897:. However, the precise way in which this has "officially" been done has changed many times, as measurement techniques and thinking on the topic developed. The overall history of the unit of electric current, and of the related question of how to define a set of equations for describing electromagnetic phenomena, is very complicated. Briefly, the basic reason why
1160:
Historically, several different systems (including the two described above) were in use simultaneously. In particular, physicists and engineers used different systems, and physicists used three different systems for different parts of physics theory and a fourth different system (the engineers'
877:
was a defined value, and was not the result of experimental measurement (see below). In the new SI system, the permeability of vacuum no longer has a defined value, but is a measured quantity, with an uncertainty related to that of the (measured) dimensionless fine structure constant.
1161:
system) for laboratory experiments. In 1948, international decisions were made by standards organizations to adopt the rmks system, and its related set of electrical quantities and units, as the single main international system for describing electromagnetic phenomena in the
892:
In principle, there are several equation systems that could be used to set up a system of electrical quantities and units. Since the late 19th century, the fundamental definitions of current units have been related to the definitions of mass, length, and time units, using
419:
575:
688:
427:
was defined as "that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to
1065:
746:
The current in this definition needed to be measured with a known weight and known separation of the wires, defined in terms of the international standards of mass, length and time in order to produce a standard for the
1265:
987:
1497:
869:
The name "magnetic constant" was briefly used by standards organizations in order to avoid use of the terms "permeability" and "vacuum", which have physical meanings. The change of name had been made because
1371:
744:
317:
484:
579:
1534:
820:
is the 2022 CODATA value in the new system (and the Kibble balance has become an instrument for measuring weight from a known current, rather than measuring current from a known weight).
1667:
Parker, Richard H.; Yu, Chenghui; Zhong, Weicheng; Estey, Brian; Müller, Holger (2018-04-13). "Measurement of the fine-structure constant as a test of the
Standard Model".
999:
796:
461:
1381:. Between 1948 and 2018, this relation was used by BIPM (International Bureau of Weights and Measures) and NIST (National Institute of Standards and Technology) as a
1736:
Davis, Richard S. (2017). "Determining the value of the fine-structure constant from a current balance: Getting acquainted with some upcoming changes to the SI".
1505:, only the fine structure constant is a measured value in SI units in the expression on the right, since the remaining constants have defined values in SI units.
1524:
1215:
933:
1096:". A practical unit to be used by electricians and engineers, the ampere, was then defined as equal to one tenth of the electromagnetic unit of current.
1437:
2005:
1314:
2111:
1805:
1629:
1099:
In another system, the "rationalized metre–kilogram–second (rmks) system" (or alternatively the "metre–kilogram–second–ampere (mksa) system"),
1078:
692:
1074:
needs to be chosen in order to set up a system of equations, and a value then needs to be allocated in order to define the unit of current.
907:
Ampère's force law describes the experimentally-derived fact that, for two thin, straight, stationary, parallel wires, a distance
2027:
1826:
2087:
2053:
1904:
209:
1514:
1289:
1853:
261:
1088:
was chosen to be a pure number equal to 2, distance was measured in centimetres, force was measured in the cgs unit
1868:
1197:
2232:
1092:, and the currents defined by this equation were measured in the "electromagnetic unit (emu) of current", the "
414:{\displaystyle {\frac {|\mathbf {F} _{\text{m}}|}{L}}={\mu _{0} \over 2\pi }{I^{2} \over |{\boldsymbol {r}}|}.}
1519:
1162:
570:{\displaystyle {\frac {\mathbf {F} _{\text{m}}}{L}}={\mu _{0} \over 2\pi }\mathrm {(1\,A)^{2} \over {1\,m}} }
1827:"Comptes Rendus des Séances de la Neuvième Conférence Générale des Poids et Mesures Réunie à Paris en 1948"
683:{\displaystyle {2\times 10^{-7}\ \mathrm {N/m} }={\mu _{0} \over 2\pi }\mathrm {(1\,A)^{2} \over {1\,m}} }
249:
The deviation of the recommended measured value from the former defined value is within it uncertainty.
1882:
Magnetic
Permeability, and Analogues in Electro-static Induction, Conduction of Heat, and Fluid Motion
1650:
1601:
stems from the "rationalization" of the equations used to describe physical electromagnetic phenomena.
1196:, and relate them to their sources. In particular, it appears in relationship to quantities such as
1193:
2204:
2166:
1978:
165:, with no other dependencies with experimental uncertainty. Its value in SI units as recommended by
2079:
894:
300:
1411:
756:
257:
154:
135:
1131:
was chosen such that the rmks unit of current is equal in size to the ampere in the emu system:
2199:
1973:
1374:
1181:
1881:
774:
439:
253:
91:
2071:
153:
is an experimentally determined constant, its value being proportional to the dimensionless
2191:
2033:
1965:
1755:
1686:
8:
2072:
1539:
1301:
20:
2195:
2037:
1969:
1841:
1759:
1690:
2181:
1955:
1779:
1745:
1718:
1676:
1529:
1502:
2032:. World Scientific Series in Contemporary Chemical Physics. Vol. 17. p. 10.
19:
This article is about the magnetic constant. For the analogous electric constant, see
2083:
2049:
1900:
1849:
1783:
1771:
1710:
1702:
1427:
764:
99:
2209:
2145:
NIST reference on constants, units, and uncertainty: Fundamental physical constants
2041:
1983:
1940:
1763:
1722:
1694:
1407:
presented as a derived result contingent upon the validity of
Maxwell's equations.
1378:
293:
124:
116:
95:
1621:
1920:
1797:
1419:
1060:{\displaystyle {\frac {F_{\mathrm {m} }}{L}}=k_{\mathrm {m} }{\frac {I^{2}}{r}}.}
2133:
1563:
2103:
1293:
1189:
1185:
752:
112:
2213:
1987:
1124:
is a measurement-system constant called the "magnetic constant". The value of
2226:
1775:
1706:
1201:
866:
Variations thereof, such as "permeability of free space", remain widespread.
128:
120:
58:
1698:
1714:
1153:
1149:
473:
269:
2068:
For an introduction to the subject of choices for independent units, see
1651:"Convocationde la Conférence générale des poids et mesures (26e réunion)"
111:(pronounced "mu nought" or "mu zero"). It quantifies the strength of the
1260:{\displaystyle \mathbf {H} ={\mathbf {B} \over \mu _{0}}-\mathbf {M} ,}
982:{\displaystyle {\frac {F_{\mathrm {m} }}{L}}\propto {\frac {I^{2}}{r}}.}
881:
2167:"CODATA recommended values of the fundamental physical constants: 2006"
1941:"CODATA Recommended Values of the Fundamental Physical Constants: 2006"
927:
289:
1767:
1897:
Physics for
Scientists and Engineers, Third Edition, Extended Version
1535:
Sinusoidal plane-wave solutions of the electromagnetic wave equation
1750:
1681:
1093:
436:
newton per metre of length". This is equivalent to a definition of
2186:
1960:
2045:
2013:
Symbols, Units, Nomenclature and
Fundamental Constants in Physics
2001:
1492:{\displaystyle \mu _{0}={\frac {2\alpha }{e^{2}}}{\frac {h}{c}}.}
123:, it has the unit kg⋅m⋅s·A. It can be also expressed in terms of
1272:
768:
760:
748:
424:
166:
62:
1418:), the permeability can be derived from the latter (using the
851:
477:
1571:
1366:{\displaystyle c^{2}={1 \over {\mu _{0}\varepsilon _{0}}}.}
1089:
284:
Two thin, straight, stationary, parallel wires, a distance
2006:"Recommended values of the fundamental physical constants"
1848:. Facts on File science library. New York: Facts On File.
739:{\displaystyle \mu _{0}=4\pi \times 10^{-7}{\text{ H/m}}}
2165:
Mohr, Peter J; Taylor, Barry N; Newell, David B (2008).
1939:
Mohr, Peter J; Taylor, Barry N; Newell, David B (2008).
1561:
This choice defines the SI unit of current, the ampere:
1212:-field. In real media, this relationship has the form:
839:. Prior to the 2019 revision, it was referred to as the
2108:
The NIST Reference on
Constants, Units, and Uncertainty
1802:
The NIST Reference on
Constants, Units, and Uncertainty
1626:
The NIST Reference on
Constants, Units, and Uncertainty
926:, that one wire exerts upon the other in the vacuum of
1525:
Mathematical descriptions of the electromagnetic field
1403:. During this period of standards definitions, it was
208:
had a defined value (per the former definition of the
2025:
1440:
1317:
1218:
1204:, such as the relationship that defines the magnetic
1002:
936:
777:
695:
582:
487:
442:
320:
279:
1396:
and, prior to 2018, the defined numerical value for
854:
Red book, for example, this constant was called the
1168:
882:Systems of units and historical origin of value of
2069:
1666:
1590:The decision to explicitly include the factor of 2
1491:
1410:Conversely, as the permittivity is related to the
1365:
1259:
1059:
981:
858:. Another, now rather rare and obsolete, term is "
790:
738:
682:
569:
455:
413:
2026:Lalanne, J.-R.; Carmona, F.; Servant, L. (1999).
1798:"2022 CODATA Value: vacuum magnetic permeability"
264:in 1872. The modern notation of permeability as
2224:
2164:
1938:
1557:
1555:
2029:Optical spectroscopies of electronic absorption
1899:. New York, NY: Worth Publishers. p. 826.
1377:of classical electromagnetism in the medium of
1614:
1300:, is related to the magnetic constant and the
157:, which is known to a relative uncertainty of
2104:"2022 CODATA Value: speed of light in vacuum"
1552:
2156:This formula determining the exact value of
1921:"CODATA Value: vacuum magnetic permeability"
1790:
1622:"2022 CODATA Value: fine-structure constant"
1392:in terms of the defined numerical value for
2096:
2078:(Third ed.). New York: Wiley. p.
989:Writing the constant of proportionality as
1839:
2203:
2185:
1977:
1959:
1749:
1680:
673:
654:
560:
541:
2131:The exact numerical value is found at:
2062:
2019:
2000:
1302:electric constant (vacuum permittivity)
1079:"electromagnetic (emu)" system of units
396:
2225:
1931:
1894:
1735:
904:has the value it does is as follows.
850:has had different names. In the 1987
299:, will exert a force on each other.
2163:is found in Table 1, p. 637 of
1081:, defined in the late 19th century,
2125:
1564:"Unit of electric current (ampere)"
1373:This relation can be derived using
1184:, which describe the properties of
763:is defined exactly in terms of the
146:were fixed as defined quantities),
13:
1893:See for example equation 25-14 in
1515:Characteristic impedance of vacuum
1290:International System of Quantities
1031:
1011:
945:
915:flows, the force per unit length,
911:apart, in each of which a current
674:
655:
615:
607:
561:
542:
280:Ampere-defined vacuum permeability
14:
2244:
1271:is the magnetization density. In
276:has been in use since the 1950s.
262:William Thomson, 1st Baron Kelvin
1250:
1230:
1220:
1208:-field in terms of the magnetic
1169:Significance in electromagnetism
492:
331:
1994:
1913:
1584:
860:magnetic permittivity of vacuum
798:is determined experimentally; 4
303:states that the magnetic force
1887:
1875:
1833:
1819:
1729:
1660:
1643:
823:
659:
648:
546:
535:
401:
391:
342:
325:
1:
1608:
1520:Electromagnetic wave equation
1163:International System of Units
862:". See, for example, Servant
843:. Historically, the constant
1568:Historical context of the SI
837:vacuum magnetic permeability
102:, conventionally written as
72:vacuum magnetic permeability
7:
2070:John David Jackson (1998).
1738:American Journal of Physics
1508:
423:From 1948 until 2019 the
10:
2249:
755:was designed for). In the
136:revision of the SI in 2019
80:permeability of free space
18:
2214:10.1103/RevModPhys.80.633
2174:Reviews of Modern Physics
2074:Classical electrodynamics
1988:10.1103/RevModPhys.80.633
1948:Reviews of Modern Physics
1194:electromagnetic radiation
119:. Expressed in terms of
1895:Tipler, Paul A. (1992).
1842:"Permeability (Physics)"
1545:
791:{\displaystyle \mu _{0}}
456:{\displaystyle \mu _{0}}
1846:Encyclopedia of Physics
1699:10.1126/science.aap7706
1412:fine-structure constant
757:2019 revision of the SI
751:(and this is what the
155:fine-structure constant
1493:
1367:
1261:
1173:The magnetic constant
1061:
983:
856:permeability of vacuum
828:NIST/CODATA refers to
792:
740:
684:
571:
457:
415:
84:permeability of vacuum
2233:Fundamental constants
1869:registration required
1494:
1368:
1262:
1202:magnetization density
1062:
984:
793:
741:
685:
572:
458:
416:
92:magnetic permeability
2134:"Electric constant,
1438:
1315:
1216:
1000:
934:
775:
693:
580:
485:
440:
318:
138:(when the values of
2196:2008RvMP...80..633M
2038:1999WSSCP..17.....L
1970:2008RvMP...80..633M
1840:Rosen, Joe (2004).
1760:2017AmJPh..85..364D
1691:2018Sci...360..191P
1540:Vacuum permittivity
1375:Maxwell's equations
1311:, by the equation:
1182:Maxwell's equations
771:, and the value of
252:The terminology of
201:From 1948 to 2019,
76:vacuum permeability
21:vacuum permittivity
1530:New SI definitions
1489:
1363:
1257:
1057:
979:
930:would be given by
895:Ampère's force law
788:
736:
680:
567:
453:
411:
301:Ampère's force law
292:, each carrying a
260:was introduced by
2089:978-0-471-30932-1
2055:978-981-02-3861-2
1906:978-0-87901-434-6
1768:10.1119/1.4976701
1675:(6385): 191–195.
1484:
1474:
1428:elementary charge
1358:
1244:
1052:
1020:
974:
954:
841:magnetic constant
818:10 H⋅m
765:elementary charge
734:
678:
643:
605:
565:
530:
505:
499:
406:
375:
350:
338:
178: =
100:physical constant
88:magnetic constant
68:
67:
16:Physical constant
2240:
2218:
2217:
2207:
2189:
2171:
2155:
2153:
2152:
2129:
2123:
2122:
2120:
2119:
2100:
2094:
2093:
2077:
2066:
2060:
2059:
2023:
2017:
2016:
2010:
1998:
1992:
1991:
1981:
1963:
1945:
1935:
1929:
1928:
1925:physics.nist.gov
1917:
1911:
1910:
1891:
1885:
1879:
1873:
1872:
1865:
1863:
1862:
1837:
1831:
1830:
1823:
1817:
1816:
1814:
1813:
1794:
1788:
1787:
1753:
1733:
1727:
1726:
1684:
1664:
1658:
1657:
1655:
1647:
1641:
1640:
1638:
1637:
1618:
1602:
1588:
1582:
1581:
1579:
1578:
1559:
1498:
1496:
1495:
1490:
1485:
1477:
1475:
1473:
1472:
1463:
1455:
1450:
1449:
1379:classical vacuum
1372:
1370:
1369:
1364:
1359:
1357:
1356:
1355:
1346:
1345:
1332:
1327:
1326:
1284:
1266:
1264:
1263:
1258:
1253:
1245:
1243:
1242:
1233:
1228:
1223:
1156:
1066:
1064:
1063:
1058:
1053:
1048:
1047:
1038:
1036:
1035:
1034:
1021:
1016:
1015:
1014:
1004:
988:
986:
985:
980:
975:
970:
969:
960:
955:
950:
949:
948:
938:
819:
817:
813:
810:
807:
797:
795:
794:
789:
787:
786:
745:
743:
742:
737:
735:
732:
730:
729:
705:
704:
689:
687:
686:
681:
679:
677:
668:
667:
666:
646:
644:
642:
634:
633:
624:
619:
618:
614:
603:
602:
601:
576:
574:
573:
568:
566:
564:
555:
554:
553:
533:
531:
529:
521:
520:
511:
506:
501:
500:
497:
495:
489:
480:
471:
462:
460:
459:
454:
452:
451:
435:
433:
420:
418:
417:
412:
407:
405:
404:
399:
394:
388:
387:
378:
376:
374:
366:
365:
356:
351:
346:
345:
340:
339:
336:
334:
328:
322:
246:
244:
240:
237:
234:
228:
226:
198:
195:
193:
189:
186:
183:
164:
162:
125:SI derived units
117:electric current
96:classical vacuum
56:
54:
50:
47:
44:
26:
25:
2248:
2247:
2243:
2242:
2241:
2239:
2238:
2237:
2223:
2222:
2221:
2205:10.1.1.150.1225
2169:
2162:
2150:
2148:
2140:
2132:
2130:
2126:
2117:
2115:
2102:
2101:
2097:
2090:
2067:
2063:
2056:
2024:
2020:
2008:
1999:
1995:
1979:10.1.1.150.1225
1943:
1937:See Table 1 in
1936:
1932:
1919:
1918:
1914:
1907:
1892:
1888:
1880:
1876:
1866:
1860:
1858:
1856:
1838:
1834:
1825:
1824:
1820:
1811:
1809:
1796:
1795:
1791:
1734:
1730:
1665:
1661:
1653:
1649:
1648:
1644:
1635:
1633:
1620:
1619:
1615:
1611:
1606:
1605:
1600:
1589:
1585:
1576:
1574:
1562:
1560:
1553:
1548:
1511:
1476:
1468:
1464:
1456:
1454:
1445:
1441:
1439:
1436:
1435:
1420:Planck constant
1402:
1391:
1351:
1347:
1341:
1337:
1336:
1331:
1322:
1318:
1316:
1313:
1312:
1310:
1276:
1249:
1238:
1234:
1229:
1227:
1219:
1217:
1214:
1213:
1179:
1171:
1143:
1137:
1130:
1123:
1112:
1105:
1087:
1073:
1043:
1039:
1037:
1030:
1029:
1025:
1010:
1009:
1005:
1003:
1001:
998:
997:
995:
965:
961:
959:
944:
943:
939:
937:
935:
932:
931:
921:
903:
890:
888:
876:
849:
834:
826:
815:
811:
808:
805:
803:
782:
778:
776:
773:
772:
731:
722:
718:
700:
696:
694:
691:
690:
669:
662:
658:
647:
645:
635:
629:
625:
623:
610:
606:
594:
590:
583:
581:
578:
577:
556:
549:
545:
534:
532:
522:
516:
512:
510:
496:
491:
490:
488:
486:
483:
482:
469:
464:
447:
443:
441:
438:
437:
431:
429:
400:
395:
390:
389:
383:
379:
377:
367:
361:
357:
355:
341:
335:
330:
329:
324:
323:
321:
319:
316:
315:
309:
282:
247:
242:
238:
235:
232:
230:
224:
222:
220:
207:
199:
196:
191:
187:
184:
181:
179:
177:
160:
158:
152:
109:
52:
48:
45:
42:
40:
35:
24:
17:
12:
11:
5:
2246:
2236:
2235:
2220:
2219:
2180:(2): 633–730.
2160:
2138:
2124:
2095:
2088:
2061:
2054:
2018:
1993:
1954:(2): 633–730.
1930:
1912:
1905:
1886:
1874:
1854:
1832:
1818:
1789:
1744:(5): 364–368.
1728:
1659:
1642:
1612:
1610:
1607:
1604:
1603:
1598:
1583:
1550:
1549:
1547:
1544:
1543:
1542:
1537:
1532:
1527:
1522:
1517:
1510:
1507:
1488:
1483:
1480:
1471:
1467:
1462:
1459:
1453:
1448:
1444:
1400:
1389:
1362:
1354:
1350:
1344:
1340:
1335:
1330:
1325:
1321:
1308:
1294:speed of light
1256:
1252:
1248:
1241:
1237:
1232:
1226:
1222:
1177:
1170:
1167:
1135:
1128:
1121:
1110:
1106:is written as
1103:
1085:
1071:
1056:
1051:
1046:
1042:
1033:
1028:
1024:
1019:
1013:
1008:
993:
978:
973:
968:
964:
958:
953:
947:
942:
919:
901:
889:
886:
880:
874:
847:
832:
825:
822:
785:
781:
753:Kibble balance
728:
725:
721:
717:
714:
711:
708:
703:
699:
676:
672:
665:
661:
657:
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310:per length
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2151:2012-01-22
2118:2024-05-18
2114:. May 2024
1861:2010-02-04
1812:2024-05-18
1808:. May 2024
1751:1610.02910
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1632:. May 2024
1609:References
1577:2007-08-11
1426:, and the
1383:definition
928:free space
290:free space
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