899:
1468:. It can be seen that it fails for time varying currents by considering the case of a circuit consisting of a battery charging a capacitor through a resistor. It can be verified experimentally that the current in this circuit creates a magnetic field, yet any closed curve encircling the conductor can be spanned by a surface passing between the capacitor plates, through which no current passes, from which the equation would give zero magnetic field. Ărsted's law was modified by
1001:
76:
883:
902:
906:
905:
901:
900:
907:
25:
904:
1400:
950:
next to a wire carrying current turned so that the needle was perpendicular to the wire. Ărsted investigated and found the physical law describing the magnetic field, now known as Ărsted's law. Ărsted's discovery was the first connection found between
903:
1175:
1012:
The direction of the magnetic field at a point, the direction of the arrowheads on the magnetic field lines, which is the direction that the "north pole" of the compass needle points, can be found from the current by the
1318:
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633:
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869:
638:
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473:
488:
110:
1395:{\displaystyle \oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {\ell }}=\mu _{0}\iint _{S}\mathbf {J} \cdot \mathrm {d} \mathbf {S} \,}
1631:
1526:
368:
100:
283:
1604:
1577:
862:
628:
105:
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1621:
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301:
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343:
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273:
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208:
943:
786:
666:
353:
991:
The strength of the field at any point is inversely proportional to the distance of the point from the wire.
791:
761:
193:
183:
178:
1021:, flow of positive charge), the fingers will curl around the wire in the direction of the magnetic field.
964:
613:
383:
158:
1234:
is related to the direction of current by the right hand rule. The law can be expressed in terms of the
711:
398:
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338:
328:
75:
1473:
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1017:. If the right hand is wrapped around the wire so the thumb points in the direction of the current (
243:
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143:
67:
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985:
If the direction of the current is reversed, the direction of the magnetic field reverses.
766:
691:
686:
553:
428:
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288:
253:
153:
1430:
1409:
1295:
1274:
1216:
1170:{\displaystyle \oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {\ell }}=\mu _{0}I\,}
1091:
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806:
936:
726:
721:
543:
433:
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126:
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988:
The strength of the field is directly proportional to the magnitude of the current.
928:
890:, indicated by red field lines) around wire carrying an electric current (marked
821:
716:
681:
623:
558:
443:
323:
198:
1029:
The above rules can be generalized to give the modern vector form of Ărsted's law
478:
1654:, Addison-Wesley Publishing Company, Inc. Reading, MA, LCCCN: 63-15265 (no ISBN).
952:
741:
593:
423:
85:
1544:"Experiments on the effect of a current of electricity on the magnetic needles"
882:
1472:
to cover the case of time-varying currents by adding a new source term called
975:Ărsted found that, for a straight wire carrying a steady direct current (DC):
458:
963:. These two laws became part of the equations that govern electromagnetism,
1461:
956:
781:
756:
568:
493:
90:
1465:
1456:
currents, which don't change with time. Therefore, it only holds for DC
533:
528:
148:
503:
588:
95:
999:
982:
The magnetic field lines lie in a plane perpendicular to the wire.
881:
1620:
Arfken, George Brown; Hans-Jurgen Weber; Frank E. Harris (2012).
1564:
H. A. M. Snelders, "Oersted's discovery of electromagnetism" in
911:
Compass and wire apparatus showing Ărsted's experiment (video)
18:
979:
The magnetic field lines encircle the current-carrying wire.
959:, and the first of two laws that link the two; the other is
1623:
Mathematical
Methods for Physicists: A Comprehensive Guide
942:
This was discovered on 21 April 1820 by Danish physicist
1566:
Cunningham, Andrew
Cunningham; Nicholas Jardine (1990).
39:
1496:
Presentation (2015) by O. Zajkov, Physics
Institute,
1433:
1412:
1321:
1298:
1277:
1243:
1219:
1187:
1121:
1094:
1073:
1039:
1652:University Physics Third Edition (Complete Volume)
1440:
1419:
1394:
1305:
1284:
1263:
1226:
1201:
1169:
1101:
1080:
1059:
946:(1777â1851), when he noticed that the needle of a
1109:passing through any surface bounded by the curve.
16:Hans Christian Ărsted's law on electric current
863:
8:
1498:Ss. Cyril and Methodius University of Skopje
1264:{\displaystyle \mathbf {J} (\mathbf {x} )\,}
1060:{\displaystyle \mathbf {B} (\mathbf {x} )\,}
1521:. Courier Dover Publications. p. 172.
1008:to find the direction of the magnetic field
1213:, and the direction of integration around
870:
856:
74:
58:
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1120:
1098:
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1072:
1056:
1048:
1040:
1038:
1510:
1508:
1506:
1033:The line integral of the magnetic field
897:
1518:Electromagnetic Fields and Interactions
1489:
1346:
1146:
619:Electromagnetism and special relativity
66:
1554:. London: Baldwin, Craddock, Joy: 273.
1088:is proportional to the total current
639:Maxwell equations in curved spacetime
7:
1650:F. W. Sears and M. W. Zemansky 1964
1596:Basic Electrical Engineering, Vol. 1
1382:
1341:
1141:
14:
1599:. Tata McGraw-Hill. p. 96.
1387:
1374:
1333:
1253:
1245:
1133:
1049:
1041:
23:
1626:. Academic Press. p. 168.
996:Direction of the magnetic field
1292:instead of the total current
1257:
1249:
1053:
1045:
1:
644:Relativistic electromagnetism
1572:. CUP Archive. p. 228.
1569:Romanticism and the Sciences
1452:Ărsted's law only holds for
886:The magnetic field (marked
34:may have misleading content
1684:
1202:{\displaystyle \mu _{0}\,}
961:Faraday's law of induction
369:LiĂ©nardâWiechert potential
1209:= 4ÏĂ10 V·s/(A·m) is the
634:Mathematical descriptions
344:Electromagnetic radiation
334:Electromagnetic induction
274:Magnetic vector potential
269:Magnetic scalar potential
1515:Becker, Richard (2013).
1427:is any surface spanning
1067:around any closed curve
1542:Oersted, H. C. (1820).
1478:AmpereâMaxwell equation
184:Electrostatic induction
179:Electrostatic discharge
1442:
1421:
1396:
1307:
1286:
1265:
1228:
1203:
1171:
1111:
1103:
1082:
1061:
1025:Vector form of the law
1009:
912:
895:
614:Electromagnetic tensor
1443:
1422:
1397:
1308:
1287:
1266:
1229:
1204:
1172:
1104:
1083:
1062:
1031:
1003:
970:
944:Hans Christian Ărsted
910:
885:
607:Covariant formulation
399:Synchrotron radiation
339:Electromagnetic pulse
329:Electromagnetic field
1548:Annals of Philosophy
1474:displacement current
1431:
1410:
1319:
1296:
1275:
1271:through the surface
1241:
1217:
1185:
1119:
1092:
1071:
1037:
1019:conventional current
649:Stressâenergy tensor
574:Reluctance (complex)
319:Displacement current
1441:{\displaystyle C\,}
1420:{\displaystyle S\,}
1306:{\displaystyle I\,}
1285:{\displaystyle S\,}
1227:{\displaystyle C\,}
1102:{\displaystyle I\,}
1081:{\displaystyle C\,}
965:Maxwell's equations
564:Magnetomotive force
449:Electromotive force
419:Alternating current
354:Jefimenko equations
314:Cyclotron radiation
40:clarify the content
1438:
1417:
1392:
1303:
1282:
1261:
1224:
1199:
1167:
1099:
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1010:
913:
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412:Electrical network
249:Gauss magnetic law
214:Static electricity
174:Electric potential
1458:electric circuits
1211:magnetic constant
908:
880:
879:
579:Reluctance (real)
549:Gyratorâcapacitor
494:Resonant cavities
384:Maxwell equations
57:
56:
1675:
1668:Electromagnetism
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1087:
1085:
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1052:
1044:
933:electric current
931:stating that an
917:electromagnetism
909:
872:
865:
858:
539:Electric machine
522:Magnetic circuit
484:Parallel circuit
474:Network analysis
439:Electric current
374:London equations
219:Triboelectricity
209:Potential energy
78:
68:Electromagnetism
59:
52:
49:
43:
27:
26:
19:
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1634:
1619:
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1607:
1593:Dhogal (1986).
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1363:
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1293:
1273:
1272:
1239:
1238:
1236:current density
1215:
1214:
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1183:
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1153:
1122:
1117:
1116:
1090:
1089:
1069:
1068:
1035:
1034:
1027:
1015:right-hand rule
1006:right hand rule
998:
973:
923:, also spelled
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876:
847:
846:
662:
654:
653:
609:
599:
598:
554:Induction motor
524:
514:
513:
429:Current density
414:
404:
403:
394:Poynting vector
304:
302:Electrodynamics
294:
293:
289:Right-hand rule
254:Magnetic dipole
244:BiotâSavart law
234:
224:
223:
159:Electric dipole
154:Electric charge
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44:
37:
28:
24:
17:
12:
11:
5:
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1640:
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1633:978-0123846549
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1578:
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1534:
1528:978-0486318509
1527:
1502:
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1402:
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1280:
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1255:
1251:
1247:
1222:
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1191:
1179:
1178:
1177:
1165:
1160:
1156:
1152:
1148:
1143:
1139:
1135:
1129:
1125:
1097:
1076:
1055:
1051:
1047:
1043:
1026:
1023:
997:
994:
993:
992:
989:
986:
983:
980:
972:
971:Ărsted's rules
969:
937:magnetic field
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874:
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652:
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646:
641:
636:
631:
629:Four-potential
626:
621:
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546:
544:Electric motor
541:
536:
531:
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520:
519:
516:
515:
512:
511:
506:
501:
499:Series circuit
496:
491:
486:
481:
476:
471:
469:Kirchhoff laws
466:
461:
456:
451:
446:
441:
436:
434:Direct current
431:
426:
421:
415:
410:
409:
406:
405:
402:
401:
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391:
389:Maxwell tensor
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366:
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359:Larmor formula
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309:Bremsstrahlung
305:
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259:Magnetic field
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232:Magnetostatics
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186:
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176:
171:
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164:Electric field
161:
156:
151:
146:
141:
136:
134:Charge density
130:
127:Electrostatics
125:
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120:
119:
118:
113:
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103:
98:
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71:
70:
64:
63:
62:Articles about
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31:
29:
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15:
13:
10:
9:
6:
4:
3:
2:
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1602:
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1503:
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1490:
1483:
1481:
1479:
1476:, giving the
1475:
1471:
1467:
1463:
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1405:
1378:
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1327:
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1315:
1314:
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1278:
1237:
1220:
1212:
1193:
1189:
1180:
1163:
1158:
1154:
1150:
1137:
1127:
1123:
1115:
1114:
1113:
1112:
1110:
1095:
1074:
1030:
1024:
1022:
1020:
1016:
1007:
1002:
995:
990:
987:
984:
981:
978:
977:
976:
968:
966:
962:
958:
954:
949:
945:
940:
938:
934:
930:
926:
925:Oersted's law
922:
918:
893:
889:
884:
873:
868:
866:
861:
859:
854:
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703:
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518:
517:
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497:
495:
492:
490:
487:
485:
482:
480:
477:
475:
472:
470:
467:
465:
464:Joule heating
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379:Lorentz force
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279:Magnetization
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264:Magnetic flux
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169:Electric flux
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106:Computational
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41:
35:
32:This article
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21:
20:
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1622:
1615:
1595:
1588:
1568:
1560:
1551:
1547:
1537:
1517:
1500:, Macedonia.
1492:
1453:
1451:
1032:
1028:
1011:
974:
941:
929:physical law
924:
921:Ărsted's law
920:
914:
891:
887:
624:Four-current
559:Linear motor
444:Electrolysis
324:Eddy current
284:Permeability
204:Polarization
199:Permittivity
48:October 2023
45:
38:Please help
33:
1313:through it
953:electricity
594:Transformer
424:Capacitance
349:Faraday law
144:Coulomb law
86:Electricity
1645:References
1606:0074515861
1579:0521356857
1462:capacitors
1460:, with no
1004:Using the
935:creates a
661:Scientists
509:Waveguides
489:Resistance
459:Inductance
239:AmpĂšre law
1484:Footnotes
1466:inductors
1379:⋅
1365:∬
1355:μ
1347:ℓ
1338:⋅
1324:∮
1190:μ
1155:μ
1147:ℓ
1138:⋅
1124:∮
957:magnetism
927:, is the
817:Steinmetz
747:Kirchhoff
732:Jefimenko
727:Hopkinson
712:Helmholtz
707:Heaviside
569:Permeance
454:Impedance
194:Insulator
189:Gauss law
139:Conductor
116:Phenomena
111:Textbooks
91:Magnetism
1662:Category
842:Wiechert
797:Poynting
687:Einstein
534:DC motor
529:AC motor
364:Lenz law
149:Electret
1470:Maxwell
948:compass
827:Thomson
802:Ritchie
792:Poisson
777:Neumann
772:Maxwell
767:Lorentz
762:Liénard
692:Faraday
677:Coulomb
504:Voltage
479:Ohm law
101:History
1630:
1603:
1576:
1525:
1454:steady
1406:where
1181:where
812:Singer
807:Savart
787:Ărsted
752:Larmor
742:Kelvin
697:Fizeau
667:AmpĂšre
589:Stator
96:Optics
837:Weber
832:Volta
822:Tesla
737:Joule
722:Hertz
717:Henry
702:Gauss
584:Rotor
1628:ISBN
1601:ISBN
1574:ISBN
1523:ISBN
955:and
757:Lenz
682:Davy
672:Biot
1464:or
919:,
915:In
782:Ohm
1664::
1552:16
1550:.
1546:.
1505:^
1480:.
967:.
939:.
894:).
1636:.
1609:.
1582:.
1531:.
1448:.
1435:C
1414:S
1388:S
1383:d
1375:J
1369:S
1359:0
1351:=
1342:d
1334:B
1328:C
1300:I
1279:S
1258:)
1254:x
1250:(
1246:J
1221:C
1194:0
1164:I
1159:0
1151:=
1142:d
1134:B
1128:C
1096:I
1075:C
1054:)
1050:x
1046:(
1042:B
892:I
888:B
871:e
864:t
857:v
50:)
46:(
42:.
36:.
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