908:. 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
1171:
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'
888:
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.
1172:
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
903:
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
430:
586:
699:
438:
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
1076:
757:
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
1276:
998:
1545:
1508:
880:
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
1382:
755:
328:
495:
590:
831:
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).
1535:
1678:
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".
1010:
807:
472:
1392:. 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
1089:
2122:
1816:
1747:
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".
1640:
1516:, 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.
1226:
944:
1107:". 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.
1448:
2016:
1325:
1110:
In another system, the "rationalized metre–kilogram–second (rmks) system" (or alternatively the "metre–kilogram–second–ampere (mksa) system"),
703:
2098:
2064:
1915:
1085:
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.
1525:
1300:
1864:
272:
918:
Ampère's force law describes the experimentally-derived fact that, for two thin, straight, stationary, parallel wires, a distance
2038:
1837:
1208:
2243:
1530:
1173:
220:
1099:
was chosen to be a pure number equal to 2, distance was measured in centimetres, force was measured in the cgs unit
1879:
1204:
1103:, and the currents defined by this equation were measured in the "electromagnetic unit (emu) of current", the "
425:{\displaystyle {\frac {|\mathbf {F} _{\text{m}}|}{L}}={\mu _{0} \over 2\pi }{I^{2} \over |{\boldsymbol {r}}|}.}
905:
311:
581:{\displaystyle {\frac {\mathbf {F} _{\text{m}}}{L}}={\mu _{0} \over 2\pi }\mathrm {(1\,A)^{2} \over {1\,m}} }
1422:
767:
268:
165:
146:
1838:"Comptes Rendus des Séances de la Neuvième Conférence Générale des Poids et Mesures Réunie à Paris en 1948"
2210:
1984:
1385:
1192:
694:{\displaystyle {2\times 10^{-7}\ \mathrm {N/m} }={\mu _{0} \over 2\pi }\mathrm {(1\,A)^{2} \over {1\,m}} }
264:
260:
The deviation of the recommended measured value from the former defined value is within it uncertainty.
102:
1893:
Magnetic
Permeability, and Analogues in Electro-static Induction, Conduction of Heat, and Fluid Motion
1661:
1612:
stems from the "rationalization" of the equations used to describe physical electromagnetic phenomena.
2202:
2044:
1976:
1766:
1697:
1207:, and relate them to their sources. In particular, it appears in relationship to quantities such as
2215:
2177:
1989:
176:, with no other dependencies with experimental uncertainty. Its value in SI units as recommended by
2090:
1550:
1312:
31:
2192:
1966:
1790:
1756:
1729:
1687:
1540:
1513:
1142:
was chosen such that the rmks unit of current is equal in size to the ampere in the emu system:
2094:
2060:
1911:
1892:
1860:
1782:
1721:
1713:
1438:
785:
775:
450:
110:
2220:
2082:
2052:
1994:
1774:
1705:
304:
164:
is an experimentally determined constant, its value being proportional to the dimensionless
135:
127:
106:
1430:
17:
2083:
2206:
2048:
1980:
1852:
1770:
1701:
1304:
1200:
1196:
763:
123:
2043:. World Scientific Series in Contemporary Chemical Physics. Vol. 17. p. 10.
30:
This article is about the magnetic constant. For the analogous electric constant, see
2237:
1794:
1212:
139:
131:
69:
2156:
NIST reference on constants, units, and uncertainty: Fundamental physical constants
1951:
1733:
1418:
presented as a derived result contingent upon the validity of
Maxwell's equations.
1164:
1160:
484:
280:
1632:
1931:
1808:
1071:{\displaystyle {\frac {F_{\mathrm {m} }}{L}}=k_{\mathrm {m} }{\frac {I^{2}}{r}}.}
2144:
1574:
2114:
2224:
1998:
1135:
is a measurement-system constant called the "magnetic constant". The value of
938:
300:
1786:
1717:
877:
Variations thereof, such as "permeability of free space", remain widespread.
1709:
1725:
2079:
For an introduction to the subject of choices for independent units, see
1662:"Convocationde la Conférence générale des poids et mesures (26e réunion)"
1104:
122:(pronounced "mu nought" or "mu zero"). It quantifies the strength of the
1271:{\displaystyle \mathbf {H} ={\mathbf {B} \over \mu _{0}}-\mathbf {M} ,}
993:{\displaystyle {\frac {F_{\mathrm {m} }}{L}}\propto {\frac {I^{2}}{r}}.}
2178:"CODATA recommended values of the fundamental physical constants: 2006"
2012:
1952:"CODATA Recommended Values of the Fundamental Physical Constants: 2006"
1778:
1908:
Physics for
Scientists and Engineers, Third Edition, Extended Version
1389:
1283:
779:
771:
759:
435:
177:
73:
1546:
Sinusoidal plane-wave solutions of the electromagnetic wave equation
1761:
1692:
447:
newton per metre of length". This is equivalent to a definition of
2197:
1971:
862:
488:
2056:
2024:
Symbols, Units, Nomenclature and
Fundamental Constants in Physics
1503:{\displaystyle \mu _{0}={\frac {2\alpha }{e^{2}}}{\frac {h}{c}}.}
134:, it has the unit kg⋅m⋅s·A. It can be also expressed in terms of
1582:
1100:
1429:), the permeability can be derived from the latter (using the
1377:{\displaystyle c^{2}={1 \over {\mu _{0}\varepsilon _{0}}}.}
295:
Two thin, straight, stationary, parallel wires, a distance
2017:"Recommended values of the fundamental physical constants"
1859:. Facts on File science library. New York: Facts On File.
750:{\displaystyle \mu _{0}=4\pi \times 10^{-7}{\text{ H/m}}}
2176:
Mohr, Peter J; Taylor, Barry N; Newell, David B (2008).
1950:
Mohr, Peter J; Taylor, Barry N; Newell, David B (2008).
1572:
This choice defines the SI unit of current, the ampere:
1223:-field. In real media, this relationship has the form:
850:. Prior to the 2019 revision, it was referred to as the
2119:
The NIST Reference on
Constants, Units, and Uncertainty
1813:
The NIST Reference on
Constants, Units, and Uncertainty
1637:
The NIST Reference on
Constants, Units, and Uncertainty
937:, that one wire exerts upon the other in the vacuum of
1536:
Mathematical descriptions of the electromagnetic field
1414:. During this period of standards definitions, it was
219:
had a defined value (per the former definition of the
1451:
1328:
1229:
1215:, such as the relationship that defines the magnetic
1013:
947:
788:
706:
593:
498:
453:
331:
1407:
and, prior to 2018, the defined numerical value for
865:
Red book, for example, this constant was called the
893:Systems of units and historical origin of value of
1601:The decision to explicitly include the factor of 2
1502:
1421:Conversely, as the permittivity is related to the
1376:
1270:
1070:
992:
869:. Another, now rather rare and obsolete, term is "
801:
749:
693:
580:
466:
424:
2037:Lalanne, J.-R.; Carmona, F.; Servant, L. (1999).
1809:"2022 CODATA Value: vacuum magnetic permeability"
275:in 1872. The modern notation of permeability as
1568:
1566:
2040:Optical spectroscopies of electronic absorption
1910:. New York, NY: Worth Publishers. p. 826.
1388:of classical electromagnetism in the medium of
1311:, is related to the magnetic constant and the
168:, which is known to a relative uncertainty of
2115:"2022 CODATA Value: speed of light in vacuum"
8:
2167:This formula determining the exact value of
1932:"CODATA Value: vacuum magnetic permeability"
1633:"2022 CODATA Value: fine-structure constant"
1403:in terms of the defined numerical value for
2089:(Third ed.). New York: Wiley. p.
1000:Writing the constant of proportionality as
36:
2214:
2196:
1988:
1970:
1760:
1691:
1487:
1479:
1465:
1456:
1450:
1362:
1352:
1347:
1342:
1333:
1327:
1260:
1249:
1240:
1238:
1230:
1228:
1054:
1048:
1041:
1040:
1021:
1020:
1014:
1012:
976:
970:
955:
954:
948:
946:
793:
787:
742:
733:
711:
705:
684:
680:
673:
665:
656:
640:
634:
621:
617:
605:
594:
592:
571:
567:
560:
552:
543:
527:
521:
507:
502:
499:
497:
458:
452:
411:
406:
401:
394:
388:
372:
366:
352:
346:
341:
335:
332:
330:
2142:The exact numerical value is found at:
1624:
1562:
1313:electric constant (vacuum permittivity)
1090:"electromagnetic (emu)" system of units
407:
915:has the value it does is as follows.
861:has had different names. In the 1987
310:, will exert a force on each other.
7:
2174:is found in Table 1, p. 637 of
1092:, defined in the late 19th century,
1575:"Unit of electric current (ampere)"
1384:This relation can be derived using
1195:, which describe the properties of
774:is defined exactly in terms of the
157:were fixed as defined quantities),
1904:See for example equation 25-14 in
1526:Characteristic impedance of vacuum
1301:International System of Quantities
1042:
1022:
956:
926:flows, the force per unit length,
922:apart, in each of which a current
685:
666:
626:
618:
572:
553:
291:Ampere-defined vacuum permeability
25:
1282:is the magnetization density. In
287:has been in use since the 1950s.
273:William Thomson, 1st Baron Kelvin
1261:
1241:
1231:
1219:-field in terms of the magnetic
1180:Significance in electromagnetism
503:
342:
871:magnetic permittivity of vacuum
809:is determined experimentally; 4
314:states that the magnetic force
670:
659:
557:
546:
412:
402:
353:
336:
1:
1531:Electromagnetic wave equation
1174:International System of Units
873:". See, for example, Servant
854:. Historically, the constant
1579:Historical context of the SI
848:vacuum magnetic permeability
113:, conventionally written as
83:vacuum magnetic permeability
2081:John David Jackson (1998).
1749:American Journal of Physics
434:From 1948 until 2019 the
2260:
766:was designed for). In the
147:revision of the SI in 2019
91:permeability of free space
29:
18:Permeability of free space
2225:10.1103/RevModPhys.80.633
2185:Reviews of Modern Physics
2085:Classical electrodynamics
1999:10.1103/RevModPhys.80.633
1959:Reviews of Modern Physics
1205:electromagnetic radiation
130:. Expressed in terms of
1906:Tipler, Paul A. (1992).
1853:"Permeability (Physics)"
802:{\displaystyle \mu _{0}}
467:{\displaystyle \mu _{0}}
1857:Encyclopedia of Physics
1710:10.1126/science.aap7706
1423:fine-structure constant
768:2019 revision of the SI
762:(and this is what the
166:fine-structure constant
1504:
1378:
1272:
1184:The magnetic constant
1072:
994:
867:permeability of vacuum
839:NIST/CODATA refers to
803:
751:
695:
582:
468:
426:
95:permeability of vacuum
2244:Fundamental constants
1880:registration required
1505:
1379:
1273:
1213:magnetization density
1073:
995:
804:
752:
696:
583:
469:
427:
103:magnetic permeability
2145:"Electric constant,
1449:
1326:
1227:
1011:
945:
786:
704:
591:
496:
451:
329:
149:(when the values of
2207:2008RvMP...80..633M
2049:1999WSSCP..17.....L
1981:2008RvMP...80..633M
1851:Rosen, Joe (2004).
1771:2017AmJPh..85..364D
1702:2018Sci...360..191P
1551:Vacuum permittivity
1386:Maxwell's equations
1322:, by the equation:
1193:Maxwell's equations
782:, and the value of
263:The terminology of
212:From 1948 to 2019,
87:vacuum permeability
32:vacuum permittivity
1541:New SI definitions
1500:
1374:
1268:
1068:
990:
941:would be given by
906:Ampère's force law
799:
747:
691:
578:
464:
422:
312:Ampère's force law
303:, each carrying a
271:was introduced by
2100:978-0-471-30932-1
2066:978-981-02-3861-2
1917:978-0-87901-434-6
1779:10.1119/1.4976701
1686:(6385): 191–195.
1495:
1485:
1439:elementary charge
1369:
1255:
1063:
1031:
985:
965:
852:magnetic constant
829:10 H⋅m
776:elementary charge
745:
689:
654:
616:
576:
541:
516:
510:
417:
386:
361:
349:
189: =
111:physical constant
99:magnetic constant
79:
78:
27:Physical constant
16:(Redirected from
2251:
2229:
2228:
2218:
2200:
2182:
2166:
2164:
2163:
2140:
2134:
2133:
2131:
2130:
2111:
2105:
2104:
2088:
2077:
2071:
2070:
2034:
2028:
2027:
2021:
2009:
2003:
2002:
1992:
1974:
1956:
1946:
1940:
1939:
1936:physics.nist.gov
1928:
1922:
1921:
1902:
1896:
1890:
1884:
1883:
1876:
1874:
1873:
1848:
1842:
1841:
1834:
1828:
1827:
1825:
1824:
1805:
1799:
1798:
1764:
1744:
1738:
1737:
1695:
1675:
1669:
1668:
1666:
1658:
1652:
1651:
1649:
1648:
1629:
1613:
1599:
1593:
1592:
1590:
1589:
1570:
1509:
1507:
1506:
1501:
1496:
1488:
1486:
1484:
1483:
1474:
1466:
1461:
1460:
1390:classical vacuum
1383:
1381:
1380:
1375:
1370:
1368:
1367:
1366:
1357:
1356:
1343:
1338:
1337:
1295:
1277:
1275:
1274:
1269:
1264:
1256:
1254:
1253:
1244:
1239:
1234:
1167:
1077:
1075:
1074:
1069:
1064:
1059:
1058:
1049:
1047:
1046:
1045:
1032:
1027:
1026:
1025:
1015:
999:
997:
996:
991:
986:
981:
980:
971:
966:
961:
960:
959:
949:
830:
828:
824:
821:
818:
808:
806:
805:
800:
798:
797:
756:
754:
753:
748:
746:
743:
741:
740:
716:
715:
700:
698:
697:
692:
690:
688:
679:
678:
677:
657:
655:
653:
645:
644:
635:
630:
629:
625:
614:
613:
612:
587:
585:
584:
579:
577:
575:
566:
565:
564:
544:
542:
540:
532:
531:
522:
517:
512:
511:
508:
506:
500:
491:
482:
473:
471:
470:
465:
463:
462:
446:
444:
431:
429:
428:
423:
418:
416:
415:
410:
405:
399:
398:
389:
387:
385:
377:
376:
367:
362:
357:
356:
351:
350:
347:
345:
339:
333:
257:
255:
251:
248:
245:
239:
237:
209:
206:
204:
200:
197:
194:
175:
173:
136:SI derived units
128:electric current
107:classical vacuum
67:
65:
61:
58:
55:
37:
21:
2259:
2258:
2254:
2253:
2252:
2250:
2249:
2248:
2234:
2233:
2232:
2216:10.1.1.150.1225
2180:
2175:
2173:
2161:
2159:
2151:
2143:
2141:
2137:
2128:
2126:
2113:
2112:
2108:
2101:
2080:
2078:
2074:
2067:
2036:
2035:
2031:
2019:
2011:
2010:
2006:
1990:10.1.1.150.1225
1954:
1949:
1948:See Table 1 in
1947:
1943:
1930:
1929:
1925:
1918:
1905:
1903:
1899:
1891:
1887:
1877:
1871:
1869:
1867:
1850:
1849:
1845:
1836:
1835:
1831:
1822:
1820:
1807:
1806:
1802:
1746:
1745:
1741:
1677:
1676:
1672:
1664:
1660:
1659:
1655:
1646:
1644:
1631:
1630:
1626:
1622:
1617:
1616:
1611:
1600:
1596:
1587:
1585:
1573:
1571:
1564:
1559:
1522:
1475:
1467:
1452:
1447:
1446:
1431:Planck constant
1413:
1402:
1358:
1348:
1329:
1324:
1323:
1321:
1287:
1245:
1225:
1224:
1190:
1182:
1154:
1148:
1141:
1134:
1123:
1116:
1098:
1084:
1050:
1036:
1016:
1009:
1008:
1006:
972:
950:
943:
942:
932:
914:
901:
899:
887:
860:
845:
837:
826:
822:
819:
816:
814:
789:
784:
783:
729:
707:
702:
701:
669:
658:
646:
636:
601:
589:
588:
556:
545:
533:
523:
501:
494:
493:
480:
475:
454:
449:
448:
442:
440:
400:
390:
378:
368:
340:
334:
327:
326:
320:
293:
258:
253:
249:
246:
243:
241:
235:
233:
231:
218:
210:
207:
202:
198:
195:
192:
190:
188:
171:
169:
163:
120:
63:
59:
56:
53:
51:
46:
35:
28:
23:
22:
15:
12:
11:
5:
2257:
2255:
2247:
2246:
2236:
2235:
2231:
2230:
2191:(2): 633–730.
2171:
2149:
2135:
2106:
2099:
2072:
2065:
2029:
2004:
1965:(2): 633–730.
1941:
1923:
1916:
1897:
1885:
1865:
1843:
1829:
1800:
1755:(5): 364–368.
1739:
1670:
1653:
1623:
1621:
1618:
1615:
1614:
1609:
1594:
1561:
1560:
1558:
1555:
1554:
1553:
1548:
1543:
1538:
1533:
1528:
1521:
1518:
1499:
1494:
1491:
1482:
1478:
1473:
1470:
1464:
1459:
1455:
1411:
1400:
1373:
1365:
1361:
1355:
1351:
1346:
1341:
1336:
1332:
1319:
1305:speed of light
1267:
1263:
1259:
1252:
1248:
1243:
1237:
1233:
1188:
1181:
1178:
1146:
1139:
1132:
1121:
1117:is written as
1114:
1096:
1082:
1067:
1062:
1057:
1053:
1044:
1039:
1035:
1030:
1024:
1019:
1004:
989:
984:
979:
975:
969:
964:
958:
953:
930:
912:
900:
897:
891:
885:
858:
843:
836:
833:
796:
792:
764:Kibble balance
739:
736:
732:
728:
725:
722:
719:
714:
710:
687:
683:
676:
672:
668:
664:
661:
652:
649:
643:
639:
633:
628:
624:
620:
611:
608:
604:
600:
597:
574:
570:
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256:10 N/A
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2129:2024-05-18
2125:. May 2024
1872:2010-02-04
1823:2024-05-18
1819:. May 2024
1762:1610.02910
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1643:. May 2024
1620:References
1588:2007-08-11
1437:, and the
1394:definition
939:free space
301:free space
145:Since the
109:. It is a
2211:CiteSeerX
2198:0801.0028
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1972:0801.0028
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1201:magnetic
1197:electric
1128:, where
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760:ampere
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184:μ
178:CODATA
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2193:arXiv
2181:(PDF)
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1967:arXiv
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1791:S2CID
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1730:S2CID
1688:arXiv
1665:(PDF)
1557:Notes
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