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Vacuum permeability

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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'
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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.
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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
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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
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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
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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
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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
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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).
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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"),
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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.
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Ampère's force law describes the experimentally-derived fact that, for two thin, straight, stationary, parallel wires, a distance
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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.
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Magnetic Permeability, and Analogues in Electro-static Induction, Conduction of Heat, and Fluid Motion
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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:
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is an experimentally determined constant, its value being proportional to the dimensionless
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This article is about the magnetic constant. For the analogous electric constant, see
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NIST reference on constants, units, and uncertainty: Fundamental physical constants
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presented as a derived result contingent upon the validity of Maxwell's equations.
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is a measurement-system constant called the "magnetic constant". The value of
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Variations thereof, such as "permeability of free space", remain widespread.
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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
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Sinusoidal plane-wave solutions of the electromagnetic wave equation
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newton per metre of length". This is equivalent to a definition of
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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).
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Mohr, Peter J; Taylor, Barry N; Newell, David B (2008).
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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
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The NIST Reference on Constants, Units, and Uncertainty
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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
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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: 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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: 563: 559: 555: 551: 548: 539: 536: 530: 526: 520: 515: 505: 461: 457: 421: 414: 409: 404: 397: 393: 384: 381: 375: 371: 365: 360: 355: 344: 338: 318: 292: 289: 269:susceptibility 229: 225: 216: 186: 182: 161: 126:induced by an 124:magnetic field 118: 77: 76: 48: 47: 44: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 2256: 2245: 2242: 2241: 2239: 2226: 2222: 2217: 2212: 2208: 2204: 2199: 2194: 2190: 2186: 2179: 2170: 2157: 2153: 2148: 2139: 2136: 2124: 2120: 2116: 2110: 2107: 2102: 2096: 2092: 2087: 2086: 2076: 2073: 2068: 2062: 2058: 2054: 2050: 2046: 2042: 2041: 2033: 2030: 2026:. p. 54. 2025: 2018: 2014: 2008: 2005: 2000: 1996: 1991: 1986: 1982: 1978: 1973: 1968: 1964: 1960: 1953: 1945: 1942: 1937: 1933: 1927: 1924: 1919: 1913: 1909: 1901: 1898: 1895:, March 1872. 1894: 1889: 1886: 1881: 1868: 1866:9780816049745 1862: 1858: 1854: 1847: 1844: 1839: 1833: 1830: 1818: 1814: 1810: 1804: 1801: 1796: 1792: 1788: 1784: 1780: 1776: 1772: 1768: 1763: 1758: 1754: 1750: 1743: 1740: 1735: 1731: 1727: 1723: 1719: 1715: 1711: 1707: 1703: 1699: 1694: 1689: 1685: 1681: 1674: 1671: 1663: 1657: 1654: 1642: 1638: 1634: 1628: 1625: 1619: 1608: 1604: 1598: 1595: 1584: 1580: 1576: 1569: 1567: 1563: 1556: 1552: 1549: 1547: 1544: 1542: 1539: 1537: 1534: 1532: 1529: 1527: 1524: 1523: 1519: 1517: 1515: 1510: 1497: 1492: 1489: 1480: 1476: 1471: 1468: 1462: 1457: 1453: 1444: 1440: 1436: 1432: 1428: 1424: 1419: 1417: 1410: 1406: 1399: 1395: 1391: 1387: 1371: 1363: 1359: 1353: 1349: 1344: 1339: 1334: 1330: 1318: 1314: 1310: 1306: 1302: 1297: 1294: 1290: 1285: 1281: 1265: 1257: 1250: 1246: 1235: 1222: 1218: 1214: 1210: 1206: 1202: 1198: 1194: 1187: 1179: 1177: 1175: 1169: 1166: 1162: 1158: 1152: 1145: 1138: 1131: 1127: 1120: 1113: 1108: 1106: 1102: 1095: 1091: 1086: 1081: 1065: 1060: 1055: 1051: 1037: 1033: 1028: 1017: 1003: 987: 982: 977: 973: 967: 962: 951: 940: 936: 929: 925: 921: 916: 911: 907: 896: 892: 890: 884: 878: 876: 872: 868: 864: 857: 853: 849: 842: 834: 832: 813: ×  812: 794: 790: 781: 777: 773: 769: 765: 761: 737: 734: 730: 726: 723: 720: 717: 712: 708: 681: 674: 662: 650: 647: 641: 637: 631: 622: 609: 606: 602: 598: 595: 568: 561: 549: 537: 534: 528: 524: 518: 513: 490: 486: 479: 459: 455: 437: 432: 419: 395: 391: 382: 379: 373: 369: 363: 358: 324: 317: 313: 309: 306: 302: 298: 290: 288: 286: 282: 278: 274: 270: 266: 261: 228: 224: 223:), equal to: 222: 215: 185: 181: 179: 167: 160: 156: 152: 148: 143: 141: 137: 133: 132:SI base units 129: 125: 121: 117: 112: 108: 104: 100: 96: 92: 88: 84: 75: 71: 50: 49: 43: 39: 38: 33: 19: 2188: 2184: 2168: 2160:. Retrieved 2155: 2146: 2138: 2127:. Retrieved 2118: 2109: 2084: 2075: 2057:10.1142/4088 2039: 2032: 2023: 2007: 1962: 1958: 1944: 1935: 1926: 1907: 1900: 1888: 1870:. Retrieved 1856: 1846: 1832: 1821:. Retrieved 1812: 1803: 1752: 1748: 1742: 1683: 1679: 1673: 1656: 1645:. Retrieved 1636: 1627: 1606: 1602: 1597: 1586:. Retrieved 1578: 1514:new SI units 1511: 1442: 1434: 1426: 1420: 1415: 1408: 1404: 1397: 1393: 1316: 1308: 1298: 1292: 1288: 1279: 1220: 1216: 1209:permeability 1185: 1183: 1170: 1156: 1150: 1143: 1136: 1129: 1125: 1118: 1111: 1109: 1093: 1087: 1079: 1078:The form of 1001: 934: 927: 923: 919: 917: 909: 902: 894: 882: 879: 874: 870: 866: 855: 851: 847: 840: 838: 810: 477: 433: 325:is given by 322: 315: 307: 296: 294: 284: 281:permittivity 276: 265:permeability 262: 259: 226: 213: 211: 183: 158: 154: 150: 144: 115: 114: 98: 94: 90: 86: 82: 80: 41: 1307:in vacuum, 1303:(ISQ), the 1203:fields and 1191:appears in 1088:In the old 835:Terminology 474:of exactly 321:per length 256:10 N/A 238:10 H/m 205:10 N⋅A 85:(variously 2162:2012-01-22 2129:2024-05-18 2125:. May 2024 1872:2010-02-04 1823:2024-05-18 1819:. May 2024 1762:1610.02910 1693:1812.04130 1647:2024-05-18 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 1985:CiteSeerX 1972:0801.0028 1795:119283799 1787:0002-9505 1718:0036-8075 1472:α 1454:μ 1360:ε 1350:μ 1258:− 1247:μ 968:∝ 791:μ 744: H/m 735:− 727:× 724:π 709:μ 651:π 638:μ 607:− 599:× 538:π 525:μ 492:, since 456:μ 383:π 370:μ 299:apart in 221:SI ampere 101:) is the 40:Value of 2238:Category 2015:(1987). 1726:29650669 1520:See also 1201:magnetic 1197:electric 1128:, where 1105:abampere 778:and the 483:10  2203:Bibcode 2045:Bibcode 2013:SUNAMCO 1977:Bibcode 1767:Bibcode 1734:4875011 1698:Bibcode 1680:Science 1512:In the 1299:In the 1151:defined 846:as the 305:current 208:‍ 2213:  2158:. 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Index

Permeability of free space
vacuum permittivity
N
A
magnetic permeability
classical vacuum
physical constant
magnetic field
electric current
SI base units
SI derived units
N
revision of the SI in 2019
fine-structure constant
CODATA
SI ampere
permeability
susceptibility
William Thomson, 1st Baron Kelvin
permittivity
free space
current
Ampère's force law
ampere
H
m
ampere
Kibble balance
2019 revision of the SI
ampere

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