measurement <ref>[http://www.nagy-instruments.de/ohm_sq___od1.html Measure Sheet Resistance of conductive thin coatings on non-conductive substrates (metallization/ wafers/ ITO / CVD / PVD ]</ref>
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| *[[Eddy current separator]] for metal separation <ref>[http://www.cogelme.com/eng/e-eddy-current-metal-separator.htm Eddy current separator]</ref>
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| *Mechanical [[speedometer]]s
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| *Safety Hazard and defect detection applications
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| ==References==
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| {{Reflist}}
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| * {{Cite book| first=A. E. | last=Fitzgerald | authorlink= | coauthors=Kingsley, Charles Jr. and Umans, Stephen D. | year=1983 | title=Electric Machinery | edition=4th |pages=20| publisher=Mc-Graw-Hill, Inc. | location= | isbn=0-07-021145-0 }}
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| * {{Cite book| first=Francis Weston | last=Sears | authorlink= | coauthors=Zemansky, Mark W. | year=1955 | title=University Physics | edition=2nd |pages=616–618| publisher=Addison-Wesley }}
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| ==Further reading==
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| * {{Cite book| first=R. L. | last=Stoll | title=The analysis of eddy currents | publisher=Oxford University Press| year=1974}}
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| * {{Cite book| title=Numerical modelling of eddy currents | first=Andrzej | last=Krawczyk| coauthors= J. A. Tegopoulos}}
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| ==External links==
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| * [http://www.magnet.fsu.edu/education/community/slideshows/eddycurrents/index.html Eddy Currents and Lenz's Law] (Audio slideshow from the National High Magnetic Field Laboratory)
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| * [http://www.cogelme.com/eng/e-eddy-current-metal-separator.htm Eddy Current Separator Cogelme for non-ferrous metals separation] – Info and Video in Cogelme site
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| {{DEFAULTSORT:Eddy Current}}
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| [[Category:Electrodynamics]]
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| [[Category:Mechanical biological treatment]]
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