526:
2462:
238:
2093:
992:
492:
2911:
226:
2316:"poles" where the field lines emerge from the core, a special analogy called a magnetic-charge model which assumes the magnetic field is produced by fictitious 'magnetic charges' on the surface of the poles. This model assumes point-like poles instead of the really existing surfaces, and thus it only yields a good approximation when the distance between the magnets is much larger than their diameter, so it is useful just for a force between them.
325:
1565:
102:
214:
93:
2799:
940:
477:
2555:, and resists changes in the current through its windings. Any sudden changes in the winding current cause large voltage spikes across the windings. This is because when the current through the magnet is increased, such as when it is turned on, energy from the circuit must be stored in the magnetic field. When it is turned off the energy in the field is returned to the circuit.
511:
1133:(T) for most high permeability core steels. The B field increases quickly with increasing current up to that value, but above that value the field levels off and becomes almost constant, regardless of how much current is sent through the windings. The maximum strength of the magnetic field possible from an iron core electromagnet is limited to around 1.6 to 2 T.
465:
3791:
43:
2828:. These allow enormous currents to flow, which generate intense magnetic fields. Superconducting magnets are limited by the field strength at which the winding material ceases to be superconducting. Current designs are limited to 10–20 T, with the current (2017) record of 32 T. The necessary refrigeration equipment and
2736:, oriented parallel to the magnetic field, with an insulating coating on the surface. The insulation layers prevent eddy current from flowing between the sheets. Any remaining eddy currents must flow within the cross-section of each individual lamination, which reduces losses greatly. Another alternative is to use a
2895:
The factor limiting the strength of electromagnets is the inability to dissipate the enormous waste heat, so more powerful fields, up to 100 T, have been obtained from resistive magnets by sending brief pulses of high current through them; the inactive period after each pulse allows the heat produced
2914:
A hollow tube type of explosively pumped flux compression generator. The hollow copper tube acts like a single-turn secondary winding of a transformer; when the pulse of current from the capacitor in the windings creates a pulse of magnetic field, this creates a strong circumferential current in the
930:
Some improvements can be made on the basic design. The ends of the stop and plunger are often conical. For example, the plunger may have a pointed end that fits into a matching recess in the stop. The shape makes the solenoid's pull more uniform as a function of separation. Another improvement is to
273:
to insulate it from the windings. When a current was passed through the coil, the iron became magnetized and attracted other pieces of iron; when the current was stopped, it lost magnetization. Sturgeon displayed its power by showing that although it only weighed seven ounces (roughly 200 grams), it
2575:
is used to prevent voltage spikes by providing a path for the current to recirculate through the winding until the energy is dissipated as heat. The diode is connected across the winding, oriented so it is reverse-biased during steady state operation and does not conduct. When the supply voltage is
2562:
is used to control the winding current, this can cause sparks at the terminals of the switch. This does not occur when the magnet is switched on, because the limited supply voltage causes the current through the magnet and the field energy to increase slowly, but when it is switched off, the energy
2535:
or lowering the resistance is that the windings take up more room between the magnet's core pieces. If the area available for the windings is filled up, more turns require going to a smaller diameter of wire, which has higher resistance, which cancels the advantage of using more turns. So in large
2302:
a flat cylindrical design is often used. The winding is wrapped around a short wide cylindrical core that forms one pole, and a thick metal housing that wraps around the outside of the windings forms the other part of the magnetic circuit, bringing the magnetic field to the front to form the other
553:
and plunger. The solenoid is a coil of wire, and the plunger is made of a material such as soft iron. Applying a current to the solenoid applies a force to the plunger and may make it move. The plunger stops moving when the forces upon it are balanced. For example, the forces are balanced when the
2731:
in the core are the major problem. Eddy currents are closed loops of current that flow in planes perpendicular to the magnetic field. The energy dissipated is proportional to the area enclosed by the loop. To prevent them, the cores of AC electromagnets are made of stacks of thin steel sheets, or
2315:
and do not apply when a large part of the magnetic field path is outside the core. A non-circuit example would be a magnet with a straight cylindrical core like the one shown at the top of this article. Only focusing on the force between two electromagnets (or permanent magnets) with well-defined
1136:
When the current in the coil is turned off, in the magnetically soft materials that are nearly always used as cores, most of the domains lose alignment and return to a random state and the field disappears. However, some of the alignment persists, because the domains have difficulty turning their
1663:
Since most of the magnetic field is confined within the outlines of the core loop, this allows a simplification of the mathematical analysis. See the drawing at right. A common simplifying assumption satisfied by many electromagnets, which will be used in this section, is that the magnetic field
1105:
penetrates the iron, and causes the domains to turn, aligning parallel to the magnetic field, so their tiny magnetic fields add to the wire's field, creating a large magnetic field that extends into the space around the magnet. The effect of the core is to concentrate the field, and the magnetic
1518:
1101:). Before the current in the electromagnet is turned on, the domains in the soft iron core point in random directions, so their tiny magnetic fields cancel each other out, and the iron has no large-scale magnetic field. When a current is passed through the wire wrapped around the iron, its
674:
The maximum pull is increased when a magnetic stop is inserted into the solenoid. The stop becomes a magnet that will attract the plunger; it adds little to the solenoid pull when the plunger is far away but dramatically increases the pull when they are close. An approximation for the pull
2880:. The disks are pierced with holes through which cooling water passes to carry away the heat caused by the high current. The strongest continuous field achieved solely with a resistive magnet is 41.5 tesla as of 22 August 2017, produced by a Bitter electromagnet at the
1683:), if any, between core sections. In the gaps, the magnetic field lines are no longer confined by the core. So they 'bulge' out beyond the outlines of the core before curving back to enter the next piece of core material, reducing the field strength in the gap. The bulges (
274:
could lift nine pounds (roughly 4 kilos) when the current of a single-cell power supply was applied. However, Sturgeon's magnets were weak because the uninsulated wire he used could only be wrapped in a single spaced-out layer around the core, limiting the number of turns.
1113:
The larger the current passed through the wire coil, the more the domains align, and the stronger the magnetic field is. Finally, all the domains are lined up, and further increases in current only cause slight increases in the magnetic field: this phenomenon is called
96:
A simple electromagnet consisting of a coil of wire wrapped around an iron core. A core of ferromagnetic material like iron serves to increase the magnetic field created. The strength of the magnetic field generated is proportional to the amount of current through the
1536:
However, computing the magnetic field and force exerted by ferromagnetic materials in general is difficult for two reasons. First, because the strength of the field varies from point to point in a complicated way, particularly outside the core and in air gaps, where
2832:
make them much more expensive than ordinary electromagnets. However, in high power applications this can be offset by lower operating costs, since after startup no power is required for the windings, since no energy is lost to ohmic heating. They are used in
164:
is that the magnetic field can be quickly changed by controlling the amount of electric current in the winding. However, unlike a permanent magnet that needs no power, an electromagnet requires a continuous supply of current to maintain the magnetic field.
903:
1970:
926:
for units of inches, pounds, and amperes with slender solenoids is about 2660. The second term within the bracket represents the same force as the stop-less solenoid above; the first term represents the attraction between the stop and the plunger.
1220:
1704:) will take 'short cuts' and not pass through the entire core circuit, and thus will not contribute to the force exerted by the magnet. This also includes field lines that encircle the wire windings but do not enter the core. This is called
1863:
2871:
made of a stack of conducting disks, arranged so that the current moves in a helical path through them, with a hole through the center where the maximum field is created. This design has the mechanical strength to withstand the extreme
2083:
depends strongly on the length of the air gap, and the length of the flux path in the core does not matter much. Given an air gap of 1mm, a magnetomotive force of about 796 Ampere-turns is required to produce a magnetic field of 1T.
3731:
289:, he was able to wind multiple layers of wire onto cores, creating powerful magnets with thousands of turns of wire, including one that could support 2,063 lb (936 kg). The first major use for electromagnets was in
1358:
1551:
functions of the current, depending on the nonlinear relation between B and H for the particular core material used. For precise calculations, computer programs that can produce a model of the magnetic field using the
2527:
halves the power loss, as does doubling the area of the wire. In either case, increasing the amount of wire reduces the ohmic losses. For this reason, electromagnets often have a significant thickness of windings.
1018:
with many turns of wire lying side by side. The magnetic field of all the turns of wire passes through the center of the coil, creating a strong magnetic field there. A coil forming the shape of a straight tube (a
109:(coil of wire). This drawing shows a cross-section through the center of the coil. The crosses are wires in which current is moving into the page; the dots are wires in which current is moving up out of the page.
3477:
2272:
1660:) to the magnetic field than air, so a stronger field can be obtained if most of the magnetic field's path is within the core. This is why the core and magnetic field lines are in the form of closed loops.
3824:
2437:
2892:. The previous record was 37.5 T. The strongest continuous magnetic field overall, 45 T, was achieved in June 2000 with a hybrid device consisting of a Bitter magnet inside a superconducting magnet.
3200:
2576:
removed, the voltage spike forward-biases the diode and the reactive current continues to flow through the winding, through the diode, and back into the winding. A diode used in this way is called a
2077:
4046:
3887:
2637:
2670:
design, below, used in very high-field research magnets, the windings are constructed as flat disks to resist the radial forces, and clamped in an axial direction to resist the axial ones.
1319:
4077:
1247:
around any closed loop is equal to the sum of the current flowing through the loop. Another equation used, that gives the magnetic field due to each small segment of current, is the
606:
2639:
acting on the moving charges within the wire. The
Lorentz force is perpendicular to both the axis of the wire and the magnetic field. It can be visualized as a pressure between the
3245:
2158:
3290:
931:
add a magnetic return path around the outside of the solenoid (an "iron-clad solenoid"). The magnetic return path, just as the stop, has little impact until the air gap is small.
685:
2358:
1873:
1676:) will be approximately uniform across any cross-section, so if in addition, the core has roughly constant area throughout its length, the field in the core will be constant.
2511:, increases with the square of the current but only increases approximately linearly with the number of windings, the power lost in the windings can be minimized by reducing
3973:
3340:
2453:
There are several side effects which occur in electromagnets which must be provided for in their design. These generally become more significant in larger electromagnets.
1245:
1149:. In alternating current electromagnets, such as are used in motors, the core's magnetization is constantly reversed, and the remanence contributes to the motor's losses.
2855:
Both iron-core and superconducting electromagnets have limits to the field they can produce. Therefore, the most powerful man-made magnetic fields have been generated by
1694:. However, as long as the length of the gap is smaller than the cross-section dimensions of the core, the field in the gap will be approximately the same as in the core.
3511:
3407:
2923:
The most powerful manmade magnetic fields have been created by using explosives to compress the magnetic field inside an electromagnet as it is pulsed; these are called
1652:
In many practical applications of electromagnets, such as motors, generators, transformers, lifting magnets, and loudspeakers, the iron core is in the form of a loop or
1167:
2802:
The most powerful electromagnet in the world, the 45 T hybrid Bitter-superconducting magnet at the US National High
Magnetic Field Laboratory, Tallahassee, Florida, USA
3370:
1042:) through the windings, the thumb points in the direction of the field inside the coil. The side of the magnet that the field lines emerge from is defined to be the
2023:
Moreover, if the magnetomotive force is well above saturation, so the core material is in saturation, the magnetic field will be approximately the saturation value
1761:
4301:
3573:
3543:
3138:
3108:
3076:
3046:
3013:
2983:
1668:
is constant around the magnetic circuit (within the core and air gaps) and zero outside it. Most of the magnetic field will be concentrated in the core material (
4431:
3817:
2924:
2905:
981:
961:
2595:, which prevent voltage spikes by accomplishing current changes slowly, in gentle ramps. It may take several minutes to energize or deenergize a large magnet.
1533:
Given a core geometry, the B field needed for a given force can be calculated from (1); if it comes out to much more than 1.6 T, a larger core must be used.
2647:
The field lines within the axis of the coil exert a radial force on each turn of the windings, tending to push them outward in all directions. This causes a
265:
invented the electromagnet in 1824. His first electromagnet was a horseshoe-shaped piece of iron that was wrapped with about 18 turns of bare copper wire. (
4454:
2727:
of the conductor, so they are a cause of energy loss. Since the magnet's iron core is conductive, and most of the magnetic field is concentrated there,
1513:{\displaystyle {\frac {F}{A}}={\frac {(B_{\text{sat}})^{2}}{2\mu _{0}}}\approx 1000\ \mathrm {kPa} =10^{6}\mathrm {N/m^{2}} =145\ \mathrm {lbf/in^{2}} }
2034:. For a closed magnetic circuit (no air gap) most core materials saturate at a magnetomotive force of roughly 800 ampere-turns per meter of flux path.
1078:, is placed inside the coil. A core can increase the magnetic field to thousands of times the strength of the field of the coil alone, due to the high
3879:
4030:
2768:
graph. To minimize this loss, magnetic cores used in transformers and other AC electromagnets are made of "soft" low coercivity materials, such as
2108:
For a closed magnetic circuit (no air gap), such as would be found in an electromagnet lifting a piece of iron bridged across its poles, equation (
4462:
2881:
2935:
redirects the blast outwardly to minimize harm to the experiment. These devices are known as destructive pulsed electromagnets. They are used in
4106:
2365:
4061:
3858:
3788:
3768:
3663:
4466:
4266:
2919:
within. The explosives then collapse the tube, reducing its diameter, and the field lines are forced closer together, increasing the field.
639:
is around 0.009 to 0.010 psi (maximum pull pounds per square inch of plunger cross-sectional area). For example, a 12-inch long coil (
4401:
3414:
2298:
is preferred (this also applies to magnets with an air gap). To achieve this, in applications like lifting magnets (see photo above) and
4015:
4249:
3774:
433:
equipment is used for separating magnetic from nonmagnetic material, for example separating ferrous metal from other material in scrap.
4215:
4188:
4071:
4040:
3725:
2654:
The leakage field lines between each turn of the coil exert an attractive force between adjacent turns, tending to pull them together.
2481:
of the windings, and is dissipated as heat. Some large electromagnets require water cooling systems in the windings to carry off the
2190:
3803:
1530:. In more intuitive units it is useful to remember that at 1 T the magnetic pressure is approximately 4 atmospheres, or kg/cm.
525:
79:
1000:
200:
equipment. Electromagnets are also employed in industry for picking up and moving heavy iron objects such as scrap iron and steel.
2662:. In large electromagnets the windings must be firmly clamped in place, to prevent motion on power-up and power-down from causing
2442:
2040:
1118:. This is why the very strongest electromagnets, such as superconducting and very high current electromagnets, cannot use cores.
3715:
1079:
3145:
2931:
compresses the magnetic field to values of around 1000 T for a few microseconds. While this method may seem very destructive,
1648:
Both the leakage flux and the fringing fields get larger as the gaps are increased, reducing the force exerted by the magnet.
995:
The magnetic field lines of a current-carrying loop of wire pass through the center of the loop, concentrating the field there
557:
The maximum uniform pull happens when one end of the plunger is at the middle of the solenoid. An approximation for the force
2928:
2100:) are flat copper strips to withstand the Lorentz force of the magnetic field. The core is formed by the thick iron housing (
635:
is the length of the solenoid. For units using inches, pounds force, and amperes with long, slender, solenoids, the value of
61:
53:
2712:
1259:
Likewise on the solenoid, the force exerted by an electromagnet on a conductor located at a section of core material is:
2322:
1082:μ of the material. Not all electromagnets use cores, so this is called a ferromagnetic-core or iron-core electromagnet.
4309:
4427:
2609:
1723:
any air gaps between sections of core material are not large compared with the cross-sectional dimensions of the core.
4145:
1267:
193:
281:
systematically improved and popularised the electromagnet. By using wire insulated by silk thread and inspired by
4510:
4505:
2096:
Cross section of lifting electromagnet like that in above photo, showing cylindrical construction. The windings (
1008:
4135:
The most widely used magnetic core material, 3% silicon steel, has saturation induction of 20 kilogauss (2 T).
1137:
direction of magnetization, leaving the core magnetized as a weak permanent magnet. This phenomenon is called
255:
251:
2571:
is sometimes used across the contacts, which reduces arcing by temporarily storing the current. More often a
2536:
magnets there is a minimum amount of heat loss that cannot be reduced. This increases with the square of the
2441:
Each electromagnet has two poles, so the total force on a given magnet due to another magnet is equal to the
898:{\displaystyle P=ANI\left={\frac {AN^{2}I^{2}}{(\ell _{\mathrm {a} })^{2}(C_{1})^{2}}}+{\frac {CANI}{\ell }}}
567:
133:. A current through the wire creates a magnetic field which is concentrated in the hole in the center of the
3603:
266:
3211:
2461:
2122:
1965:{\displaystyle NI=B\left({\frac {L_{\mathrm {core} }}{\mu }}+{\frac {L_{\mathrm {gap} }}{\mu _{0}}}\right)}
1348:
The 1.6 T limit on the field mentioned above sets a limit on the maximum force per unit core area, or
3259:
2813:
2807:
2500:
can be chosen to minimize heat losses, as long as their product is constant. Since the power dissipation,
1064:
4354:""Design, Construction, and First Testing of a 41.5 T All-Resistive Magnet at the NHMFL in Tallahassee,""
4330:
254:
discovered in 1820 that electric currents create magnetic fields. In the same year, the French scientist
2825:
2724:
2478:
2092:
2079:. So in equation (2) above, the second term dominates. Therefore, in magnetic circuits with an air gap,
1553:
1115:
137:. The magnetic field disappears when the current is turned off. The wire turns are often wound around a
2603:
In powerful electromagnets, the magnetic field exerts a force on each turn of the windings, due to the
237:
4365:
4114:
2864:
2850:
2834:
2667:
2640:
1035:
1015:
453:
420:
304:, and the detailed modern quantum mechanical theory of ferromagnetism was worked out in the 1920s by
134:
130:
1248:
3850:
3627:– a combination of magnets and electromagnets used mainly to affect the motion of charged particles
3619:
3304:
2777:
2679:
1748:
1215:{\displaystyle \int \mathbf {J} \cdot d\mathbf {A} =\oint \mathbf {H} \cdot d{\boldsymbol {\ell }}}
1126:
439:
430:
301:
197:
3994:
3655:
1228:
4383:
2695:
2577:
2017:
1989:
391:
355:
173:
4274:
3488:
3384:
2563:
in the magnetic field is suddenly returned to the circuit, causing a large voltage spike and an
1034:. If the fingers of the right hand are curled around the coil in the direction of current flow (
917:
is the distance between the end of the stop and the end of the plunger. The additional constant
2910:
4405:
4211:
4184:
4178:
4067:
4036:
3967:
3799:
3764:
3721:
3624:
2940:
2817:
1858:{\displaystyle NI=H_{\mathrm {core} }L_{\mathrm {core} }+H_{\mathrm {gap} }L_{\mathrm {gap} }}
1349:
991:
491:
483:
449:
415:
344:
305:
290:
282:
4205:
4009:
4373:
3758:
3614:
3598:
3354:
2716:
2312:
1752:
1653:
1548:
1094:
262:
225:
161:
126:
31:
1030:
The direction of the magnetic field through a coil of wire can be found from a form of the
324:
3795:
2761:
2749:
2744:
2009:
1628:– average length of the magnetic circuit used in eq. 1 below. It is the sum of the length
1338:
1039:
1031:
984:
624:
297:
4490:
3557:
3527:
3122:
3092:
3060:
3030:
2997:
2967:
1717:
the magnetic circuit is a single loop of core material, possibly broken by a few air gaps
1158:
4369:
3988:
3080:
3017:
2860:
2648:
2592:
2474:
2445:
sum of the forces of the other magnet's poles acting on each pole of the given magnet.
1564:
1102:
1098:
1007:
An electric current flowing in a wire creates a magnetic field around the wire, due to
966:
946:
502:
351:
213:
169:
122:
101:
3789:
Groundbreaking
Scientific Experiments, Inventions, and Discoveries of the 19th Century
1601:
the magnetic field lines "bulge" out, so the field strength is less than in the core:
300:
theory of how ferromagnetic cores work was first proposed in 1906 by French physicist
92:
4499:
3592:
3518:
2932:
2873:
2821:
2769:
2699:
2663:
2604:
2581:
2537:
2519:
proportionally, or using thicker wire to reduce the resistance. For example, halving
1122:
1086:
1071:
1067:
1060:
517:
425:
395:
370:
154:
146:
142:
138:
2798:
258:
showed that iron can be magnetized by inserting it in an electrically fed solenoid.
4387:
3912:
Dawes, Chester L. (1967). "Electrical
Engineering". In Baumeister, Theodore (ed.).
2780:
is constant for each of these processes, so the power loss increases linearly with
2773:
2737:
2728:
2720:
2707:
2588:
2564:
1706:
1620:
1543:
1130:
443:
286:
278:
1656:, possibly broken by a few narrow air gaps. Iron presents much less "resistance" (
1014:. To concentrate the magnetic field in an electromagnet, the wire is wound into a
336:
is one designed to just hold material in place; an example is a lifting magnet. A
168:
Electromagnets are widely used as components of other electrical devices, such as
2885:
2698:, the magnetic field is constantly changing. This causes energy losses in their
2683:
2567:
across the switch contacts, which can damage them. With small electromagnets, a
2299:
654:
476:
376:
360:
313:
185:
4097:
Saturation flux levels of various magnetic materials range up to 24.5 kilogauss
939:
4378:
4353:
3609:
2916:
2812:
When a magnetic field higher than the ferromagnetic limit of 1.6 T is needed,
2757:
2753:
2733:
2552:
2482:
1657:
1146:
1138:
1107:
309:
17:
4107:"Power Supply Magnetics Part 1: Selecting transformer/inductor core material"
2469:(Laboratoire National des Champs Magnétiques Intenses) high field laboratory.
2781:
2702:
that is dissipated as heat in the core. The losses stem from two processes:
2568:
1142:
403:
380:
189:
3851:"Joseph Henry's contributions to the electromagnet and the electric motor"
510:
3714:
Merzouki, Rochdi; Samantaray, Arun Kumar; Pathak, Pushparaj Mani (2012).
2868:
2829:
2691:
2687:
2643:, pushing them apart. It has two effects on an electromagnet's windings:
2290:
It can be seen that to maximize the force, a core with a short flux path
1720:
the core has roughly the same cross-sectional area throughout its length.
1024:
550:
544:
385:
177:
106:
4137:
2587:
Large electromagnets are usually powered by variable current electronic
2943:
research to study the properties of materials at high magnetic fields.
2936:
2889:
2465:
Large aluminum busbars carrying current into the electromagnets at the
1735:
The magnetic field created by an electromagnet is proportional to both
1547:
must be considered. Second, because the magnetic field B and force are
999:
270:
231:
One of Henry's electromagnets that could lift hundreds of pounds, 1830s
1713:
The equations in this section are valid for electromagnets for which:
1345:
is force times distance. Rearranging terms yields the equation above.
2559:
1342:
1157:
The magnetic field of electromagnets in the general case is given by
498:
118:
4273:. National High Magnetic Field Laboratory, USA. 2008. Archived from
1623:; magnetic field lines which do not follow complete magnetic circuit
464:
3472:{\displaystyle 4\pi (10^{-7})\ \mathrm {N} \cdot \mathrm {A} ^{-2}}
2752:
in the core material each cycle causes energy loss, because of the
2909:
2797:
2572:
2466:
2460:
2091:
1563:
1055:
For definitions of the variables below, see box at end of article.
1020:
998:
990:
938:
365:
323:
181:
100:
2816:
can be used. Instead of using ferromagnetic materials, these use
3717:
Intelligent
Mechatronic Systems: Modeling, Control and Diagnosis
1090:
1075:
1003:
The magnetic field generated by passing a current through a coil
150:
4210:. New York: Addison-Wesley. pp. 36–9 to 36–11, eq. 36–26.
2760:. The energy lost per cycle is proportional to the area of the
2267:{\displaystyle F={\frac {\mu ^{2}N^{2}I^{2}A}{2\mu _{0}L^{2}}}}
470:
Laboratory electromagnet. Produces 2 T field with 20 A current.
2838:
408:
399:
36:
4404:. High Field Magnet Laboratory. 31 March 2014. Archived from
4234:
Fitzgerald, A.; Kingsley, Charles; Kusko, Alexander (1971).
4032:
Introduction to Basic
Electricity and Electronics Technology
3745:
Sturgeon, W. (1825). "Improved
Electro Magnetic Apparatus".
2723:. The energy in these currents is dissipated as heat in the
2319:
Magnetic pole strength of electromagnets can be found from:
3720:. Springer Science & Business Media. pp. 403–405.
1145:. The residual magnetization of the core can be removed by
3747:
Trans. Royal
Society of Arts, Manufactures, & Commerce
2867:. Instead of wire windings, a Bitter magnet consists of a
2859:
nonsuperconducting electromagnets of a design invented by
2477:
electromagnet under steady-state conditions is due to the
2432:{\displaystyle F={\frac {\mu _{0}m_{1}m_{2}}{4\pi r^{2}}}}
2311:
The above methods are applicable to electromagnets with a
2030:
for the material, and would not vary much with changes in
4333:. National High Magnetic Field Laboratory. 22 August 2017
4308:. National High Magnetic Field Laboratory. Archived from
3515:
Relative permeability of the electromagnet core material
3195:{\displaystyle L_{\mathrm {core} }+L_{\mathrm {gap} }\,}
2896:
during the pulse to be removed, before the next pulse.
2488:
Since the magnetic field is proportional to the product
4331:"MagLab Reclaims Record for Strongest Resistive Magnet"
3818:"Series and Parallel Experimenting with Electromagnets"
3249:
Length of the magnetic field path in the core material
4138:"Material Properties, 3% grain-oriented silicon steel"
3662:. Dept. of Physics and Astronomy, Georgia State Univ.
1225:
which says that the integral of the magnetizing field
664:) had a maximum pull of 8.75 pounds (corresponding to
646:) with a long plunger of 1-square inch cross section (
129:. Electromagnets usually consist of wire wound into a
4402:"HFML sets world record with a new 37.5 tesla magnet"
4252:. National High Magnetic Field Laboratory, USA. 2018.
3560:
3530:
3491:
3417:
3387:
3357:
3307:
3262:
3214:
3148:
3125:
3095:
3063:
3033:
3000:
2970:
2612:
2368:
2325:
2193:
2125:
2043:
1876:
1764:
1361:
1270:
1231:
1170:
969:
949:
688:
570:
549:
A common tractive electromagnet is a uniformly-wound
2072:{\displaystyle \mu _{r}\approx 2000{\text{–}}6000\,}
1059:
Much stronger magnetic fields can be produced if a "
343:
Electromagnets are very widely used in electric and
4066:(12 ed.). Cengage Learning. pp. 205–206.
4060:Shipman, James; Jerry, Wilson; Todd, Aaron (2009).
2008:value used must be obtained from the core material
3760:Electronic Control of Switched Reluctance Machines
3567:
3537:
3505:
3471:
3401:
3364:
3334:
3284:
3239:
3194:
3132:
3102:
3070:
3040:
3007:
2977:
2748:: Reversing the direction of magnetization of the
2715:, the changing magnetic field induces circulating
2631:
2431:
2352:
2266:
2152:
2071:
1964:
1857:
1512:
1313:
1239:
1214:
975:
955:
897:
600:
3577:Distance between the poles of two electromagnets
1352:, an iron-core electromagnet can exert; roughly:
328:Industrial electromagnet lifting scrap iron, 1914
4491:Electromagnets - The Feynman Lectures on Physics
3993:. Chicago: American Technical Society. pp.
3823:. Pavia Project Physics, Univ. of Pavia, Italy.
3374:Permeability of the electromagnet core material
2632:{\displaystyle q\mathbf {v} \times \mathbf {B} }
3606:- a magnetically hard electromagnet arrangement
1697:In addition, some of the magnetic field lines (
1576:of a typical electromagnet, with the iron core
56:for grammar, style, cohesion, tone, or spelling
4358:IEEE Transactions on Applied Superconductivity
4014:. London: E.& F. N. Spon. pp. 38–40.
3649:
3647:
3645:
3643:
3641:
3294:Length of the magnetic field path in air gaps
2925:explosively pumped flux compression generators
1093:or steel) is composed of small regions called
631:is the current through the solenoid wire, and
160:The main advantage of an electromagnet over a
4295:
4293:
4291:
4229:
4227:
4101:Silicon steel saturates at about 17 kilogauss
4011:Short Lectures to Electrical Artisans, 4th Ed
3547:Number of turns of wire on the electromagnet
2906:Explosively pumped flux compression generator
1314:{\displaystyle F={\frac {B^{2}A}{2\mu _{0}}}}
1129:at a certain value, which is around 1.6 to 2
8:
4428:"What is the strongest magnet in the world?"
4261:
4259:
3916:(7th ed.). McGraw-Hill. p. 15-105.
963:) through a wire produces a magnetic field (
619:is the cross-sectional area of the plunger,
4173:Magnetic steel fully saturates at about 2 T
4144:. Magnetic Materials Co. 2013. p. 16.
3907:
3905:
3886:. National High Magnetic Field Laboratory.
3709:
3707:
3705:
3703:
3701:
2016:is unknown, the equation must be solved by
1337:The force equation can be derived from the
1141:and the remaining magnetic field is called
4455:"7. Pulsed Magnets: Brief Shining Moments"
3914:Standard Handbook for Mechanical Engineers
3798:, xxii, Greenwood Publishing Group, 2003,
3699:
3697:
3695:
3693:
3691:
3689:
3687:
3685:
3683:
3681:
983:). The field is oriented according to the
531:Sextupole focusing magnet in a synchrotron
4377:
4091:
4089:
4087:
3564:
3559:
3534:
3529:
3502:
3496:
3490:
3460:
3455:
3446:
3431:
3416:
3398:
3392:
3386:
3361:
3356:
3331:
3325:
3312:
3306:
3281:
3268:
3267:
3261:
3236:
3220:
3219:
3213:
3191:
3178:
3177:
3154:
3153:
3147:
3129:
3124:
3099:
3094:
3067:
3062:
3037:
3032:
3004:
2999:
2974:
2969:
2756:of the material. These losses are called
2624:
2616:
2611:
2420:
2402:
2392:
2382:
2375:
2367:
2332:
2324:
2255:
2245:
2227:
2217:
2207:
2200:
2192:
2132:
2124:
2068:
2060:
2048:
2042:
1949:
1932:
1931:
1925:
1901:
1900:
1894:
1875:
1842:
1841:
1824:
1823:
1800:
1799:
1779:
1778:
1763:
1503:
1491:
1481:
1465:
1456:
1452:
1446:
1428:
1410:
1395:
1385:
1375:
1362:
1360:
1302:
1284:
1277:
1269:
1232:
1230:
1207:
1196:
1185:
1174:
1169:
1012:(see drawing of wire with magnetic field)
968:
948:
874:
862:
852:
839:
828:
827:
812:
802:
792:
774:
762:
752:
739:
728:
727:
709:
687:
577:
569:
80:Learn how and when to remove this message
4167:
4165:
4163:
3987:Millikin, Robert; Bishop, Edwin (1917).
3142:Total length of the magnetic field path
2950:
1580:forming a closed loop with two air gaps
285:use of multiple turns of wire to make a
91:
30:For broader coverage of this topic, see
4463:National High Magnetic Field Laboratory
4148:from the original on September 20, 2014
4111:Power Conversion and Intelligent Motion
3949:
3947:
3666:from the original on September 22, 2014
3637:
2882:National High Magnetic Field Laboratory
1672:). Within the core the magnetic field (
1635:in the iron core pieces and the length
1208:
1106:field passes through the core in lower
601:{\displaystyle F={\frac {CANI}{\ell }}}
269:wire did not then exist.) The iron was
27:Magnet created with an electric current
3411:Permeability of free space (or air) =
2492:, the number of turns in the windings
2000:. For an exact solution, the value of
243:Closeup of a large Henry electromagnet
4434:from the original on February 5, 2017
4250:"32 Tesla All-Superconducting Magnet"
3953:
3938:
3926:
3240:{\displaystyle L_{\mathrm {core} }\,}
2153:{\displaystyle B={\frac {NI\mu }{L}}}
1751:. For an electromagnet with a single
1110:than when it would pass through air.
554:plunger is centered in the solenoid.
340:applies a force and moves something.
153:; the magnetic core concentrates the
7:
4180:Electric Power Distribution Handbook
3890:from the original on 17 October 2017
3285:{\displaystyle L_{\mathrm {gap} }\,}
2184:
2116:
1867:
1261:
4352:Toth, J.; Bole, S.T. (April 2018).
3830:from the original on March 15, 2016
3344:Pole strength of the electromagnet
2900:Explosively pumped flux compression
2776:. The energy loss per cycle of the
2515:and increasing the number of turns
3456:
3447:
3275:
3272:
3269:
3230:
3227:
3224:
3221:
3185:
3182:
3179:
3164:
3161:
3158:
3155:
2876:of the field, which increase with
2353:{\displaystyle m={\frac {NIA}{L}}}
1939:
1936:
1933:
1911:
1908:
1905:
1902:
1849:
1846:
1843:
1831:
1828:
1825:
1810:
1807:
1804:
1801:
1789:
1786:
1783:
1780:
1731:Magnetic field in magnetic circuit
1523:for saturation limit of the core,
1500:
1496:
1488:
1485:
1482:
1462:
1453:
1435:
1432:
1429:
1085:This is because the material of a
829:
729:
157:and makes a more powerful magnet.
25:
4238:. USA: McGraw-Hill. pp. 3–5.
4035:. Cengage Learning. p. 184.
2719:inside nearby conductors, called
2658:The Lorentz forces increase with
2551:An electromagnet has significant
2531:However, the limit to increasing
2104:) that wraps around the windings.
1726:there is negligible leakage flux.
1597:– "fringing fields". In the gaps
1339:energy stored in a magnetic field
4105:Pauley, Donald E. (March 1996).
4080:from the original on 2017-01-11.
4063:Introduction to Physical Science
4049:from the original on 2017-01-10.
4018:from the original on 2017-01-11.
3976:from the original on 2016-05-01.
3972:. D. Van Nostrand. p. 113.
3777:from the original on 2016-12-03.
3734:from the original on 2016-12-03.
3050:Force exerted by magnetic field
2824:, which conduct current without
2625:
2617:
2362:The force between two poles is:
2294:and a wide cross-sectional area
1233:
1197:
1186:
1175:
1097:that act like tiny magnets (see
524:
509:
490:
475:
463:
452:for cooking, manufacturing, and
277:Beginning in 1830, US scientist
236:
224:
212:
41:
4430:. Apex magnets. November 2014.
3861:from the original on 2012-06-08
3857:. The Smithsonian Institution.
3595:– the most basic form of magnet
1255:Force exerted by magnetic field
615:is a proportionality constant,
4302:"Magnets: from Mini to Mighty"
4008:Fleming, John Ambrose (1892).
3966:Underhill, Charles R. (1906).
3880:"Schweigger Multiplier – 1820"
3440:
3424:
2814:superconducting electromagnets
2794:Superconducting electromagnets
1392:
1378:
1125:materials is that the B field
1121:The main nonlinear feature of
859:
845:
836:
820:
759:
745:
736:
720:
320:Applications of electromagnets
219:Sturgeon's electromagnet, 1824
196:, scientific instruments, and
1:
3335:{\displaystyle m_{1},m_{2}\,}
2987:cross sectional area of core
2682:(AC) electromagnets, used in
2473:The only power consumed in a
414:Scientific equipment such as
105:Magnetic field produced by a
4204:Feynman, Richard P. (1963).
4177:Short, Thomas Allen (2003).
3112:Current in the winding wire
2915:tube, trapping the magnetic
2307:Force between electromagnets
1589:– magnetic field in the core
1240:{\displaystyle \mathbf {H} }
394:and data storage equipment:
4459:Magnets from Mini to Mighty
4207:Lectures on Physics, Vol. 2
2178:
2110:
1755:, Ampere's Law reduces to:
178:electromechanical solenoids
4527:
4236:Electric Machinery, 3rd Ed
4183:. CRC Press. p. 214.
3506:{\displaystyle \mu _{r}\,}
3402:{\displaystyle \mu _{0}\,}
2903:
2848:
2805:
2740:, which is a nonconductor.
2713:Faraday's law of induction
1679:This leaves the air gaps (
542:
436:Industrial lifting magnets
29:
4379:10.1109/TASC.2017.2775578
3481:newton per square ampere
3377:newton per square ampere
2789:High-field electromagnets
2037:For most core materials,
3020:(Magnetic flux density)
2964:
2666:in the windings. In the
2547:Inductive voltage spikes
497:AC electromagnet on the
4453:Coyne, Kristin (2008).
4300:Coyne, Kristin (2008).
4267:"Mag Lab World Records"
3990:Elements of Electricity
3855:The Joseph Henry Papers
3849:Sherman, Roger (2007).
3787:Windelspecht, Michael.
3604:Electropermanent magnet
2088:Closed magnetic circuit
334:portative electromagnet
3757:Miller, T.J.E (2001).
3654:Nave, Carl R. (2012).
3569:
3539:
3507:
3473:
3403:
3366:
3365:{\displaystyle \mu \,}
3336:
3286:
3241:
3196:
3134:
3104:
3072:
3042:
3009:
2979:
2920:
2808:Superconducting magnet
2803:
2633:
2470:
2433:
2354:
2268:
2154:
2105:
2073:
1966:
1859:
1743:, hence this product,
1649:
1514:
1315:
1241:
1216:
1004:
996:
988:
977:
957:
899:
602:
338:tractive electromagnet
329:
110:
98:
3941:, p. 15-106, Table 25
3816:Cavicchi, Elizabeth.
3763:. Newnes. p. 7.
3570:
3540:
3508:
3474:
3404:
3367:
3337:
3287:
3242:
3197:
3135:
3105:
3073:
3043:
3010:
2980:
2913:
2865:Bitter electromagnets
2845:Bitter electromagnets
2835:particle accelerators
2826:electrical resistance
2820:windings cooled with
2801:
2725:electrical resistance
2634:
2464:
2434:
2355:
2269:
2155:
2095:
2074:
1967:
1860:
1567:
1554:finite element method
1515:
1316:
1242:
1217:
1080:magnetic permeability
1002:
994:
978:
958:
942:
900:
603:
421:Particle accelerators
327:
252:Hans Christian Ørsted
104:
95:
4117:on December 24, 2014
4029:Gates, Earl (2013).
3558:
3528:
3489:
3415:
3385:
3355:
3305:
3260:
3212:
3146:
3123:
3093:
3061:
3031:
2998:
2968:
2851:Bitter electromagnet
2641:magnetic field lines
2610:
2366:
2323:
2191:
2123:
2041:
1874:
1762:
1747:, is given the name
1359:
1268:
1229:
1168:
1074:) material, such as
1036:conventional current
967:
947:
686:
568:
454:hyperthermia therapy
347:devices, including:
4408:on 4 September 2015
4370:2018ITAS...2875578T
3620:Pulsed field magnet
3568:{\displaystyle r\,}
3538:{\displaystyle N\,}
3133:{\displaystyle L\,}
3103:{\displaystyle I\,}
3071:{\displaystyle H\,}
3041:{\displaystyle F\,}
3008:{\displaystyle B\,}
2978:{\displaystyle A\,}
2947:Definition of terms
2778:alternating current
2680:alternating current
2176:Substituting into (
1749:magnetomotive force
1152:
440:magnetic levitation
431:Magnetic separation
302:Pierre-Ernest Weiss
198:magnetic separation
3929:, p. 15-105–15-106
3794:2017-01-11 at the
3565:
3535:
3503:
3469:
3399:
3362:
3332:
3282:
3237:
3192:
3130:
3100:
3068:
3038:
3005:
2975:
2921:
2804:
2629:
2591:, controlled by a
2578:freewheeling diode
2471:
2429:
2350:
2264:
2150:
2106:
2069:
1990:nonlinear equation
1962:
1855:
1650:
1510:
1311:
1237:
1212:
1143:remanent magnetism
1005:
997:
989:
973:
953:
895:
598:
416:mass spectrometers
392:Magnetic recording
330:
291:telegraph sounders
261:British scientist
256:André-Marie Ampère
125:is produced by an
111:
99:
60:You can assist by
3969:The Electromagnet
3770:978-0-7506-5073-1
3625:Quadrupole magnet
3584:
3583:
3445:
3085:ampere per meter
3081:Magnetizing field
2941:materials science
2745:Hysteresis losses
2717:electric currents
2427:
2348:
2288:
2287:
2262:
2182:), the force is:
2174:
2173:
2148:
2063:
2018:numerical methods
1986:
1985:
1955:
1920:
1480:
1427:
1417:
1388:
1370:
1350:magnetic pressure
1335:
1334:
1309:
976:{\displaystyle B}
956:{\displaystyle I}
893:
869:
782:
769:
627:in the solenoid,
596:
484:mass spectrometer
450:Induction heating
345:electromechanical
306:Werner Heisenberg
250:Danish scientist
149:material such as
90:
89:
82:
16:(Redirected from
4518:
4511:Types of magnets
4506:Electromagnetism
4478:
4477:
4475:
4474:
4465:. Archived from
4450:
4444:
4443:
4441:
4439:
4424:
4418:
4417:
4415:
4413:
4398:
4392:
4391:
4381:
4364:(3). IEEE: 1–4.
4349:
4343:
4342:
4340:
4338:
4327:
4321:
4320:
4318:
4317:
4297:
4286:
4285:
4283:
4282:
4263:
4254:
4253:
4246:
4240:
4239:
4231:
4222:
4221:
4201:
4195:
4194:
4169:
4158:
4157:
4155:
4153:
4133:
4127:
4126:
4124:
4122:
4113:. Archived from
4099:" (2.5 T) p.1 "
4093:
4082:
4081:
4057:
4051:
4050:
4026:
4020:
4019:
4005:
3999:
3998:
3984:
3978:
3977:
3963:
3957:
3951:
3942:
3936:
3930:
3924:
3918:
3917:
3909:
3900:
3899:
3897:
3895:
3876:
3870:
3869:
3867:
3866:
3846:
3840:
3839:
3837:
3835:
3829:
3822:
3813:
3807:
3785:
3779:
3778:
3754:
3742:
3736:
3735:
3711:
3676:
3675:
3673:
3671:
3651:
3615:Magnetic bearing
3599:Electromagnetism
3574:
3572:
3571:
3566:
3544:
3542:
3541:
3536:
3512:
3510:
3509:
3504:
3501:
3500:
3478:
3476:
3475:
3470:
3468:
3467:
3459:
3450:
3443:
3439:
3438:
3408:
3406:
3405:
3400:
3397:
3396:
3371:
3369:
3368:
3363:
3341:
3339:
3338:
3333:
3330:
3329:
3317:
3316:
3291:
3289:
3288:
3283:
3280:
3279:
3278:
3246:
3244:
3243:
3238:
3235:
3234:
3233:
3201:
3199:
3198:
3193:
3190:
3189:
3188:
3169:
3168:
3167:
3139:
3137:
3136:
3131:
3109:
3107:
3106:
3101:
3077:
3075:
3074:
3069:
3047:
3045:
3044:
3039:
3014:
3012:
3011:
3006:
2984:
2982:
2981:
2976:
2951:
2863:in 1933, called
2750:magnetic domains
2638:
2636:
2635:
2630:
2628:
2620:
2496:and the current
2438:
2436:
2435:
2430:
2428:
2426:
2425:
2424:
2408:
2407:
2406:
2397:
2396:
2387:
2386:
2376:
2359:
2357:
2356:
2351:
2349:
2344:
2333:
2313:magnetic circuit
2282:
2273:
2271:
2270:
2265:
2263:
2261:
2260:
2259:
2250:
2249:
2236:
2232:
2231:
2222:
2221:
2212:
2211:
2201:
2185:
2168:
2159:
2157:
2156:
2151:
2149:
2144:
2133:
2117:
2078:
2076:
2075:
2070:
2064:
2061:
2053:
2052:
2010:hysteresis curve
1980:
1971:
1969:
1968:
1963:
1961:
1957:
1956:
1954:
1953:
1944:
1943:
1942:
1926:
1921:
1916:
1915:
1914:
1895:
1868:
1864:
1862:
1861:
1856:
1854:
1853:
1852:
1836:
1835:
1834:
1815:
1814:
1813:
1794:
1793:
1792:
1753:magnetic circuit
1654:magnetic circuit
1642:in the air gaps
1608: <
1573:
1560:Magnetic circuit
1519:
1517:
1516:
1511:
1509:
1508:
1507:
1495:
1478:
1471:
1470:
1469:
1460:
1451:
1450:
1438:
1425:
1418:
1416:
1415:
1414:
1401:
1400:
1399:
1390:
1389:
1386:
1376:
1371:
1363:
1329:
1320:
1318:
1317:
1312:
1310:
1308:
1307:
1306:
1293:
1289:
1288:
1278:
1262:
1246:
1244:
1243:
1238:
1236:
1221:
1219:
1218:
1213:
1211:
1200:
1189:
1178:
1095:magnetic domains
982:
980:
979:
974:
962:
960:
959:
954:
925:
916:
904:
902:
901:
896:
894:
889:
875:
870:
868:
867:
866:
857:
856:
844:
843:
834:
833:
832:
818:
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793:
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783:
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768:
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743:
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578:
560:
528:
513:
494:
479:
467:
263:William Sturgeon
240:
228:
216:
162:permanent magnet
127:electric current
85:
78:
74:
71:
65:
45:
44:
37:
32:Electromagnetism
21:
4526:
4525:
4521:
4520:
4519:
4517:
4516:
4515:
4496:
4495:
4487:
4482:
4481:
4472:
4470:
4452:
4451:
4447:
4437:
4435:
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4421:
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4409:
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4395:
4351:
4350:
4346:
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4299:
4298:
4289:
4280:
4278:
4265:
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4257:
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4233:
4232:
4225:
4218:
4203:
4202:
4198:
4191:
4176:
4170:
4161:
4151:
4149:
4136:
4134:
4130:
4120:
4118:
4104:
4103:" (1.7 T) p.3
4094:
4085:
4074:
4059:
4058:
4054:
4043:
4028:
4027:
4023:
4007:
4006:
4002:
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3893:
3891:
3878:
3877:
3873:
3864:
3862:
3848:
3847:
3843:
3833:
3831:
3827:
3820:
3815:
3814:
3810:
3796:Wayback Machine
3786:
3782:
3771:
3756:
3744:
3743:
3739:
3728:
3713:
3712:
3679:
3669:
3667:
3656:"Electromagnet"
3653:
3652:
3639:
3634:
3589:
3556:
3555:
3526:
3525:
3492:
3487:
3486:
3454:
3427:
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3321:
3308:
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3302:
3263:
3258:
3257:
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3210:
3209:
3173:
3149:
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3121:
3120:
3091:
3090:
3059:
3058:
3029:
3028:
2996:
2995:
2966:
2965:
2949:
2908:
2902:
2853:
2847:
2818:superconducting
2810:
2796:
2791:
2762:hysteresis loop
2676:
2608:
2607:
2601:
2558:If an ordinary
2549:
2459:
2451:
2416:
2409:
2398:
2388:
2378:
2377:
2364:
2363:
2334:
2321:
2320:
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2280:
2251:
2241:
2237:
2223:
2213:
2203:
2202:
2189:
2188:
2166:
2134:
2121:
2120:
2090:
2044:
2039:
2038:
2028:
1978:
1945:
1927:
1896:
1893:
1889:
1872:
1871:
1837:
1819:
1795:
1774:
1760:
1759:
1733:
1702:
1692:fringing fields
1688:
1647:
1640:
1633:
1624:
1617:
1612:
1606:
1595:
1590:
1585:
1571:
1568:Magnetic field
1562:
1539:fringing fields
1528:
1499:
1461:
1442:
1406:
1402:
1391:
1381:
1377:
1357:
1356:
1327:
1298:
1294:
1280:
1279:
1266:
1265:
1257:
1249:Biot–Savart law
1227:
1226:
1166:
1165:
1155:
1089:(often made of
1052:
1040:positive charge
1032:right-hand rule
985:right-hand rule
965:
964:
945:
944:
937:
924:
918:
915:
909:
876:
858:
848:
835:
823:
819:
808:
798:
794:
758:
748:
735:
723:
719:
711:
708:
704:
684:
683:
676:
665:
658:
647:
640:
636:
632:
628:
625:number of turns
620:
616:
612:
579:
566:
565:
558:
547:
541:
539:Simple solenoid
536:
535:
534:
533:
532:
529:
521:
520:
514:
506:
505:
495:
487:
486:
480:
472:
471:
468:
322:
298:magnetic domain
248:
247:
246:
245:
244:
241:
233:
232:
229:
221:
220:
217:
206:
86:
75:
69:
66:
59:
46:
42:
35:
28:
23:
22:
15:
12:
11:
5:
4524:
4522:
4514:
4513:
4508:
4498:
4497:
4494:
4493:
4486:
4485:External links
4483:
4480:
4479:
4445:
4419:
4393:
4344:
4322:
4287:
4255:
4241:
4223:
4217:978-8185015842
4216:
4196:
4190:978-0203486504
4189:
4159:
4128:
4083:
4073:978-1111810283
4072:
4052:
4042:978-1133948513
4041:
4021:
4000:
3979:
3958:
3943:
3931:
3919:
3901:
3871:
3841:
3808:
3780:
3769:
3737:
3727:978-1447146285
3726:
3677:
3636:
3635:
3633:
3630:
3629:
3628:
3622:
3617:
3612:
3607:
3601:
3596:
3588:
3585:
3582:
3581:
3578:
3575:
3563:
3552:
3551:
3550:dimensionless
3548:
3545:
3533:
3522:
3521:
3516:
3513:
3499:
3495:
3483:
3482:
3479:
3466:
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3140:
3128:
3117:
3116:
3113:
3110:
3098:
3087:
3086:
3083:
3078:
3066:
3055:
3054:
3051:
3048:
3036:
3025:
3024:
3021:
3018:Magnetic field
3015:
3003:
2992:
2991:
2988:
2985:
2973:
2962:
2961:
2958:
2955:
2948:
2945:
2933:charge shaping
2904:Main article:
2901:
2898:
2874:Lorentz forces
2861:Francis Bitter
2849:Main article:
2846:
2843:
2806:Main article:
2795:
2792:
2790:
2787:
2786:
2785:
2741:
2700:magnetic cores
2675:
2672:
2656:
2655:
2652:
2649:tensile stress
2627:
2623:
2619:
2615:
2600:
2599:Lorentz forces
2597:
2593:microprocessor
2589:power supplies
2548:
2545:
2458:
2455:
2450:
2447:
2423:
2419:
2415:
2412:
2405:
2401:
2395:
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2371:
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2328:
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2274:
2258:
2254:
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2244:
2240:
2235:
2230:
2226:
2220:
2216:
2210:
2206:
2199:
2196:
2172:
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2160:
2147:
2143:
2140:
2137:
2131:
2128:
2089:
2086:
2067:
2059:
2056:
2051:
2047:
2026:
1984:
1983:
1974:
1972:
1960:
1952:
1948:
1941:
1938:
1935:
1930:
1924:
1919:
1913:
1910:
1907:
1904:
1899:
1892:
1888:
1885:
1882:
1879:
1866:
1865:
1851:
1848:
1845:
1840:
1833:
1830:
1827:
1822:
1818:
1812:
1809:
1806:
1803:
1798:
1791:
1788:
1785:
1782:
1777:
1773:
1770:
1767:
1732:
1729:
1728:
1727:
1724:
1721:
1718:
1700:
1686:
1638:
1631:
1615:
1604:
1593:
1561:
1558:
1556:are employed.
1526:
1521:
1520:
1506:
1502:
1498:
1494:
1490:
1487:
1484:
1477:
1474:
1468:
1464:
1459:
1455:
1449:
1445:
1441:
1437:
1434:
1431:
1424:
1421:
1413:
1409:
1405:
1398:
1394:
1384:
1380:
1374:
1369:
1366:
1333:
1332:
1323:
1321:
1305:
1301:
1297:
1292:
1287:
1283:
1276:
1273:
1256:
1253:
1235:
1223:
1222:
1210:
1206:
1203:
1199:
1195:
1192:
1188:
1184:
1181:
1177:
1173:
1154:
1151:
1103:magnetic field
1099:ferromagnetism
1051:
1048:
1023:) is called a
972:
952:
936:
933:
922:
913:
906:
905:
892:
888:
885:
882:
879:
873:
865:
861:
855:
851:
847:
842:
838:
831:
826:
822:
815:
811:
805:
801:
797:
791:
787:
781:
778:
773:
765:
761:
755:
751:
747:
742:
738:
731:
726:
722:
717:
714:
707:
703:
700:
697:
694:
691:
662:= 11,200 Aturn
609:
608:
595:
591:
588:
585:
582:
576:
573:
543:Main article:
540:
537:
530:
523:
522:
516:Magnets in an
515:
508:
507:
503:electric motor
496:
489:
488:
481:
474:
473:
469:
462:
461:
460:
459:
458:
457:
456:
447:
437:
434:
428:
426:Magnetic locks
423:
418:
412:
406:
396:tape recorders
389:
388:such as valves
383:
374:
371:Electric bells
368:
363:
358:
321:
318:
242:
235:
234:
230:
223:
222:
218:
211:
210:
209:
208:
207:
205:
202:
123:magnetic field
88:
87:
49:
47:
40:
26:
24:
18:Electro-magnet
14:
13:
10:
9:
6:
4:
3:
2:
4523:
4512:
4509:
4507:
4504:
4503:
4501:
4492:
4489:
4488:
4484:
4469:on 2014-12-20
4468:
4464:
4460:
4456:
4449:
4446:
4433:
4429:
4423:
4420:
4407:
4403:
4397:
4394:
4389:
4385:
4380:
4375:
4371:
4367:
4363:
4359:
4355:
4348:
4345:
4332:
4326:
4323:
4312:on 2008-09-17
4311:
4307:
4303:
4296:
4294:
4292:
4288:
4277:on 2008-10-07
4276:
4272:
4268:
4262:
4260:
4256:
4251:
4245:
4242:
4237:
4230:
4228:
4224:
4219:
4213:
4209:
4208:
4200:
4197:
4192:
4186:
4182:
4181:
4174:
4168:
4166:
4164:
4160:
4152:September 19,
4147:
4143:
4139:
4132:
4129:
4121:September 19,
4116:
4112:
4108:
4102:
4098:
4092:
4090:
4088:
4084:
4079:
4075:
4069:
4065:
4064:
4056:
4053:
4048:
4044:
4038:
4034:
4033:
4025:
4022:
4017:
4013:
4012:
4004:
4001:
3996:
3992:
3991:
3983:
3980:
3975:
3971:
3970:
3962:
3959:
3955:
3950:
3948:
3944:
3940:
3935:
3932:
3928:
3923:
3920:
3915:
3908:
3906:
3902:
3889:
3885:
3881:
3875:
3872:
3860:
3856:
3852:
3845:
3842:
3826:
3819:
3812:
3809:
3805:
3804:0-313-31969-3
3801:
3797:
3793:
3790:
3784:
3781:
3776:
3772:
3766:
3762:
3761:
3752:
3748:
3741:
3738:
3733:
3729:
3723:
3719:
3718:
3710:
3708:
3706:
3704:
3702:
3700:
3698:
3696:
3694:
3692:
3690:
3688:
3686:
3684:
3682:
3678:
3670:September 17,
3665:
3661:
3657:
3650:
3648:
3646:
3644:
3642:
3638:
3631:
3626:
3623:
3621:
3618:
3616:
3613:
3611:
3608:
3605:
3602:
3600:
3597:
3594:
3593:Dipole magnet
3591:
3590:
3586:
3579:
3576:
3561:
3554:
3553:
3549:
3546:
3531:
3524:
3523:
3520:
3519:dimensionless
3517:
3514:
3497:
3493:
3485:
3484:
3480:
3464:
3461:
3451:
3435:
3432:
3428:
3421:
3418:
3410:
3393:
3389:
3381:
3380:
3376:
3373:
3358:
3351:
3350:
3347:ampere meter
3346:
3343:
3326:
3322:
3318:
3313:
3309:
3301:
3300:
3296:
3293:
3264:
3256:
3255:
3251:
3248:
3216:
3208:
3207:
3203:
3174:
3170:
3150:
3141:
3126:
3119:
3118:
3114:
3111:
3096:
3089:
3088:
3084:
3082:
3079:
3064:
3057:
3056:
3052:
3049:
3034:
3027:
3026:
3022:
3019:
3016:
3001:
2994:
2993:
2990:square meter
2989:
2986:
2971:
2963:
2959:
2957:Significance
2956:
2953:
2952:
2946:
2944:
2942:
2938:
2934:
2930:
2926:
2918:
2912:
2907:
2899:
2897:
2893:
2891:
2887:
2883:
2879:
2875:
2870:
2866:
2862:
2858:
2852:
2844:
2842:
2840:
2836:
2831:
2827:
2823:
2822:liquid helium
2819:
2815:
2809:
2800:
2793:
2788:
2783:
2779:
2775:
2771:
2770:silicon steel
2767:
2763:
2759:
2755:
2751:
2747:
2746:
2742:
2739:
2735:
2730:
2729:eddy currents
2726:
2722:
2721:eddy currents
2718:
2714:
2710:
2709:
2708:Eddy currents
2705:
2704:
2703:
2701:
2697:
2693:
2689:
2685:
2681:
2673:
2671:
2669:
2665:
2664:metal fatigue
2661:
2653:
2650:
2646:
2645:
2644:
2642:
2621:
2613:
2606:
2605:Lorentz force
2598:
2596:
2594:
2590:
2585:
2583:
2582:flyback diode
2579:
2574:
2570:
2566:
2561:
2556:
2554:
2546:
2544:
2542:
2539:
2538:magnetic flux
2534:
2529:
2526:
2523:and doubling
2522:
2518:
2514:
2510:
2507:
2503:
2499:
2495:
2491:
2486:
2484:
2480:
2476:
2468:
2463:
2457:Ohmic heating
2456:
2454:
2448:
2446:
2444:
2439:
2421:
2417:
2413:
2410:
2403:
2399:
2393:
2389:
2383:
2379:
2372:
2369:
2360:
2345:
2341:
2338:
2335:
2329:
2326:
2317:
2314:
2306:
2304:
2301:
2297:
2293:
2284:
2277:
2275:
2256:
2252:
2246:
2242:
2238:
2233:
2228:
2224:
2218:
2214:
2208:
2204:
2197:
2194:
2187:
2186:
2183:
2181:
2180:
2170:
2163:
2161:
2145:
2141:
2138:
2135:
2129:
2126:
2119:
2118:
2115:
2113:
2112:
2103:
2099:
2094:
2087:
2085:
2082:
2065:
2057:
2054:
2049:
2045:
2035:
2033:
2029:
2021:
2019:
2015:
2011:
2007:
2003:
1999:
1995:
1991:
1982:
1975:
1973:
1958:
1950:
1946:
1928:
1922:
1917:
1897:
1890:
1886:
1883:
1880:
1877:
1870:
1869:
1838:
1820:
1816:
1796:
1775:
1771:
1768:
1765:
1758:
1757:
1756:
1754:
1750:
1746:
1742:
1738:
1730:
1725:
1722:
1719:
1716:
1715:
1714:
1711:
1709:
1708:
1703:
1695:
1693:
1690:) are called
1689:
1682:
1677:
1675:
1671:
1667:
1661:
1659:
1655:
1645:
1641:
1634:
1627:
1622:
1618:
1611:
1607:
1600:
1596:
1588:
1583:
1579:
1575:
1566:
1559:
1557:
1555:
1550:
1546:
1545:
1540:
1534:
1531:
1529:
1504:
1492:
1475:
1472:
1466:
1457:
1447:
1443:
1439:
1422:
1419:
1411:
1407:
1403:
1396:
1382:
1372:
1367:
1364:
1355:
1354:
1353:
1351:
1346:
1344:
1340:
1331:
1324:
1322:
1303:
1299:
1295:
1290:
1285:
1281:
1274:
1271:
1264:
1263:
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1162:
1160:
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1148:
1144:
1140:
1134:
1132:
1128:
1124:
1123:ferromagnetic
1119:
1117:
1111:
1109:
1104:
1100:
1096:
1092:
1088:
1087:magnetic core
1083:
1081:
1077:
1073:
1072:ferrimagnetic
1069:
1068:ferromagnetic
1066:
1062:
1061:magnetic core
1057:
1056:
1050:Magnetic core
1049:
1047:
1045:
1041:
1037:
1033:
1028:
1026:
1022:
1017:
1013:
1010:
1001:
993:
986:
970:
950:
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928:
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912:
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886:
883:
880:
877:
871:
863:
853:
849:
840:
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809:
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799:
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785:
779:
776:
771:
763:
753:
749:
740:
724:
715:
712:
705:
701:
698:
695:
692:
689:
682:
681:
680:
672:
668:
661:
656:
653:) and 11,200
650:
643:
626:
593:
589:
586:
583:
580:
574:
571:
564:
563:
562:
555:
552:
546:
538:
527:
519:
518:electric bell
512:
504:
500:
493:
485:
478:
466:
455:
451:
448:
445:
441:
438:
435:
432:
429:
427:
424:
422:
419:
417:
413:
410:
407:
405:
401:
397:
393:
390:
387:
384:
382:
378:
375:
372:
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364:
362:
359:
357:
353:
350:
349:
348:
346:
341:
339:
335:
326:
319:
317:
315:
311:
307:
303:
299:
294:
292:
288:
284:
280:
275:
272:
268:
264:
259:
257:
253:
239:
227:
215:
203:
201:
199:
195:
191:
187:
183:
179:
175:
171:
166:
163:
158:
156:
155:magnetic flux
152:
148:
147:ferrimagnetic
144:
143:ferromagnetic
140:
139:magnetic core
136:
132:
128:
124:
121:in which the
120:
117:is a type of
116:
115:electromagnet
108:
103:
94:
84:
81:
73:
70:February 2024
63:
57:
55:
50:This article
48:
39:
38:
33:
19:
4471:. Retrieved
4467:the original
4458:
4448:
4436:. Retrieved
4422:
4410:. Retrieved
4406:the original
4396:
4361:
4357:
4347:
4335:. Retrieved
4325:
4314:. Retrieved
4310:the original
4306:Magnet Lab U
4305:
4279:. Retrieved
4275:the original
4271:Media Center
4270:
4244:
4235:
4206:
4199:
4179:
4172:
4150:. Retrieved
4141:
4131:
4119:. Retrieved
4115:the original
4110:
4100:
4096:
4062:
4055:
4031:
4024:
4010:
4003:
3989:
3982:
3968:
3961:
3934:
3922:
3913:
3892:. Retrieved
3883:
3874:
3863:. Retrieved
3854:
3844:
3832:. Retrieved
3811:
3783:
3759:
3750:
3746:
3740:
3716:
3668:. Retrieved
3660:Hyperphysics
3659:
2922:
2894:
2877:
2856:
2854:
2811:
2774:soft ferrite
2765:
2743:
2738:ferrite core
2706:
2684:transformers
2677:
2659:
2657:
2651:in the wire.
2602:
2586:
2557:
2550:
2540:
2532:
2530:
2524:
2520:
2516:
2512:
2508:
2505:
2501:
2497:
2493:
2489:
2487:
2472:
2452:
2449:Side effects
2440:
2361:
2318:
2310:
2300:loudspeakers
2295:
2291:
2289:
2278:
2177:
2175:
2164:
2109:
2107:
2101:
2097:
2080:
2036:
2031:
2024:
2022:
2013:
2005:
2001:
1997:
1996:varies with
1993:
1987:
1976:
1744:
1740:
1736:
1734:
1712:
1707:leakage flux
1705:
1698:
1696:
1691:
1684:
1680:
1678:
1673:
1669:
1665:
1662:
1651:
1643:
1636:
1629:
1625:
1621:leakage flux
1613:
1609:
1602:
1598:
1591:
1586:
1581:
1577:
1569:
1544:leakage flux
1542:
1538:
1535:
1532:
1524:
1522:
1347:
1336:
1325:
1258:
1224:
1159:Ampere's Law
1156:
1153:Ampere's law
1135:
1120:
1112:
1084:
1058:
1054:
1053:
1043:
1029:
1011:
1009:Ampere's law
1006:
929:
919:
910:
907:
673:
669:= 0.0094 psi
666:
659:
655:ampere-turns
648:
641:
610:
556:
548:
482:Magnet in a
444:maglev train
442:, used in a
377:Loudspeakers
361:Transformers
342:
337:
333:
331:
316:and others.
295:
287:galvanometer
283:Schweigger's
279:Joseph Henry
276:
260:
249:
194:MRI machines
186:loudspeakers
167:
159:
141:made from a
114:
112:
76:
67:
54:copy editing
52:may require
51:
4438:February 5,
3956:, p. 15-106
2917:field lines
2886:Tallahassee
2734:laminations
2674:Core losses
2114:) becomes:
373:and buzzers
314:Felix Bloch
4500:Categories
4473:2014-05-21
4316:2008-08-31
4281:2008-08-31
3954:Dawes 1967
3939:Dawes 1967
3927:Dawes 1967
3894:17 October
3865:2008-08-27
3834:August 22,
3632:References
3610:Field coil
2841:machines.
2758:hysteresis
2754:coercivity
2696:generators
2553:inductance
2483:waste heat
2479:resistance
1992:, because
1988:This is a
1658:reluctance
1147:degaussing
1139:hysteresis
1116:saturation
1108:reluctance
1044:north pole
1038:, flow of
404:hard disks
381:headphones
356:generators
310:Lev Landau
190:hard disks
174:generators
62:editing it
3755:cited in
3494:μ
3462:−
3452:⋅
3433:−
3422:π
3390:μ
3359:μ
2929:implosion
2782:frequency
2692:AC motors
2688:inductors
2622:×
2569:capacitor
2414:π
2380:μ
2243:μ
2205:μ
2142:μ
2055:≈
2046:μ
1947:μ
1918:μ
1664:strength
1549:nonlinear
1420:≈
1408:μ
1300:μ
1209:ℓ
1202:⋅
1194:∮
1180:⋅
1172:∫
1127:saturates
943:Current (
891:ℓ
825:ℓ
780:ℓ
725:ℓ
594:ℓ
446:or trains
386:Actuators
271:varnished
267:Insulated
4432:Archived
4146:Archived
4078:Archived
4047:Archived
4016:Archived
3974:Archived
3888:Archived
3859:Archived
3825:Archived
3792:Archived
3775:Archived
3753:: 37–52.
3732:Archived
3664:Archived
3587:See also
2869:solenoid
2857:air-core
2830:cryostat
2062:–
1025:solenoid
551:solenoid
545:Solenoid
411:machines
107:solenoid
97:winding.
4388:7923594
4366:Bibcode
4142:Catalog
3115:ampere
3053:newton
2937:physics
2890:Florida
2764:in the
2711:: From
2004:at the
1063:" of a
935:Physics
644:= 12 in
623:is the
204:History
4412:21 May
4386:
4337:14 May
4214:
4187:
4070:
4039:
3884:Maglab
3802:
3767:
3724:
3580:meter
3444:
3297:meter
3252:meter
3204:meter
3023:tesla
2927:. The
2690:, and
2668:Bitter
2560:switch
2443:vector
2303:pole.
1584:in it.
1479:
1426:
1343:Energy
1131:teslas
651:= 1 in
611:where
501:of an
499:stator
366:Relays
352:Motors
182:relays
170:motors
119:magnet
4384:S2CID
3828:(PDF)
3821:(PDF)
2960:Unit
2954:Term
2573:diode
2467:LNCMI
2012:. If
1572:green
1021:helix
908:Here
4440:2017
4414:2014
4339:2023
4212:ISBN
4185:ISBN
4154:2014
4123:2014
4068:ISBN
4037:ISBN
3896:2017
3836:2015
3800:ISBN
3765:ISBN
3722:ISBN
3672:2014
2939:and
2837:and
2694:and
2066:6000
2058:2000
2020:.
1739:and
1632:core
1541:and
1423:1000
1091:iron
1076:iron
1070:(or
1065:soft
1016:coil
400:VCRs
379:and
354:and
296:The
151:iron
135:coil
131:coil
4374:doi
3995:125
2884:in
2839:MRI
2772:or
2678:In
2580:or
2565:arc
2027:sat
1639:gap
1527:sat
1476:145
1387:sat
679:is
671:).
660:N I
561:is
409:MRI
145:or
113:An
4502::
4461:.
4457:.
4382:.
4372:.
4362:28
4360:.
4356:.
4304:.
4290:^
4269:.
4258:^
4226:^
4175:"
4162:^
4140:.
4109:.
4086:^
4076:.
4045:.
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3904:^
3882:.
3853:.
3773:.
3751:43
3749:.
3730:.
3680:^
3658:.
3640:^
3429:10
2888:,
2766:BH
2686:,
2584:.
2543:.
2504:=
2490:NI
2485:.
2475:DC
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1745:NI
1710:.
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1251:.
1161::
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1027:.
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4476:.
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4368::
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3997:.
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3806:.
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3327:2
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2784:.
2660:B
2626:B
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2327:m
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2198:=
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2167:3
2165:(
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2130:=
2127:B
2111:2
2102:D
2098:C
2081:B
2050:r
2025:B
2014:B
2006:B
2002:μ
1998:B
1994:μ
1981:)
1979:2
1977:(
1959:)
1951:0
1940:p
1937:a
1934:g
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1769:I
1766:N
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1670:C
1666:B
1646:.
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1570:(
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1493:/
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693:=
690:P
677:P
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575:=
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559:F
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77:(
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34:.
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