60:
2208:
2682:
The time-dependent behavior of magnetization becomes important when considering nanoscale and nanosecond timescale magnetization. Rather than simply aligning with an applied field, the individual magnetic moments in a material begin to precess around the applied field and come into alignment through
2648:
2551:
1834:
1314:
2425:
1700:
2758:
One application of demagnetization is to eliminate unwanted magnetic fields. For example, magnetic fields can interfere with electronic devices such as cell phones or computers, and with machining by making cuttings cling to their parent.
2341:
2566:
1094:
2472:
1731:
1979:
1236:
2277:
2137:
2755:, the source of ferromagnetic order, and destroy that order. Another way is to pull it out of an electric coil with alternating current running through it, giving rise to fields that oppose the magnetization.
1208:
2077:
1548:
2352:
1498:
2571:
2477:
2189:
2211:
When the microscopic currents induced by the magnetization (black arrows) do not balance out, bound volume currents (blue arrows) and bound surface currents (red arrows) appear in the medium.
30:
This article is about magnetization as it appears in
Maxwell's equations of classical electrodynamics. For a microscopic description of how magnetic materials react to a magnetic field, see
1341:
1123:
1616:
1153:
1932:
1896:
1870:
1048:
617:
2726:
2832:
2643:{\displaystyle {\begin{aligned}\mathbf {\nabla \times E} &=\mathbf {0} \\\mathbf {\nabla \cdot E} &={\frac {\rho }{\epsilon _{0}}}\end{aligned}}}
590:
2695:
with respect to its initial direction, from one stable orientation to the opposite one. Technologically, this is one of the most important processes in
2292:
2546:{\displaystyle {\begin{aligned}\mathbf {\nabla \times H} &=\mathbf {0} \\\mathbf {\nabla \cdot H} &=-\nabla \cdot \mathbf {M} \end{aligned}}}
1171:
602:
2717:
1829:{\displaystyle -\mathbf {M} \cdot \mathbf {B} =-\chi \mathbf {H} \cdot \mathbf {B} =-{\frac {\chi }{1+\chi }}{\frac {\mathbf {B} ^{2}}{\mu _{0}}},}
3058:
2997:
1937:
1840:
2237:
2094:
853:
622:
2691:
Magnetization reversal, also known as switching, refers to the process that leads to a 180° (arc) re-orientation of the magnetization
3026:
2034:
632:
1309:{\displaystyle \mathbf {P} ={\mathrm {d} \mathbf {p} \over \mathrm {d} V},\quad \mathbf {p} =\iiint \mathbf {P} \,\mathrm {d} V,}
1509:
2420:{\displaystyle \mathbf {J} =\mathbf {J} _{\mathrm {f} }+\nabla \times \mathbf {M} +{\frac {\partial \mathbf {P} }{\partial t}}}
457:
2881:
472:
467:
94:
1451:
482:
2154:
1017:
materials have a weak induced magnetization in a magnetic field, which disappears when the magnetic field is removed.
2747:
Demagnetization is the reduction or elimination of magnetization. One way to do this is to heat the object above its
84:
1354:
as a "moments per unit volume" are widely adopted, though in some cases they can lead to ambiguities and paradoxes.
352:
2199:
Whereas magnetization is given with the unit ampere/meter, the magnetic polarization is given with the unit tesla.
1714:
267:
17:
846:
612:
89:
2707:. As it is known today, there are only a few possible ways to reverse the magnetization of a metallic magnet:
1319:
1101:
954:
in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quantity of
2839:
1695:{\displaystyle \mathbf {M} =\chi \mathbf {H} ,\,\mathbf {B} =\mu \mathbf {H} =\mu _{0}(1+\chi )\mathbf {H} ,}
627:
332:
492:
232:
99:
3001:
222:
1214:
is an ordinary magnetic moment and the triple integral denotes integration over a volume. This makes the
1007:
of the electrons or the nuclei. Net magnetization results from the response of a material to an external
785:
660:
557:
532:
452:
935:
918:
285:
1033:. Magnetization is not necessarily uniform within a material, but may vary between different points.
839:
800:
327:
317:
257:
252:
192:
2441:), the second term is the contribution from the magnetization, and the last term is related to the
1133:
337:
1901:
770:
272:
2658:
1710:
650:
177:
167:
162:
1875:
1849:
775:
745:
2677:
2463:
1424:
1227:
951:
597:
367:
142:
2798:"Definition for Polarization P and Magnetization M Fully Consistent with Maxwell's Equations"
2773:
2752:
2730:
2442:
2088:
984:
as well as the way the material changes the magnetic field, and can be used to calculate the
695:
382:
372:
322:
312:
2932:
2896:
1219:
991:
The origin of the magnetic moments responsible for magnetization can be either microscopic
966:
820:
720:
685:
437:
302:
202:
187:
122:
59:
8:
2700:
2665:
1997:
1559:
780:
760:
755:
562:
547:
432:
402:
297:
227:
2936:
2900:
2980:
655:
395:
197:
157:
477:
2972:
2797:
2748:
715:
2984:
2962:
2954:
2904:
2812:
2692:
1030:
992:
815:
730:
690:
680:
567:
522:
505:
422:
357:
127:
51:
2958:
2336:{\displaystyle \mathbf {K} _{\mathrm {m} }=\mathbf {M} \times \mathbf {\hat {n}} }
2864:
2704:
2222:
1718:
1416:
1126:
955:
750:
675:
670:
537:
412:
377:
237:
137:
790:
2721:
2712:
2457:
2139:. The magnetic polarization thus differs from the magnetization by a factor of
1722:
1551:
1436:
1408:
1396:
1384:
1157:
1008:
1004:
981:
974:
970:
710:
705:
527:
417:
342:
292:
242:
215:
172:
147:
117:
110:
35:
34:. For mathematical description of fields surrounding magnets and currents, see
2346:
so that the total current density that enters
Maxwell's equations is given by
1089:{\displaystyle \mathbf {M} ={\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} V}}}
3052:
2557:
1022:
1018:
825:
810:
795:
735:
447:
362:
347:
247:
152:
2976:
2768:
1014:
959:
943:
900:
805:
700:
665:
607:
542:
462:
427:
307:
182:
2817:
2657:
plays the role of a fictitious "magnetic charge density" analogous to the
1985:
1974:{\displaystyle \mathbf {M} \approx \chi {\frac {\mathbf {B} }{\mu _{0}}}}
969:, which is the measure of the corresponding response of a material to an
725:
577:
407:
69:
2742:
1843:
on the paramagnet (or diamagnet) per unit volume (i.e. force density).
1607:
442:
2967:
2908:
2272:{\displaystyle \mathbf {J} _{\mathrm {m} }=\nabla \times \mathbf {M} }
2132:{\displaystyle \mathbf {D} =\varepsilon _{0}\mathbf {E} +\mathbf {P} }
1168:
concerned. This is better illustrated through the following relation:
1029:
to have magnetization in the absence of an external field, becoming a
2696:
2462:
In the absence of free electric currents and time-dependent effects,
1603:
765:
740:
552:
74:
31:
1233:
generated by a similar region or manifold with such a polarization:
1025:
materials have strong magnetization in a magnetic field, and can be
2192:
2080:
1165:
996:
980:
Magnetization also describes how a material responds to an applied
517:
512:
132:
2437:
is the electric current density of free charges (also called the
2207:
947:
883:
487:
1164:-field is the distribution of magnetic moments in the region or
2795:
1583:
1579:
1363:
1203:{\displaystyle \mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V}
911:
888:
572:
79:
2072:{\displaystyle \mathbf {B} =\mu _{0}\mathbf {H} +\mathbf {I} }
1725:) of the paramagnet (or diamagnet) in the magnetic field is:
1587:
1367:
985:
907:
892:
2869:. U.S. Department of Commerce, National Bureau of Standards.
2751:, where thermal fluctuations have enough energy to overcome
1575:
1543:{\displaystyle \mathbf {B} =\mathbf {H} +4\pi \mathbf {M} }
1045:-field can be defined according to the following equation:
1000:
27:
Physical quantity, density of magnetic moment per volume
2008:
Alternatively to the magnetization, one can define the
1501:
1441:
The magnetization defines the auxiliary magnetic field
1372:
2862:
2683:
relaxation as energy is transferred into the lattice.
2791:
2789:
2569:
2475:
2355:
2295:
2240:
2157:
2097:
2037:
1940:
1904:
1878:
1852:
1734:
1619:
1512:
1493:{\displaystyle \mathbf {B} =\mu _{0}(\mathbf {H+M} )}
1454:
1322:
1239:
1174:
1136:
1104:
1051:
2727:
magnetization reversal by circularly polarized light
1427:. The role of the magnetization is described below.
2922:
2920:
2918:
2873:
2729:; i.e., incident electromagnetic radiation that is
2028:is used, not to be confused with current density).
2929:Magnetism: From fundamentals to Nanoscale Dynamics
2786:
2642:
2545:
2419:
2335:
2271:
2183:
2131:
2071:
1973:
1926:
1890:
1864:
1828:
1694:
1558:which is convenient for various calculations. The
1542:
1492:
1335:
1308:
1202:
1147:
1117:
1088:
2327:
2184:{\displaystyle \mathbf {I} =\mu _{0}\mathbf {M} }
3050:
3000:. Magnetic Component Engineering. Archived from
2915:
1430:
2556:These equations can be solved in analogy with
1988:there is no one-to-one correspondence between
2926:
2879:
2838:. Lake Shore Cryotronics, Inc. Archived from
2466:describing the magnetic quantities reduce to
847:
3031:Introduction to Magnetic Particle Inspection
2796:C.A. Gonano; R.E. Zich; M. Mussetta (2015).
2942:
2856:
1343:is the elementary electric dipole moment.
854:
840:
58:
2966:
2816:
1639:
1378:
1294:
1191:
2206:
2202:
2003:
1336:{\displaystyle \mathrm {d} \mathbf {p} }
1118:{\displaystyle \mathrm {d} \mathbf {m} }
958:per unit volume. It is represented by a
2948:
2805:Progress in Electromagnetics Research B
988:that result from those interactions.
603:Electromagnetism and special relativity
14:
3059:Electric and magnetic fields in matter
3051:
1839:the negative gradient of which is the
3021:
3019:
623:Maxwell equations in curved spacetime
2949:Stanciu, C. D.; et al. (2007),
2927:Stohr, J.; Siegmann, H. C. (2006),
1218:-field completely analogous to the
965:. Magnetization can be compared to
24:
3016:
2736:
2602:
2575:
2528:
2508:
2481:
2408:
2398:
2381:
2372:
2304:
2258:
2249:
1610:, the relation is usually linear:
1324:
1296:
1264:
1252:
1193:
1138:
1106:
1076:
1064:
25:
3070:
2451:
2087:This is by direct analogy to the
2998:"Magnetic Component Engineering"
2953:, vol. 99, p. 217204,
2608:
2593:
2581:
2535:
2514:
2499:
2487:
2402:
2388:
2366:
2357:
2324:
2314:
2298:
2265:
2243:
2177:
2159:
2125:
2117:
2099:
2065:
2057:
2039:
1955:
1942:
1801:
1769:
1761:
1747:
1739:
1685:
1652:
1641:
1632:
1621:
1536:
1522:
1514:
1483:
1480:
1477:
1456:
1329:
1290:
1279:
1257:
1241:
1187:
1176:
1111:
1069:
1053:
2863:Francis Briggs Silsbee (1962).
2833:"Units for Magnetic Properties"
2703:process such as used in modern
2699:that is linked to the magnetic
1721:per unit volume (i.e. magnetic
1277:
2990:
2825:
1914:
1906:
1711:volume magnetic susceptibility
1681:
1669:
1487:
1473:
1226:-field, used to determine the
13:
1:
2959:10.1103/PhysRevLett.99.217204
2779:
2720:via a beam of particles with
1602:exists in many materials. In
1431:Relations between B, H, and M
1148:{\displaystyle \mathrm {d} V}
1036:
995:resulting from the motion of
628:Relativistic electromagnetism
2882:"Bound charges and currents"
2221:makes a contribution to the
1927:{\displaystyle |\chi |\ll 1}
7:
2889:American Journal of Physics
2866:Systems of Electrical Units
2762:
2686:
2671:
1220:electric polarisation field
1041:The magnetization field or
10:
3075:
2740:
2675:
2455:
1891:{\displaystyle \chi >0}
1865:{\displaystyle \chi <0}
1434:
936:classical electromagnetism
353:LiĂ©nardâWiechert potential
29:
1719:magnetic potential energy
917:
898:
882:
868:
618:Mathematical descriptions
328:Electromagnetic radiation
318:Electromagnetic induction
258:Magnetic vector potential
253:Magnetic scalar potential
950:of permanent or induced
2951:Physical Review Letters
2659:electric charge density
952:magnetic dipole moments
168:Electrostatic induction
163:Electrostatic discharge
2880:A. Herczynski (2013).
2678:Magnetization dynamics
2644:
2547:
2421:
2337:
2273:
2230:magnetization current.
2212:
2185:
2133:
2073:
1975:
1928:
1892:
1866:
1830:
1713:, and Ό is called the
1696:
1544:
1494:
1379:In Maxwell's equations
1361:-field is measured in
1337:
1310:
1228:electric dipole moment
1204:
1160:; in other words, the
1149:
1119:
1090:
598:Electromagnetic tensor
3033:. NDT Resource Center
2818:10.2528/PIERB15100606
2774:Orbital magnetization
2753:exchange interactions
2645:
2548:
2443:electric polarization
2422:
2338:
2284:bound surface current
2274:
2210:
2203:Magnetization current
2186:
2134:
2089:electric polarization
2074:
2010:magnetic polarization
2004:Magnetic polarization
1976:
1929:
1893:
1867:
1831:
1717:of the material. The
1715:magnetic permeability
1697:
1545:
1495:
1346:Those definitions of
1338:
1311:
1205:
1150:
1120:
1091:
967:electric polarization
591:Covariant formulation
383:Synchrotron radiation
323:Electromagnetic pulse
313:Electromagnetic field
3004:on December 17, 2010
2731:circularly polarized
2567:
2473:
2353:
2293:
2238:
2155:
2095:
2035:
1938:
1902:
1876:
1850:
1732:
1617:
1510:
1452:
1320:
1237:
1172:
1134:
1102:
1049:
633:Stressâenergy tensor
558:Reluctance (complex)
303:Displacement current
2937:2006mffn.book.....S
2931:, Springer-Verlag,
2901:2013AmJPh..81..202H
2666:demagnetizing field
2464:Maxwell's equations
1998:magnetic hysteresis
1872:) and paramagnets (
1594:A relation between
1568:is, approximately,
1560:vacuum permeability
1552:Gaussian quantities
1425:Maxwell's equations
946:that expresses the
548:Magnetomotive force
433:Electromotive force
403:Alternating current
338:Jefimenko equations
298:Cyclotron radiation
2640:
2638:
2543:
2541:
2417:
2333:
2269:
2215:The magnetization
2213:
2181:
2129:
2069:
2020:(often the symbol
1971:
1924:
1888:
1862:
1826:
1692:
1540:
1490:
1423:) is described by
1333:
1306:
1200:
1145:
1125:is the elementary
1115:
1086:
902:SI base units
396:Electrical network
233:Gauss magnetic law
198:Static electricity
158:Electric potential
3027:"Demagnetization"
2909:10.1119/1.4773441
2749:Curie temperature
2653:In this sense âââ
2634:
2415:
2330:
1969:
1821:
1795:
1272:
1084:
993:electric currents
932:
931:
864:
863:
563:Reluctance (real)
533:Gyratorâcapacitor
478:Resonant cavities
368:Maxwell equations
16:(Redirected from
3066:
3043:
3042:
3040:
3038:
3023:
3014:
3013:
3011:
3009:
2994:
2988:
2987:
2970:
2946:
2940:
2939:
2924:
2913:
2912:
2886:
2877:
2871:
2870:
2860:
2854:
2853:
2851:
2850:
2844:
2837:
2829:
2823:
2822:
2820:
2802:
2793:
2705:hard disk drives
2649:
2647:
2646:
2641:
2639:
2635:
2633:
2632:
2620:
2611:
2596:
2584:
2552:
2550:
2549:
2544:
2542:
2538:
2517:
2502:
2490:
2426:
2424:
2423:
2418:
2416:
2414:
2406:
2405:
2396:
2391:
2377:
2376:
2375:
2369:
2360:
2342:
2340:
2339:
2334:
2332:
2331:
2323:
2317:
2309:
2308:
2307:
2301:
2278:
2276:
2275:
2270:
2268:
2254:
2253:
2252:
2246:
2190:
2188:
2187:
2182:
2180:
2175:
2174:
2162:
2147:
2138:
2136:
2135:
2130:
2128:
2120:
2115:
2114:
2102:
2078:
2076:
2075:
2070:
2068:
2060:
2055:
2054:
2042:
2027:
2019:
1980:
1978:
1977:
1972:
1970:
1968:
1967:
1958:
1953:
1945:
1934:, and therefore
1933:
1931:
1930:
1925:
1917:
1909:
1897:
1895:
1894:
1889:
1871:
1869:
1868:
1863:
1835:
1833:
1832:
1827:
1822:
1820:
1819:
1810:
1809:
1804:
1798:
1796:
1794:
1780:
1772:
1764:
1750:
1742:
1701:
1699:
1698:
1693:
1688:
1668:
1667:
1655:
1644:
1635:
1624:
1590:
1573:
1549:
1547:
1546:
1541:
1539:
1525:
1517:
1499:
1497:
1496:
1491:
1486:
1472:
1471:
1459:
1383:The behavior of
1342:
1340:
1339:
1334:
1332:
1327:
1315:
1313:
1312:
1307:
1299:
1293:
1282:
1273:
1271:
1267:
1261:
1260:
1255:
1249:
1244:
1209:
1207:
1206:
1201:
1196:
1190:
1179:
1154:
1152:
1151:
1146:
1141:
1124:
1122:
1121:
1116:
1114:
1109:
1095:
1093:
1092:
1087:
1085:
1083:
1079:
1073:
1072:
1067:
1061:
1056:
1031:permanent magnet
903:
878:
866:
865:
856:
849:
842:
523:Electric machine
506:Magnetic circuit
468:Parallel circuit
458:Network analysis
423:Electric current
358:London equations
203:Triboelectricity
193:Potential energy
62:
52:Electromagnetism
43:
42:
21:
3074:
3073:
3069:
3068:
3067:
3065:
3064:
3063:
3049:
3048:
3047:
3046:
3036:
3034:
3025:
3024:
3017:
3007:
3005:
2996:
2995:
2991:
2947:
2943:
2925:
2916:
2884:
2878:
2874:
2861:
2857:
2848:
2846:
2842:
2835:
2831:
2830:
2826:
2800:
2794:
2787:
2782:
2765:
2745:
2739:
2737:Demagnetization
2689:
2680:
2674:
2637:
2636:
2628:
2624:
2619:
2612:
2601:
2598:
2597:
2592:
2585:
2574:
2570:
2568:
2565:
2564:
2560:problems where
2540:
2539:
2534:
2518:
2507:
2504:
2503:
2498:
2491:
2480:
2476:
2474:
2471:
2470:
2460:
2454:
2436:
2407:
2401:
2397:
2395:
2387:
2371:
2370:
2365:
2364:
2356:
2354:
2351:
2350:
2322:
2321:
2313:
2303:
2302:
2297:
2296:
2294:
2291:
2290:
2264:
2248:
2247:
2242:
2241:
2239:
2236:
2235:
2228:, known as the
2223:current density
2205:
2176:
2170:
2166:
2158:
2156:
2153:
2152:
2146:
2140:
2124:
2116:
2110:
2106:
2098:
2096:
2093:
2092:
2064:
2056:
2050:
2046:
2038:
2036:
2033:
2032:
2021:
2013:
2006:
1963:
1959:
1954:
1952:
1941:
1939:
1936:
1935:
1913:
1905:
1903:
1900:
1899:
1877:
1874:
1873:
1851:
1848:
1847:
1846:In diamagnets (
1815:
1811:
1805:
1800:
1799:
1797:
1784:
1779:
1768:
1760:
1746:
1738:
1733:
1730:
1729:
1684:
1663:
1659:
1651:
1640:
1631:
1620:
1618:
1615:
1614:
1571:
1569:
1567:
1535:
1521:
1513:
1511:
1508:
1507:
1476:
1467:
1463:
1455:
1453:
1450:
1449:
1439:
1433:
1417:current density
1397:electric fields
1385:magnetic fields
1381:
1328:
1323:
1321:
1318:
1317:
1295:
1289:
1278:
1263:
1262:
1256:
1251:
1250:
1248:
1240:
1238:
1235:
1234:
1192:
1186:
1175:
1173:
1170:
1169:
1137:
1135:
1132:
1131:
1127:magnetic moment
1110:
1105:
1103:
1100:
1099:
1075:
1074:
1068:
1063:
1062:
1060:
1052:
1050:
1047:
1046:
1039:
956:magnetic moment
901:
874:
871:
860:
831:
830:
646:
638:
637:
593:
583:
582:
538:Induction motor
508:
498:
497:
413:Current density
398:
388:
387:
378:Poynting vector
288:
286:Electrodynamics
278:
277:
273:Right-hand rule
238:Magnetic dipole
228:BiotâSavart law
218:
208:
207:
143:Electric dipole
138:Electric charge
113:
39:
28:
23:
22:
18:Demagnetization
15:
12:
11:
5:
3072:
3062:
3061:
3045:
3044:
3015:
2989:
2941:
2914:
2895:(3): 202â205.
2872:
2855:
2824:
2784:
2783:
2781:
2778:
2777:
2776:
2771:
2764:
2761:
2741:Main article:
2738:
2735:
2734:
2733:
2724:
2718:spin injection
2715:
2713:magnetic field
2688:
2685:
2676:Main article:
2673:
2670:
2651:
2650:
2631:
2627:
2623:
2618:
2615:
2613:
2610:
2607:
2604:
2600:
2599:
2595:
2591:
2588:
2586:
2583:
2580:
2577:
2573:
2572:
2554:
2553:
2537:
2533:
2530:
2527:
2524:
2521:
2519:
2516:
2513:
2510:
2506:
2505:
2501:
2497:
2494:
2492:
2489:
2486:
2483:
2479:
2478:
2458:Magnetostatics
2456:Main article:
2453:
2452:Magnetostatics
2450:
2434:
2428:
2427:
2413:
2410:
2404:
2400:
2394:
2390:
2386:
2383:
2380:
2374:
2368:
2363:
2359:
2344:
2343:
2329:
2326:
2320:
2316:
2312:
2306:
2300:
2280:
2279:
2267:
2263:
2260:
2257:
2251:
2245:
2204:
2201:
2197:
2196:
2179:
2173:
2169:
2165:
2161:
2144:
2127:
2123:
2119:
2113:
2109:
2105:
2101:
2085:
2084:
2067:
2063:
2059:
2053:
2049:
2045:
2041:
2005:
2002:
1966:
1962:
1957:
1951:
1948:
1944:
1923:
1920:
1916:
1912:
1908:
1887:
1884:
1881:
1861:
1858:
1855:
1841:magnetic force
1837:
1836:
1825:
1818:
1814:
1808:
1803:
1793:
1790:
1787:
1783:
1778:
1775:
1771:
1767:
1763:
1759:
1756:
1753:
1749:
1745:
1741:
1737:
1723:energy density
1709:is called the
1703:
1702:
1691:
1687:
1683:
1680:
1677:
1674:
1671:
1666:
1662:
1658:
1654:
1650:
1647:
1643:
1638:
1634:
1630:
1627:
1623:
1565:
1556:
1555:
1538:
1534:
1531:
1528:
1524:
1520:
1516:
1505:
1489:
1485:
1482:
1479:
1475:
1470:
1466:
1462:
1458:
1437:Magnetic field
1435:Main article:
1432:
1429:
1409:charge density
1380:
1377:
1331:
1326:
1305:
1302:
1298:
1292:
1288:
1285:
1281:
1276:
1270:
1266:
1259:
1254:
1247:
1243:
1199:
1195:
1189:
1185:
1182:
1178:
1158:volume element
1144:
1140:
1113:
1108:
1082:
1078:
1071:
1066:
1059:
1055:
1038:
1035:
1009:magnetic field
982:magnetic field
975:electrostatics
971:electric field
930:
929:
921:
915:
914:
905:
896:
895:
886:
880:
879:
872:
870:Common symbols
869:
862:
861:
859:
858:
851:
844:
836:
833:
832:
829:
828:
823:
818:
813:
808:
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798:
793:
788:
783:
778:
773:
768:
763:
758:
753:
748:
743:
738:
733:
728:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
673:
668:
663:
658:
653:
647:
644:
643:
640:
639:
636:
635:
630:
625:
620:
615:
613:Four-potential
610:
605:
600:
594:
589:
588:
585:
584:
581:
580:
575:
570:
565:
560:
555:
550:
545:
540:
535:
530:
528:Electric motor
525:
520:
515:
509:
504:
503:
500:
499:
496:
495:
490:
485:
483:Series circuit
480:
475:
470:
465:
460:
455:
453:Kirchhoff laws
450:
445:
440:
435:
430:
425:
420:
418:Direct current
415:
410:
405:
399:
394:
393:
390:
389:
386:
385:
380:
375:
373:Maxwell tensor
370:
365:
360:
355:
350:
345:
343:Larmor formula
340:
335:
330:
325:
320:
315:
310:
305:
300:
295:
293:Bremsstrahlung
289:
284:
283:
280:
279:
276:
275:
270:
265:
260:
255:
250:
245:
243:Magnetic field
240:
235:
230:
225:
219:
216:Magnetostatics
214:
213:
210:
209:
206:
205:
200:
195:
190:
185:
180:
175:
170:
165:
160:
155:
150:
148:Electric field
145:
140:
135:
130:
125:
120:
118:Charge density
114:
111:Electrostatics
109:
108:
105:
104:
103:
102:
97:
92:
87:
82:
77:
72:
64:
63:
55:
54:
48:
47:
46:Articles about
36:magnetic field
26:
9:
6:
4:
3:
2:
3071:
3060:
3057:
3056:
3054:
3032:
3028:
3022:
3020:
3003:
2999:
2993:
2986:
2982:
2978:
2974:
2969:
2964:
2960:
2956:
2952:
2945:
2938:
2934:
2930:
2923:
2921:
2919:
2910:
2906:
2902:
2898:
2894:
2890:
2883:
2876:
2868:
2867:
2859:
2845:on 2019-01-26
2841:
2834:
2828:
2819:
2814:
2810:
2806:
2799:
2792:
2790:
2785:
2775:
2772:
2770:
2767:
2766:
2760:
2756:
2754:
2750:
2744:
2732:
2728:
2725:
2723:
2719:
2716:
2714:
2710:
2709:
2708:
2706:
2702:
2698:
2694:
2684:
2679:
2669:
2667:
2663:
2660:
2656:
2629:
2625:
2621:
2616:
2614:
2605:
2589:
2587:
2578:
2563:
2562:
2561:
2559:
2558:electrostatic
2531:
2525:
2522:
2520:
2511:
2495:
2493:
2484:
2469:
2468:
2467:
2465:
2459:
2449:
2447:
2444:
2440:
2433:
2411:
2392:
2384:
2378:
2361:
2349:
2348:
2347:
2318:
2310:
2289:
2288:
2287:
2285:
2261:
2255:
2234:
2233:
2232:
2231:
2227:
2224:
2220:
2219:
2209:
2200:
2194:
2171:
2167:
2163:
2151:
2150:
2149:
2143:
2121:
2111:
2107:
2103:
2090:
2082:
2061:
2051:
2047:
2043:
2031:
2030:
2029:
2026:
2025:
2018:
2017:
2011:
2001:
1999:
1995:
1991:
1987:
1982:
1964:
1960:
1949:
1946:
1921:
1918:
1910:
1885:
1882:
1879:
1859:
1856:
1853:
1844:
1842:
1823:
1816:
1812:
1806:
1791:
1788:
1785:
1781:
1776:
1773:
1765:
1757:
1754:
1751:
1743:
1735:
1728:
1727:
1726:
1724:
1720:
1716:
1712:
1708:
1689:
1678:
1675:
1672:
1664:
1660:
1656:
1648:
1645:
1636:
1628:
1625:
1613:
1612:
1611:
1609:
1605:
1601:
1597:
1592:
1589:
1585:
1581:
1577:
1564:
1561:
1553:
1532:
1529:
1526:
1518:
1506:
1503:
1502:SI quantities
1468:
1464:
1460:
1448:
1447:
1446:
1444:
1438:
1428:
1426:
1422:
1418:
1414:
1410:
1406:
1402:
1398:
1394:
1390:
1386:
1376:
1374:
1370:
1369:
1365:
1360:
1355:
1353:
1349:
1344:
1303:
1300:
1286:
1283:
1274:
1268:
1245:
1232:
1229:
1225:
1221:
1217:
1213:
1197:
1183:
1180:
1167:
1163:
1159:
1155:
1142:
1128:
1096:
1080:
1057:
1044:
1034:
1032:
1028:
1024:
1023:ferrimagnetic
1020:
1019:Ferromagnetic
1016:
1012:
1010:
1006:
1002:
998:
994:
989:
987:
983:
978:
976:
972:
968:
964:
961:
957:
953:
949:
945:
941:
940:magnetization
937:
928:
925:
922:
920:
916:
913:
909:
906:
904:
897:
894:
890:
887:
885:
881:
877:
873:
867:
857:
852:
850:
845:
843:
838:
837:
835:
834:
827:
824:
822:
819:
817:
814:
812:
809:
807:
804:
802:
799:
797:
794:
792:
789:
787:
784:
782:
779:
777:
774:
772:
769:
767:
764:
762:
759:
757:
754:
752:
749:
747:
744:
742:
739:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
692:
689:
687:
684:
682:
679:
677:
674:
672:
669:
667:
664:
662:
659:
657:
654:
652:
649:
648:
642:
641:
634:
631:
629:
626:
624:
621:
619:
616:
614:
611:
609:
606:
604:
601:
599:
596:
595:
592:
587:
586:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
539:
536:
534:
531:
529:
526:
524:
521:
519:
516:
514:
511:
510:
507:
502:
501:
494:
491:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
464:
461:
459:
456:
454:
451:
449:
448:Joule heating
446:
444:
441:
439:
436:
434:
431:
429:
426:
424:
421:
419:
416:
414:
411:
409:
406:
404:
401:
400:
397:
392:
391:
384:
381:
379:
376:
374:
371:
369:
366:
364:
363:Lorentz force
361:
359:
356:
354:
351:
349:
346:
344:
341:
339:
336:
334:
331:
329:
326:
324:
321:
319:
316:
314:
311:
309:
306:
304:
301:
299:
296:
294:
291:
290:
287:
282:
281:
274:
271:
269:
266:
264:
263:Magnetization
261:
259:
256:
254:
251:
249:
248:Magnetic flux
246:
244:
241:
239:
236:
234:
231:
229:
226:
224:
221:
220:
217:
212:
211:
204:
201:
199:
196:
194:
191:
189:
186:
184:
181:
179:
176:
174:
171:
169:
166:
164:
161:
159:
156:
154:
153:Electric flux
151:
149:
146:
144:
141:
139:
136:
134:
131:
129:
126:
124:
121:
119:
116:
115:
112:
107:
106:
101:
98:
96:
93:
91:
90:Computational
88:
86:
83:
81:
78:
76:
73:
71:
68:
67:
66:
65:
61:
57:
56:
53:
50:
49:
45:
44:
41:
37:
33:
19:
3035:. Retrieved
3030:
3006:. Retrieved
3002:the original
2992:
2950:
2944:
2928:
2892:
2888:
2875:
2865:
2858:
2847:. Retrieved
2840:the original
2827:
2808:
2804:
2769:Magnetometer
2757:
2746:
2701:data storage
2690:
2681:
2664:; (see also
2661:
2654:
2652:
2555:
2461:
2445:
2439:free current
2438:
2431:
2429:
2345:
2283:
2282:and for the
2281:
2229:
2225:
2217:
2216:
2214:
2198:
2141:
2086:
2023:
2022:
2015:
2014:
2009:
2007:
1993:
1989:
1986:ferromagnets
1983:
1845:
1838:
1706:
1704:
1599:
1595:
1593:
1562:
1557:
1442:
1440:
1420:
1412:
1404:
1400:
1392:
1388:
1382:
1362:
1358:
1356:
1351:
1347:
1345:
1230:
1223:
1215:
1211:
1161:
1130:
1097:
1042:
1040:
1026:
1015:Paramagnetic
1013:
990:
979:
962:
960:pseudovector
944:vector field
939:
933:
926:
923:
884:SI unit
875:
608:Four-current
543:Linear motor
428:Electrolysis
308:Eddy current
268:Permeability
262:
188:Polarization
183:Permittivity
40:
2711:an applied
1996:because of
1898:), usually
1608:paramagnets
578:Transformer
408:Capacitance
333:Faraday law
128:Coulomb law
70:Electricity
2968:2066/36522
2849:2015-06-10
2811:: 83â101.
2780:References
2743:Degaussing
1604:diamagnets
1037:Definition
1027:magnetized
645:Scientists
493:Waveguides
473:Resistance
443:Inductance
223:AmpĂšre law
3037:April 18,
3008:April 18,
2697:magnetism
2626:ϵ
2622:ρ
2606:⋅
2603:∇
2579:×
2576:∇
2532:⋅
2529:∇
2526:−
2512:⋅
2509:∇
2485:×
2482:∇
2409:∂
2399:∂
2385:×
2382:∇
2328:^
2319:×
2262:×
2259:∇
2168:μ
2108:ε
2048:μ
1961:μ
1950:χ
1947:≈
1919:≪
1911:χ
1880:χ
1854:χ
1813:μ
1792:χ
1782:χ
1777:−
1766:⋅
1758:χ
1755:−
1744:⋅
1736:−
1679:χ
1661:μ
1649:μ
1629:χ
1533:π
1465:μ
1371:(A/m) in
1287:∭
1184:∭
1003:, or the
997:electrons
919:Dimension
801:Steinmetz
731:Kirchhoff
716:Jefimenko
711:Hopkinson
696:Helmholtz
691:Heaviside
553:Permeance
438:Impedance
178:Insulator
173:Gauss law
123:Conductor
100:Phenomena
95:Textbooks
75:Magnetism
32:magnetism
3053:Category
2977:18233247
2763:See also
2687:Reversal
2672:Dynamics
2193:SI units
2081:SI units
1574:10
1166:manifold
826:Wiechert
781:Poynting
671:Einstein
518:DC motor
513:AC motor
348:Lenz law
133:Electret
2985:6787518
2933:Bibcode
2897:Bibcode
1415:), and
1375:units.
1364:amperes
1156:is the
948:density
942:is the
811:Thomson
786:Ritchie
776:Poisson
761:Neumann
756:Maxwell
751:Lorentz
746:Liénard
676:Faraday
661:Coulomb
488:Voltage
463:Ohm law
85:History
2983:
2975:
2693:vector
2430:where
1705:where
1316:where
1210:where
1098:Where
986:forces
889:Ampere
796:Singer
791:Savart
771:Ărsted
736:Larmor
726:Kelvin
681:Fizeau
651:AmpĂšre
573:Stator
80:Optics
2981:S2CID
2885:(PDF)
2843:(PDF)
2836:(PDF)
2801:(PDF)
1368:meter
1222:, or
1001:atoms
893:meter
821:Weber
816:Volta
806:Tesla
721:Joule
706:Hertz
701:Henry
686:Gauss
568:Rotor
3039:2011
3010:2011
2973:PMID
2722:spin
1992:and
1883:>
1857:<
1606:and
1598:and
1366:per
1357:The
1350:and
1129:and
1021:and
1011:.
1005:spin
741:Lenz
666:Davy
656:Biot
2963:hdl
2955:doi
2905:doi
2813:doi
2668:).
1984:In
1591:).
1445:as
1407:),
1395:),
999:in
977:.
973:in
934:In
899:In
766:Ohm
3055::
3029:.
3018:^
2979:,
2971:,
2961:,
2917:^
2903:.
2893:81
2891:.
2887:.
2809:64
2807:.
2803:.
2788:^
2448:.
2286::
2195:).
2148::
2091:,
2083:).
2012:,
2000:.
1981:.
1582:/(
1570:4Ï
1403:,
1391:,
1373:SI
938:,
3041:.
3012:.
2965::
2957::
2935::
2911:.
2907::
2899::
2852:.
2821:.
2815::
2662:Ï
2655:M
2630:0
2617:=
2609:E
2594:0
2590:=
2582:E
2536:M
2523:=
2515:H
2500:0
2496:=
2488:H
2446:P
2435:f
2432:J
2412:t
2403:P
2393:+
2389:M
2379:+
2373:f
2367:J
2362:=
2358:J
2325:n
2315:M
2311:=
2305:m
2299:K
2266:M
2256:=
2250:m
2244:J
2226:J
2218:M
2191:(
2178:M
2172:0
2164:=
2160:I
2145:0
2142:Ό
2126:P
2122:+
2118:E
2112:0
2104:=
2100:D
2079:(
2066:I
2062:+
2058:H
2052:0
2044:=
2040:B
2024:J
2016:I
1994:H
1990:M
1965:0
1956:B
1943:M
1922:1
1915:|
1907:|
1886:0
1860:0
1824:,
1817:0
1807:2
1802:B
1789:+
1786:1
1774:=
1770:B
1762:H
1752:=
1748:B
1740:M
1707:Ï
1690:,
1686:H
1682:)
1676:+
1673:1
1670:(
1665:0
1657:=
1653:H
1646:=
1642:B
1637:,
1633:H
1626:=
1622:M
1600:H
1596:M
1588:m
1586:·
1584:A
1580:s
1578:·
1576:V
1572:Ă
1566:0
1563:Ό
1554:)
1550:(
1537:M
1530:4
1527:+
1523:H
1519:=
1515:B
1504:)
1500:(
1488:)
1484:M
1481:+
1478:H
1474:(
1469:0
1461:=
1457:B
1443:H
1421:J
1419:(
1413:Ï
1411:(
1405:D
1401:E
1399:(
1393:H
1389:B
1387:(
1359:M
1352:M
1348:P
1330:p
1325:d
1304:,
1301:V
1297:d
1291:P
1284:=
1280:p
1275:,
1269:V
1265:d
1258:p
1253:d
1246:=
1242:P
1231:p
1224:P
1216:M
1212:m
1198:V
1194:d
1188:M
1181:=
1177:m
1162:M
1143:V
1139:d
1112:m
1107:d
1081:V
1077:d
1070:m
1065:d
1058:=
1054:M
1043:M
963:M
927:I
924:L
912:A
910:â
908:m
891:-
876:M
855:e
848:t
841:v
38:.
20:)
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