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1005:(1786â1853), the President of the Council of Ministers of the 2nd French Republic during the brief period 10th May to June 24, 1848 (equivalent to the current position of the French Prime Minister), 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
1027:(1819â1868) 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
927:, 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
2589:, 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 â even if the coin contains no magnetic elements, such as the US
2600:, 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
1020:, 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.
1631:, 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.
1642:, 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.
2644:. 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.
2623:
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.
2573:
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
2546:
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, as opposed to permanent
2525:
Demonstration of
Waltenhofen's pendulum, precursor of eddy current brakes. The formation and suppression of eddy currents is here demonstrated by means of this pendulum, a metal plate oscillating between the pole pieces of a strong electromagnet. As soon as a sufficiently strong magnetic field has
2492:
2537:
to slow or stop moving objects. 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
1548:
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
1075:
is directed down through the plate. The
Lorentz force of the magnetic field on the electrons in the metal induces a sideways current under the magnet. The magnetic field, acting on the sideways moving electrons, creates a Lorentz force opposite to the velocity of the sheet, which acts as a drag
1467:
The magnetic field of the magnet, acting on the electrons moving sideways under the magnet, then exerts a
Lorentz force directed to the rear, opposite to the velocity of the metal sheet. The electrons, in collisions with the metal lattice atoms, transfer this force to the sheet, exerting a drag
2517:
1549:
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.
2672:. 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
2081:
2757:
E-I transformer laminations showing flux paths. The effect of the gap where the laminations are butted together can be mitigated by alternating pairs of E laminations with pairs of I laminations, providing a path for the magnetic flux around the
1506:, the clockwise current causes a magnetic field pointed down, in the same direction as the magnet's field, creating an attractive force between the sheet and the trailing edge of the magnet. Both of these forces oppose the motion of the sheet.
2389:
2337:
2239:
1753:
1444:
toward the rear under the magnet, which circles around 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 mobile
2147:
1501:
the counterclockwise current creates a magnetic field pointed up, opposing the magnet's field, causing a repulsive force between the sheet and the leading edge of the magnet. In contrast, at the trailing edge
1260:
of the metal sheet. This force accelerates the electron giving it a component of velocity opposite to the sheet. Collisions of these electrons with the atoms of the sheet exert a drag force on the sheet.
1897:
1273:
in this drawing is shown further away from the disk than the South; this is just to leave room to show the currents. In an actual eddy current brake the pole pieces are positioned as close to the disk as
2010:
1995:
1638:. 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
2668:
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
2582:. 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.
1627:. 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
1595:
between them reduces the eddy currents. Although the field and currents are shown in one direction, they actually reverse direction with the alternating current in the transformer winding.
1849:
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.
2279:
892:
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
993:
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.
908:
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
931:
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
2612:
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.
1634:
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
2189:
1663:
615:
2487:{\displaystyle \nabla ^{2}\mathbf {H} =\mu _{0}\sigma \left({\frac {\partial \mathbf {M} }{\partial t}}+{\frac {\partial \mathbf {H} }{\partial t}}\right).}
2100:
2656:
to observe the vibration and position of rotating shafts within their bearings. This technology was originally pioneered in the 1930s by researchers at
588:
2730:
Similarly, in magnetic materials of finite conductivity, eddy currents cause the confinement of the majority of the magnetic fields to only a couple
2684:
600:
1855:
1541:
in conductors. The latter can be used for non-destructive testing of materials for geometry features, like micro-cracks. A similar effect is the
1939:
The derivation of a useful equation for modelling the effect of eddy currents in a material starts with the differential, magnetostatic form of
3045:
2677:
1961:
1344:
in the sheet in a counterclockwise direction around the magnetic field lines. This field induces a counterclockwise flow of electric current
3006:
851:
620:
1827:
This equation is valid only under the so-called quasi-static conditions, where the frequency of magnetisation does not result in the
3403:
630:
1660:, etc.) the power lost due to eddy currents per unit mass for a thin sheet or wire can be calculated from the following equation:
3030:
1088:
Forces on an electron in the metal sheet under the magnet, explaining where the drag force on the sheet comes from. The red dot
455:
3242:
1393:) in the metal sheet are moving with the sheet to the right, so the magnetic field exerts a sideways force on them due to the
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3121:
2941:
2914:
2887:
470:
465:
92:
3151:
480:
2593:. Another example involves dropping a strong magnet down a tube of copper â the magnet falls at a dramatically slow pace.
1542:
2569:'s field pattern sweeps to the left, eddy currents are left behind in the metal and this causes the field lines to lean.
2004:
1845:
In very fast-changing fields, the magnetic field does not penetrate completely into the interior of the material. This
1599:
Eddy currents generate resistive losses that transform some forms of energy, such as kinetic energy, into heat. This
2961:
1309:
through a given area of the sheet is changing. In the part of the sheet moving under the leading edge of the magnet
82:
3230:
350:
2785:
1359:
the magnetic field through a given point on the sheet is decreasing as it is moving further away from the magnet,
2076:{\displaystyle \nabla \left(\nabla \cdot \mathbf {H} \right)-\nabla ^{2}\mathbf {H} =\nabla \times \mathbf {J} .}
265:
1611:
and other devices that use changing magnetic fields. Eddy currents are minimized in these devices by selecting
3076:"Benefits and limits of using an acceleration sensor in actively damping high frequent mechanical oscillations"
844:
610:
87:
3358:
Reitz, J. R. (1970). Forces on Moving
Magnets due to Eddy Currents. Journal of Applied Physics 41, 2067-2071.
2244:
1337:
889:
625:
330:
35:
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magnets, the strength of the magnetic field can be adjusted and so the magnitude of braking effect changed.
1493:
the counterfields oppose the change in magnetic field through the sheet. At the leading edge of the magnet
2673:
2086:
1355:, in the sheet. This is the eddy current. In the part of the sheet under the trailing edge of the magnet
490:
230:
97:
17:
1940:
1480:
220:
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658:
555:
530:
450:
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Lamination of magnetic cores in transformers greatly improves the efficiency by minimising eddy currents
2590:
1531:
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which is consumed overcoming this drag force is dissipated as heat by the currents flowing through the
1282:
in a metal sheet moving through its magnetic field. See the diagram at right. It shows a metal sheet
1222:) The magnetic field acting on this sideways velocity, then exerts a Lorentz force on the particle of
283:
3075:
3063:"Speed Observer Based on Sensor Fusion Combining Ferraris Sensor and Linear Position Encoder Signals"
2556:
893:
837:
798:
325:
315:
255:
250:
190:
3042:
2956:
F. Fiorillo, Measurement and
Characterization of Magnetic Materials, Elsevier Academic Press, 2004,
1097:
shows a conduction electron in the sheet right after it has undergone a collision with an atom, and
3398:
2620:
335:
3335:
2753:
1313:
the magnetic field through a given point on the sheet is increasing as it gets nearer the magnet,
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of the material. When graphed, these circular currents within a piece of metal look vaguely like
768:
270:
3062:
3002:
1928:
648:
175:
165:
160:
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3272:
1522:. The electromagnetic forces can be used for levitation, creating movement, or to give a strong
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365:
140:
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2543:
1918:
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989:
917:
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31:
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of the magnet's north pole N passes down through the sheet. Since the metal is moving, the
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shows the same electron after it has been accelerated by the magnetic field. On average at
1084:
935:
in the material. Thus eddy currents are a cause of energy loss in alternating current (AC)
2790:
2332:{\displaystyle \nabla ^{2}\mathbf {H} =\sigma {\frac {\partial \mathbf {B} }{\partial t}}.}
1461:
964:
881:
818:
718:
683:
435:
300:
200:
185:
120:
1852:
The penetration depth for a good conductor can be calculated from the following equation:
57:
8:
3328:
2716:
2601:
2383:
778:
758:
753:
560:
545:
430:
400:
295:
225:
2660:
using vacuum tube circuitry. In the late 1950s, solid-state versions were developed by
2542:
plates extending from the car are moved between pairs of very strong permanent magnets.
2003:
on both sides of this equation and then using a common vector calculus identity for the
2795:
2605:
2534:
2530:
2507:
2000:
1635:
1523:
948:
928:
653:
393:
195:
155:
1432:
is toward the rear of the diagram (to the left when facing in the direction of motion
896:
within nearby stationary conductors by a time-varying magnetic field created by an AC
475:
3312:
2957:
2937:
2910:
2883:
2812:
2806:
2800:
2653:
1944:
1645:
1519:
1186:
960:
713:
2699:(NDE) and condition monitoring of a large variety of metallic structures, including
2687:, is a contactless sensor that uses eddy currents to measure relative acceleration.
1526:
effect. Eddy currents can also have undesirable effects, for instance power loss in
1002:
3250:
3079:
3043:"Ferraris Acceleration Sensor - Principle and Field of Application in Servo Drives"
2851:
2818:
2661:
2657:
2565:
A cross section through a linear motor placed above a thick aluminium slab. As the
1616:
1279:
877:
865:
813:
728:
688:
678:
565:
520:
503:
420:
355:
125:
49:
2722:
2186:, and assuming isotropic homogeneous conductivity, the equation can be written as
1024:
3129:
3049:
2824:
2637:
2609:
1608:
1552:
1498:
1410:
1209:
this force gives the electron a component of velocity in the sideways direction (
1190:
1028:
1006:
748:
673:
668:
535:
410:
375:
235:
135:
3300:
3159:
2875:
788:
27:
Loops of electric current induced within conductors by a changing magnetic field
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2700:
2669:
1469:
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944:
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703:
525:
415:
340:
290:
240:
213:
170:
145:
115:
108:
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3011:
1483:
each of the circular currents in the sheet creates a counter magnetic field (
1039:
3392:
2747:
2665:
2616:
2370:
1639:
1612:
1600:
1490:
1394:
1306:
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1017:
924:
897:
823:
808:
793:
733:
445:
360:
345:
260:
245:
150:
3083:
2990:
Hysteresis in
Magnetism: For Physicists, Materials Scientists, and Engineers
2929:
1080:
are counter magnetic fields generated by the circular motion of the charges.
963:
furnaces and equipment, and to detect cracks and flaws in metal parts using
2735:
2575:
2234:{\displaystyle -\nabla ^{2}\mathbf {H} =\sigma \nabla \times \mathbf {E} .}
2152:
1748:{\displaystyle P={\frac {\pi ^{2}{B_{\text{p}}}^{2}d^{2}f^{2}}{6k\rho D}},}
956:
803:
698:
663:
605:
540:
460:
425:
180:
1518:
generate heat as well as electromagnetic forces. The heat can be used for
2876:
Israel D. Vagner; B.I. Lembrikov; Peter Rudolf Wyder (17 November 2003).
2843:
2743:
2712:
2641:
1840:
1828:
1808:
1657:
1628:
1624:
1604:
1575:
1538:
1527:
1515:
1385:
Another equivalent way to understand the current is to see that the free
940:
913:
901:
723:
575:
405:
67:
1656:
Under certain assumptions (uniform material, uniform magnetic field, no
1382:, inducing a second eddy current in a clockwise direction in the sheet.
2731:
440:
3181:
2586:
2561:
1013:
763:
738:
550:
72:
3359:
3301:
Fitzgerald, A. E.; Kingsley, Charles Jr.; Umans, Stephen D. (1983).
2142:{\displaystyle -\nabla ^{2}\mathbf {H} =\nabla \times \mathbf {J} .}
2739:
1831:; that is, the electromagnetic wave fully penetrates the material.
1489:). Another way to understand the drag force is to see that due to
1450:
1390:
936:
515:
510:
130:
959:
to minimize them. Eddy currents are also used to heat objects in
3016:
1820:
951:, and other AC machinery, requiring special construction such as
485:
3381:
Eddy
Current Separator Cogelme for non-ferrous metals separation
2526:
been switched on, the pendulum is stopped on entering the field.
1799:
is a constant equal to 1 for a thin sheet and 2 for a thin wire,
1648:
makes use of eddy currents to provide heating of metal objects.
2625:
2539:
1530:. In this application, they are minimized with thin plates, by
905:
570:
77:
2703:
tubes, aircraft fuselage, and aircraft structural components.
1892:{\displaystyle \delta ={\frac {1}{\sqrt {\pi f\mu \sigma }}},}
1620:
980:
3061:
Jian Wang, Paul
Vanherck, Jan Swevers, Hendrik Van Brussel.
2585:
With a very strong handheld magnet, such as those made from
1031:
used the principles to conduct metallurgical sorting tests.
3231:
Coating
Thickness Measurement with Electromagnetic Methods
932:
909:
1783:
is the thickness of the sheet or diameter of the wire (m),
2930:
Howard
Johnson; Howard W. Johnson; Martin Graham (2003).
2640:, eddy currents are used to detect counterfeit coins, or
1623:) or by using thin sheets of magnetic material, known as
1990:{\displaystyle \nabla \times \mathbf {H} =\mathbf {J} .}
2882:. Springer Science & Business Media. pp. 73â.
2734:
of the surface of the material. This effect limits the
1615:
materials that have low electrical conductivity (e.g.,
1545:, which is caused by externally induced eddy currents.
1476:
of the metal, so the metal gets warm under the magnet.
1468:
force on the sheet proportional to its velocity. The
1142:) of the magnet's North pole N is directed down in the
3325:
2604:. Superconductors also exhibit a separate inherently
1403:
of the charges is to the right and the magnetic field
1189:. Since the electron has a negative charge, from the
2392:
2282:
2192:
2103:
2013:
1964:
1858:
1666:
1651:
3364:
3182:"Zappi - Eddy Current Conductivity Meter - Products"
1247:. From the right hand rule, this is directed in the
2933:
High-speed Signal Propagation: Advanced Black Magic
2550:
1537:Self-induced eddy currents are responsible for the
1534:of conductors or other details of conductor shape.
3327:
2869:
2695:Eddy current techniques are commonly used for the
2486:
2331:
2233:
2141:
2075:
1989:
1891:
1747:
1460:) so their motion is opposite in direction to the
1269:Eddy current brake. The North magnetic pole piece
3326:Sears, Francis Weston; Zemansky, Mark W. (1955).
3031:Hendo Hoverboards - World's first REAL hoverboard
2923:
2647:
2533:use the drag force created by eddy currents as a
1115:the electron has the same velocity as the sheet (
987:, causing localised areas of turbulence known as
3390:
2848:Safety hazard and defect detection applications
1292:under a stationary magnet. The magnetic field
904:, for example, or by relative motion between a
2683:A Ferraris acceleration sensor, also called a
1001:The first person to observe eddy currents was
3273:"Eddy Current Separator for metal separation"
845:
2936:. Prentice Hall Professional. pp. 80â.
3307:(4th ed.). Mc-Graw-Hill, Inc. p.
2782:Conductivity meters for non-magnetic metals
2652:Eddy currents are used in certain types of
2631:
2902:
2501:
852:
838:
56:
3334:(2nd ed.). Addison-Wesley. pp.
1149:direction. The magnetic field exerts a
2909:. Butterworth-Heinemann. pp. 570â.
2896:
2752:
2721:
2711:Eddy currents are the root cause of the
2619:with electronic switching comparable to
2560:
2511:
1551:
1514:Eddy currents in conductors of non-zero
1264:
1083:
1058:as it moves to the right under a magnet
1038:
3383:â Information and video in Cogelme site
2982:
1764:is the power lost per unit mass (W/kg),
601:Electromagnetism and special relativity
14:
3391:
2879:Electrodynamics of Magnetoactive Media
2386:. The diffusion equation therefore is
2180:in terms of a material's conductivity
1570:within a solid iron transformer core.
1413:the Lorentz force on positive charges
979:comes from analogous currents seen in
3365:Krawczyk, Andrzej; J. A. Tegopoulos.
3349:
2973:
2762:
2690:
1934:
621:Maxwell equations in curved spacetime
3367:Numerical Modelling of Eddy Currents
2803:(electromechanical induction meters)
2786:Eddy current adjustable-speed drives
1254:direction, opposite to the velocity
1054:induced in a conductive metal plate
912:, and inversely proportional to the
34:. For the Australian rock band, see
1453:, actually have a negative charge (
24:
3343:
3207:"Institut Dr. Foerster: SIGMATEST"
2992:, San Diego: Academic Press, 1998.
2538:some roller coasters, where heavy
2467:
2457:
2442:
2432:
2394:
2317:
2307:
2284:
2217:
2197:
2125:
2108:
2059:
2042:
2022:
2014:
1965:
1943:, providing an expression for the
1652:Power dissipation of eddy currents
1286:moving to the right with velocity
25:
3415:
3374:
3360:https://doi.org/10.1063/1.1659166
970:
2551:Repulsive effects and levitation
2461:
2436:
2404:
2311:
2294:
2224:
2207:
2168:, which relates current density
2132:
2118:
2066:
2052:
2029:
1980:
1972:
1603:reduces efficiency of iron-core
1132:direction. The magnetic field (
3404:Mechanical biological treatment
3265:
3235:
3224:
3199:
3174:
3144:
3122:"zipSTOP Zip Line Brake System"
3114:
3089:
3074:J. Fassnacht and P. Mutschler.
3068:
3055:
2978:(2nd ed.). pp. 387â8.
2903:Walt Boyes (25 November 2009).
2706:
2596:In a perfect conductor with no
2496:
2243:Using the differential form of
1811:of the material (Ί m), and
1775:is the peak magnetic field (T),
30:For the comic-book series, see
3035:
3024:
2995:
2967:
2950:
2906:Instrumentation Reference Book
2830:Coating thickness measurements
2648:Vibration and position sensing
1952:surrounding a current density
1905:is the penetration depth (m),
1834:
1034:
888:in the conductor according to
13:
1:
3352:The Analysis of Eddy Currents
2857:
1509:
626:Relativistic electromagnetism
36:Eddy Current Suppression Ring
2833:Sheet resistance measurement
2674:American Petroleum Institute
2628:but is not bound to a rail.
1574:Making the core out of thin
7:
1921:of the material (H/m), and
1409:is directed down, from the
920:or whirlpools in a liquid.
10:
3420:
3354:. Oxford University Press.
2697:nondestructive examination
2554:
2505:
1838:
1619:or iron powder mixed with
1438:). This causes a current
1340:, this creates a circular
1338:Faraday's law of induction
1278:A magnet induces circular
996:
890:Faraday's law of induction
351:LiĂŠnardâWiechert potential
29:
3152:"Our Patented Technology"
2768:Rock climbing auto belays
2557:electrodynamic suspension
2087:Gauss's law for magnetism
1397:. Since the velocity
1076:force on the sheet. The
616:Mathematical descriptions
326:Electromagnetic radiation
316:Electromagnetic induction
256:Magnetic vector potential
251:Magnetic scalar potential
2632:Identification of metals
2624:This is comparable to a
2621:electronic speed control
2578:from other metals in an
1193:this is directed in the
953:laminated magnetic cores
3247:www.nagy-instruments.de
3084:10.1109/IAS.2001.955949
2715:in conductors carrying
2676:(API) Standard 670 and
2502:Electromagnetic braking
1931:of the material (S/m).
1929:electrical conductivity
1911:is the frequency (Hz),
1823:of the material (kg/m).
166:Electrostatic induction
161:Electrostatic discharge
3156:Head Rush Technologies
3126:Head Rush Technologies
3101:Head Rush Technologies
2976:Electromagnetic Fields
2837:Eddy current separator
2821:(displacement sensors)
2759:
2727:
2636:In some coin-operated
2608:phenomenon called the
2580:eddy current separator
2570:
2567:linear induction motor
2527:
2488:
2333:
2235:
2143:
2077:
1991:
1893:
1791:is the frequency (Hz),
1749:
1596:
1578:parallel to the field
1481:Ampère's circuital law
1275:
1262:
1081:
1062:. The magnetic field
596:Electromagnetic tensor
3350:Stoll, R. L. (1974).
2756:
2725:
2564:
2544:Electrical resistance
2524:
2489:
2334:
2236:
2144:
2078:
1992:
1919:magnetic permeability
1894:
1750:
1555:
1268:
1087:
1042:
589:Covariant formulation
381:Synchrotron radiation
321:Electromagnetic pulse
311:Electromagnetic field
32:Eddy Current (comics)
3211:www.foerstergroup.de
3097:"TRUBLUE Auto Belay"
3048:27 July 2014 at the
3012:"Eddy Current Tubes"
2839:for metal separation
2827:(detection of coins)
2791:Eddy-current testing
2390:
2373:of the material and
2280:
2190:
2101:
2011:
1962:
1856:
1664:
1462:conventional current
965:eddy-current testing
631:Stressâenergy tensor
556:Reluctance (complex)
301:Displacement current
2717:alternating current
2602:magnetic levitation
2531:Eddy current brakes
2384:vacuum permeability
1636:eddy current brakes
929:eddy current brakes
546:Magnetomotive force
431:Electromotive force
401:Alternating current
336:Jefimenko equations
296:Cyclotron radiation
3330:University Physics
3304:Electric Machinery
3295:General references
2974:Wangsness, Roald.
2801:Electricity meters
2796:Eddy current brake
2763:Other applications
2760:
2728:
2691:Structural testing
2606:quantum mechanical
2571:
2528:
2508:Eddy current brake
2484:
2329:
2231:
2174:to electric field
2139:
2073:
1987:
1935:Diffusion equation
1889:
1745:
1597:
1449:in the metal, the
1276:
1263:
1082:
874:Foucault's current
394:Electrical network
231:Gauss magnetic law
196:Static electricity
156:Electric potential
3318:978-0-07-021145-2
3243:"Ohm/sq & OD"
3041:Bernhard Hiller.
2943:978-0-13-084408-8
2916:978-0-08-094188-2
2889:978-3-540-43694-2
2813:induction cooking
2807:Induction heating
2774:Free fall devices
2654:proximity sensors
2574:is separation of
2522:
2474:
2449:
2324:
1945:magnetizing field
1884:
1883:
1740:
1695:
1646:Induction heating
1520:induction heating
1280:electric currents
1187:electron's charge
1023:French physicist
961:induction heating
862:
861:
561:Reluctance (real)
531:Gyratorâcapacitor
476:Resonant cavities
366:Maxwell equations
16:(Redirected from
3411:
3370:
3355:
3339:
3333:
3322:
3288:
3287:
3285:
3283:
3269:
3263:
3262:
3260:
3258:
3249:. Archived from
3239:
3233:
3228:
3222:
3221:
3219:
3217:
3203:
3197:
3196:
3194:
3192:
3178:
3172:
3171:
3169:
3167:
3158:. Archived from
3148:
3142:
3141:
3139:
3137:
3128:. Archived from
3118:
3112:
3111:
3109:
3107:
3093:
3087:
3072:
3066:
3059:
3053:
3039:
3033:
3028:
3022:
3021:
2999:
2993:
2986:
2980:
2979:
2971:
2965:
2954:
2948:
2947:
2927:
2921:
2920:
2900:
2894:
2893:
2873:
2863:Online citations
2852:Magnetic damping
2825:Vending machines
2819:Proximity sensor
2662:Donald E. Bently
2658:General Electric
2638:vending machines
2523:
2493:
2491:
2490:
2485:
2480:
2476:
2475:
2473:
2465:
2464:
2455:
2450:
2448:
2440:
2439:
2430:
2420:
2419:
2407:
2402:
2401:
2381:
2368:
2362:
2338:
2336:
2335:
2330:
2325:
2323:
2315:
2314:
2305:
2297:
2292:
2291:
2275:
2274:
2272:
2271:
2265:
2262:
2240:
2238:
2237:
2232:
2227:
2210:
2205:
2204:
2185:
2179:
2173:
2167:
2148:
2146:
2145:
2140:
2135:
2121:
2116:
2115:
2096:
2082:
2080:
2079:
2074:
2069:
2055:
2050:
2049:
2037:
2033:
2032:
2005:curl of the curl
1996:
1994:
1993:
1988:
1983:
1975:
1957:
1951:
1926:
1916:
1910:
1904:
1898:
1896:
1895:
1890:
1885:
1870:
1866:
1818:
1806:
1798:
1790:
1782:
1774:
1763:
1754:
1752:
1751:
1746:
1741:
1739:
1725:
1724:
1723:
1714:
1713:
1704:
1703:
1698:
1697:
1696:
1693:
1685:
1684:
1674:
1591:with insulation
1588:
1586:
1567:
1565:
1543:proximity effect
1487:
1459:
1443:
1437:
1431:
1408:
1402:
1381:
1379:
1377:
1376:
1371:
1368:
1352:
1350:
1335:
1333:
1331:
1330:
1325:
1322:
1302:
1300:
1291:
1259:
1253:
1246:
1217:
1208:
1199:
1184:
1178:
1153:on the electron
1148:
1137:
1131:
1120:
1114:
1105:
1096:
1079:
1072:
1070:
1051:
1049:
878:electric current
866:electromagnetism
854:
847:
840:
521:Electric machine
504:Magnetic circuit
466:Parallel circuit
456:Network analysis
421:Electric current
356:London equations
201:Triboelectricity
191:Potential energy
60:
50:Electromagnetism
41:
40:
21:
3419:
3418:
3414:
3413:
3412:
3410:
3409:
3408:
3399:Electrodynamics
3389:
3388:
3377:
3346:
3344:Further reading
3319:
3292:
3291:
3281:
3279:
3277:www.cogelme.com
3271:
3270:
3266:
3256:
3254:
3253:on 4 March 2016
3241:
3240:
3236:
3229:
3225:
3215:
3213:
3205:
3204:
3200:
3190:
3188:
3180:
3179:
3175:
3165:
3163:
3162:on 8 March 2016
3150:
3149:
3145:
3135:
3133:
3120:
3119:
3115:
3105:
3103:
3095:
3094:
3090:
3073:
3069:
3060:
3056:
3050:Wayback Machine
3040:
3036:
3029:
3025:
3010:
3007:Wayback Machine
3000:
2996:
2987:
2983:
2972:
2968:
2955:
2951:
2944:
2928:
2924:
2917:
2901:
2897:
2890:
2874:
2870:
2860:
2778:Metal detectors
2771:Zip line brakes
2765:
2709:
2693:
2685:Ferraris sensor
2650:
2634:
2610:Meissner effect
2559:
2553:
2512:
2510:
2504:
2499:
2466:
2460:
2456:
2454:
2441:
2435:
2431:
2429:
2428:
2424:
2415:
2411:
2403:
2397:
2393:
2391:
2388:
2387:
2380:
2374:
2364:
2352:
2342:
2341:By definition,
2316:
2310:
2306:
2304:
2293:
2287:
2283:
2281:
2278:
2277:
2266:
2263:
2257:
2256:
2254:
2248:
2223:
2206:
2200:
2196:
2191:
2188:
2187:
2181:
2175:
2169:
2156:
2131:
2117:
2111:
2107:
2102:
2099:
2098:
2090:
2065:
2051:
2045:
2041:
2028:
2021:
2017:
2012:
2009:
2008:
1979:
1971:
1963:
1960:
1959:
1953:
1947:
1937:
1922:
1912:
1906:
1900:
1865:
1857:
1854:
1853:
1843:
1837:
1814:
1802:
1794:
1786:
1778:
1773:
1767:
1759:
1726:
1719:
1715:
1709:
1705:
1699:
1692:
1688:
1687:
1686:
1680:
1676:
1675:
1673:
1665:
1662:
1661:
1654:
1609:electric motors
1582:
1581:
1563:
1562:
1512:
1499:right hand rule
1485:
1454:
1447:charge carriers
1439:
1433:
1414:
1411:right hand rule
1404:
1398:
1387:charge carriers
1372:
1369:
1364:
1363:
1361:
1360:
1348:
1347:
1326:
1323:
1318:
1317:
1315:
1314:
1296:
1295:
1287:
1255:
1248:
1240:
1229:
1223:
1216:
1210:
1207:
1201:
1200:direction. At
1194:
1191:right hand rule
1180:
1164:
1158:
1143:
1133:
1126:
1116:
1113:
1107:
1104:
1098:
1095:
1089:
1077:
1066:
1065:
1047:
1046:
1037:
1029:David E. Hughes
1007:Michael Faraday
999:
973:
945:electric motors
880:induced within
876:) is a loop of
858:
829:
828:
644:
636:
635:
591:
581:
580:
536:Induction motor
506:
496:
495:
411:Current density
396:
386:
385:
376:Poynting vector
286:
284:Electrodynamics
276:
275:
271:Right-hand rule
236:Magnetic dipole
226:BiotâSavart law
216:
206:
205:
141:Electric dipole
136:Electric charge
111:
39:
28:
23:
22:
15:
12:
11:
5:
3417:
3407:
3406:
3401:
3385:
3384:
3376:
3375:External links
3373:
3372:
3371:
3362:
3356:
3345:
3342:
3341:
3340:
3323:
3317:
3297:
3296:
3290:
3289:
3264:
3234:
3223:
3198:
3173:
3143:
3132:on 6 June 2017
3113:
3088:
3067:
3054:
3034:
3023:
2994:
2981:
2966:
2949:
2942:
2922:
2915:
2895:
2888:
2867:
2866:
2865:
2864:
2859:
2856:
2855:
2854:
2849:
2846:
2840:
2834:
2831:
2828:
2822:
2816:
2809:
2804:
2798:
2793:
2788:
2783:
2780:
2775:
2772:
2769:
2764:
2761:
2748:magnetic cores
2708:
2705:
2701:heat exchanger
2692:
2689:
2670:turbomachinery
2649:
2646:
2633:
2630:
2617:electromagnets
2555:Main article:
2552:
2549:
2506:Main article:
2503:
2500:
2498:
2495:
2483:
2479:
2472:
2469:
2463:
2459:
2453:
2447:
2444:
2438:
2434:
2427:
2423:
2418:
2414:
2410:
2406:
2400:
2396:
2378:
2350:
2328:
2322:
2319:
2313:
2309:
2303:
2300:
2296:
2290:
2286:
2230:
2226:
2222:
2219:
2216:
2213:
2209:
2203:
2199:
2195:
2138:
2134:
2130:
2127:
2124:
2120:
2114:
2110:
2106:
2072:
2068:
2064:
2061:
2058:
2054:
2048:
2044:
2040:
2036:
2031:
2027:
2024:
2020:
2016:
1986:
1982:
1978:
1974:
1970:
1967:
1936:
1933:
1888:
1882:
1879:
1876:
1873:
1869:
1864:
1861:
1839:Main article:
1836:
1833:
1825:
1824:
1812:
1800:
1792:
1784:
1776:
1771:
1765:
1744:
1738:
1735:
1732:
1729:
1722:
1718:
1712:
1708:
1702:
1691:
1683:
1679:
1672:
1669:
1653:
1650:
1559:Eddy currents
1511:
1508:
1470:kinetic energy
1342:electric field
1301:, green arrows
1238:
1227:
1214:
1205:
1162:
1111:
1102:
1093:
1043:Eddy currents
1036:
1033:
1003:François Arago
998:
995:
985:fluid dynamics
972:
971:Origin of term
969:
886:magnetic field
884:by a changing
860:
859:
857:
856:
849:
842:
834:
831:
830:
827:
826:
821:
816:
811:
806:
801:
796:
791:
786:
781:
776:
771:
766:
761:
756:
751:
746:
741:
736:
731:
726:
721:
716:
711:
706:
701:
696:
691:
686:
681:
676:
671:
666:
661:
656:
651:
645:
642:
641:
638:
637:
634:
633:
628:
623:
618:
613:
611:Four-potential
608:
603:
598:
592:
587:
586:
583:
582:
579:
578:
573:
568:
563:
558:
553:
548:
543:
538:
533:
528:
526:Electric motor
523:
518:
513:
507:
502:
501:
498:
497:
494:
493:
488:
483:
481:Series circuit
478:
473:
468:
463:
458:
453:
451:Kirchhoff laws
448:
443:
438:
433:
428:
423:
418:
416:Direct current
413:
408:
403:
397:
392:
391:
388:
387:
384:
383:
378:
373:
371:Maxwell tensor
368:
363:
358:
353:
348:
343:
341:Larmor formula
338:
333:
328:
323:
318:
313:
308:
303:
298:
293:
291:Bremsstrahlung
287:
282:
281:
278:
277:
274:
273:
268:
263:
258:
253:
248:
243:
241:Magnetic field
238:
233:
228:
223:
217:
214:Magnetostatics
212:
211:
208:
207:
204:
203:
198:
193:
188:
183:
178:
173:
168:
163:
158:
153:
148:
146:Electric field
143:
138:
133:
128:
123:
118:
116:Charge density
112:
109:Electrostatics
107:
106:
103:
102:
101:
100:
95:
90:
85:
80:
75:
70:
62:
61:
53:
52:
46:
45:
44:Articles about
26:
9:
6:
4:
3:
2:
3416:
3405:
3402:
3400:
3397:
3396:
3394:
3387:
3382:
3379:
3378:
3368:
3363:
3361:
3357:
3353:
3348:
3347:
3337:
3332:
3331:
3324:
3320:
3314:
3310:
3306:
3305:
3299:
3298:
3294:
3293:
3278:
3274:
3268:
3252:
3248:
3244:
3238:
3232:
3227:
3212:
3208:
3202:
3187:
3183:
3177:
3161:
3157:
3153:
3147:
3131:
3127:
3123:
3117:
3102:
3098:
3092:
3085:
3081:
3077:
3071:
3064:
3058:
3051:
3047:
3044:
3038:
3032:
3027:
3019:
3018:
3013:
3008:
3004:
2998:
2991:
2985:
2977:
2970:
2963:
2962:0-12-257251-3
2959:
2953:
2945:
2939:
2935:
2934:
2926:
2918:
2912:
2908:
2907:
2899:
2891:
2885:
2881:
2880:
2872:
2868:
2862:
2861:
2853:
2850:
2847:
2845:
2841:
2838:
2835:
2832:
2829:
2826:
2823:
2820:
2817:
2814:
2810:
2808:
2805:
2802:
2799:
2797:
2794:
2792:
2789:
2787:
2784:
2781:
2779:
2776:
2773:
2770:
2767:
2766:
2755:
2751:
2749:
2745:
2741:
2737:
2733:
2724:
2720:
2718:
2714:
2704:
2702:
2698:
2688:
2686:
2681:
2679:
2675:
2671:
2667:
2666:Bently Nevada
2663:
2659:
2655:
2645:
2643:
2639:
2629:
2627:
2622:
2618:
2613:
2611:
2607:
2603:
2599:
2594:
2592:
2588:
2583:
2581:
2577:
2576:aluminum cans
2568:
2563:
2558:
2548:
2545:
2541:
2536:
2532:
2509:
2494:
2481:
2477:
2470:
2451:
2445:
2425:
2421:
2416:
2412:
2408:
2398:
2385:
2377:
2372:
2371:magnetization
2367:
2360:
2356:
2349:
2345:
2339:
2326:
2320:
2301:
2298:
2288:
2276:, this gives
2270:
2261:
2252:
2246:
2245:Faraday's law
2241:
2228:
2220:
2214:
2211:
2201:
2193:
2184:
2178:
2172:
2166:
2163:
2159:
2154:
2149:
2136:
2128:
2122:
2112:
2104:
2094:
2088:
2083:
2070:
2062:
2056:
2046:
2038:
2034:
2025:
2018:
2006:
2002:
1997:
1984:
1976:
1968:
1956:
1950:
1946:
1942:
1932:
1930:
1925:
1920:
1915:
1909:
1903:
1886:
1880:
1877:
1874:
1871:
1867:
1862:
1859:
1850:
1848:
1842:
1832:
1830:
1822:
1817:
1813:
1810:
1805:
1801:
1797:
1793:
1789:
1785:
1781:
1777:
1770:
1766:
1762:
1758:
1757:
1756:
1742:
1736:
1733:
1730:
1727:
1720:
1716:
1710:
1706:
1700:
1689:
1681:
1677:
1670:
1667:
1659:
1649:
1647:
1643:
1641:
1637:
1632:
1630:
1626:
1622:
1618:
1614:
1613:magnetic core
1610:
1606:
1602:
1601:Joule heating
1594:
1590:
1585:
1577:
1573:
1569:
1558:
1554:
1550:
1546:
1544:
1540:
1535:
1533:
1529:
1525:
1521:
1517:
1507:
1505:
1500:
1496:
1492:
1488:
1482:
1477:
1475:
1471:
1465:
1463:
1457:
1452:
1448:
1442:
1436:
1429:
1425:
1421:
1417:
1412:
1407:
1401:
1396:
1395:Lorentz force
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1307:magnetic flux
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1025:LĂŠon Foucault
1021:
1019:
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1009:(1791â1867).
1008:
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967:instruments.
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3280:. Retrieved
3276:
3267:
3255:. Retrieved
3251:the original
3246:
3237:
3226:
3214:. Retrieved
3210:
3201:
3189:. Retrieved
3186:zappitec.com
3185:
3176:
3164:. Retrieved
3160:the original
3155:
3146:
3134:. Retrieved
3130:the original
3125:
3116:
3104:. Retrieved
3100:
3091:
3070:
3057:
3037:
3026:
3015:
3003:Ghostarchive
3001:Archived at
2997:
2989:
2984:
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2898:
2878:
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2844:speedometers
2744:transformers
2736:flux linkage
2729:
2710:
2707:Skin effects
2694:
2682:
2651:
2635:
2614:
2595:
2584:
2572:
2529:
2497:Applications
2375:
2365:
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2354:
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2259:
2250:
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2182:
2176:
2170:
2164:
2161:
2157:
2150:
2092:
2084:
1998:
1954:
1948:
1941:Ampère's Law
1938:
1923:
1913:
1907:
1901:
1851:
1846:
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1826:
1815:
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1605:transformers
1598:
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1528:transformers
1513:
1504:(right side)
1503:
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1484:
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1011:
1000:
988:
977:eddy current
976:
974:
941:transformers
922:
873:
870:eddy current
869:
863:
606:Four-current
541:Linear motor
426:Electrolysis
306:Eddy current
305:
266:Permeability
186:Polarization
181:Permittivity
18:Eddy-current
2842:Mechanical
2732:skin depths
2713:skin effect
2007:results in
1999:Taking the
1847:skin effect
1841:Skin effect
1835:Skin effect
1829:skin effect
1809:resistivity
1658:skin effect
1629:Hall effect
1625:laminations
1576:laminations
1539:skin effect
1516:resistivity
1495:(left side)
1486:blue arrows
1311:(left side)
1220:black arrow
1140:green arrow
1123:black arrow
1078:blue arrows
1035:Explanation
914:resistivity
902:transformer
576:Transformer
406:Capacitance
331:Faraday law
126:Coulomb law
68:Electricity
3393:Categories
2964:, page. 31
2858:References
2598:resistance
1640:Lenz's law
1532:lamination
1510:Properties
1491:Lenz's law
1474:resistance
1018:Lenz's law
949:generators
925:Lenz's law
882:conductors
643:Scientists
491:Waveguides
471:Resistance
441:Inductance
221:Ampère law
2811:Cooking (
2740:inductors
2587:neodymium
2468:∂
2458:∂
2443:∂
2433:∂
2422:σ
2413:μ
2395:∇
2318:∂
2308:∂
2302:σ
2285:∇
2221:×
2218:∇
2215:σ
2198:∇
2194:−
2153:Ohm's law
2129:×
2126:∇
2109:∇
2105:−
2063:×
2060:∇
2043:∇
2039:−
2026:⋅
2023:∇
2015:∇
1969:×
1966:∇
1881:σ
1878:μ
1872:π
1860:δ
1734:ρ
1678:π
1451:electrons
1391:electrons
1274:possible.
1125:) in the
1014:Emil Lenz
1012:In 1834,
975:The term
937:inductors
799:Steinmetz
729:Kirchhoff
714:Jefimenko
709:Hopkinson
694:Helmholtz
689:Heaviside
551:Permeance
436:Impedance
176:Insulator
171:Gauss law
121:Conductor
98:Phenomena
93:Textbooks
73:Magnetism
3078:. 2001.
3046:Archived
3005:and the
2363:, where
1617:ferrites
1336:. From
1179:, where
824:Wiechert
779:Poynting
669:Einstein
516:DC motor
511:AC motor
346:Lenz law
131:Electret
3216:28 June
3166:8 March
3136:8 March
3106:8 March
3017:YouTube
2746:having
2382:is the
2369:is the
2273:
2255:
1927:is the
1917:is the
1821:density
1819:is the
1807:is the
1587:, green
1572:(right)
1524:braking
1497:by the
1479:Due to
1464:shown.
1378:
1362:
1332:
1316:
1185:is the
1071:, green
1016:stated
997:History
894:induced
809:Thomson
784:Ritchie
774:Poisson
759:Neumann
754:Maxwell
749:Lorentz
744:LiĂŠnard
674:Faraday
659:Coulomb
486:Voltage
461:Ohm law
83:History
3315:
2960:
2940:
2913:
2886:
2680:7919.
2626:maglev
2615:Using
2540:copper
2151:Using
1899:where
1755:where
1557:(left)
1458:< 0
1380:< 0
1334:> 0
990:eddies
918:eddies
906:magnet
794:Singer
789:Savart
769:Ărsted
734:Larmor
724:Kelvin
679:Fizeau
649:Ampère
571:Stator
78:Optics
3338:â618.
3282:8 May
3257:8 May
3191:8 May
2642:slugs
2591:penny
2535:brake
2097:, so
2085:From
1621:resin
1566:, red
1351:, red
1271:(top)
1050:, red
981:water
868:, an
819:Weber
814:Volta
804:Tesla
719:Joule
704:Hertz
699:Henry
684:Gauss
566:Rotor
3313:ISBN
3284:2016
3259:2016
3218:2018
3193:2022
3168:2016
3138:2016
3108:2016
2958:ISBN
2938:ISBN
2911:ISBN
2884:ISBN
2758:gap.
2742:and
2249:â Ă
2091:â â
2001:curl
1607:and
947:and
933:heat
910:flux
739:Lenz
664:Davy
654:Biot
3336:616
3080:doi
2988:G.
2738:in
2678:ISO
2664:at
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955:or
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900:or
864:In
764:Ohm
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2089:,
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1426:Ă
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1374:dt
1366:dB
1328:dt
1320:dB
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