2001:
746:
1076:
is a measurement-system constant. Its presence in the equations now used to define electromagnetic quantities is the result of the so-called "rationalization" process described below. But the method of allocating a value to it is a consequence of the result that
Maxwell's equations predict that, in
582:
1622:
One now adds the requirement that one wants force to be measured in newtons, distance in metres, and charge to be measured in the engineers' practical unit, the coulomb, which is defined as the charge accumulated when a current of 1 ampere flows for one second. This shows that the parameter
1810:
780:
as an exact number of coulombs as from 20 May 2019, with the effect that the vacuum electric permittivity no longer has an exactly determined value in SI units. The value of the electron charge became a numerically defined quantity, not measured, making
2068:
1004:
Another historical synonym was "dielectric constant of vacuum", as "dielectric constant" was sometimes used in the past for the absolute permittivity. However, in modern usage "dielectric constant" typically refers exclusively to a
930:
317:
1669:. In principle, one has a choice of deciding whether to make the coulomb or the ampere the fundamental unit of electricity and magnetism. The decision was taken internationally to use the ampere. This means that the value of
1388:
741:{\displaystyle \varepsilon _{0}\approx {\frac {1}{\left(4\pi \times 10^{-7}\,{\textrm {N/A}}^{2}\right)\left(299792458\,{\textrm {m/s}}\right)^{2}}}\approx 8.8541878176\times 10^{-12}\,{\textrm {F}}{\cdot }{\textrm {m}}^{-1}.}
1503:
1585:
1791:
504:
1996:{\displaystyle \mathbf {D} (\mathbf {r} ,\ t)=\int _{-\infty }^{t}dt'\int d^{3}\mathbf {r} '\ \varepsilon \left(\mathbf {r} ,\ t;\mathbf {r} ',\ t'\right)\mathbf {E} \left(\mathbf {r} ',\ t'\right).}
1280:
1165:
1508:
The system of equations thus generated is known as the rationalized metre–kilogram–second (RMKS) equation system, or "metre–kilogram–second–ampere (MKSA)" equation system. The new quantity
2168:
385:
1202:
In one of the systems of equations and units agreed in the late 19th century, called the "centimetre–gram–second electrostatic system of units" (the cgs esu system), the constant
997:
has been known by many different names. The terms "vacuum permittivity" or its variants, such as "permittivity in/of vacuum", "permittivity of empty space", or "permittivity of
1304:
The idea subsequently developed that it would be better, in situations of spherical geometry, to include a factor 4π in equations like
Coulomb's law, and write it in the form:
2012:
839:
231:
2158:
1430:
217:
to mechanical quantities such as length and force. For example, the force between two separated electric charges with spherical symmetry (in the
1529:
2425:
2205:
1420:
The next step was to treat the quantity representing "amount of electricity" as a fundamental quantity in its own right, denoted by the symbol
1310:
1293:. Thus, the unit of Gaussian charge can also be written 1 dyne⋅cm. "Gaussian electric charge" is not the same mathematical quantity as modern (
2566:
1745:
2543:
2504:
1289:, is such that two units, at a distance of 1 centimetre apart, repel each other with a force equal to the cgs unit of force, the
450:
2773:
2722:
2688:
2514:
2487:
2460:
2359:
1226:
1110:
2560:
2228:
2801:
1417:
generates a unit of electricity of different size, but it still has the same dimensions as the cgs esu system.
343:
1030:
is considered obsolete by most modern authors, although occasional examples of continuing usage can be found.
2148:
1298:
522:
28:
2089:
1020:
2063:{\displaystyle \mathbf {D} =\varepsilon \mathbf {E} =\varepsilon _{\text{r}}\varepsilon _{0}\mathbf {E} }
1719:
1199:: to avoid confusion, each different "interpretation" has to be allocated a distinctive name and symbol.
1093:
2639:
2796:
2346:
415:
2285:
1001:" are widespread. Standards organizations also use "electric constant" as a term for this quantity.
2635:
2547:
1641:
1591:
971:
827:
767:
2594:
1645:
1174:
is a quantity that represents the amount of electricity present at each of the two points, and
403:
1210:
2761:
2163:
1512:
is given the name "RMKS electric charge", or (nowadays) just "electric charge". The quantity
1006:
2317:
1733:
1630:
should be allocated the unit C⋅N⋅m (or an equivalent unit – in practice, farad per metre).
925:{\displaystyle \varepsilon _{0}={\frac {1}{\mu _{0}c^{2}}}={\frac {e^{2}}{2\alpha hc}}\ ,}
312:{\displaystyle F_{\text{C}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}}
8:
2178:
1699:
1640:, one makes use of the fact that if one uses the rationalized forms of Coulomb's law and
1294:
823:
20:
2321:
2617:
2307:
425:
itself is used as a unit to quantify the permittivity of various dielectric materials.
2006:
In the event that nonlocality and delay of response are not important, the result is:
1804:, but a delayed response is permitted and a spatially non-local response, so one has:
19:
This article is about the electric constant. For the analogous magnetic constant, see
2769:
2718:
2684:
2556:
2510:
2483:
2456:
2355:
1100:
between two, equal, point-like "amounts" of electricity that are situated a distance
940:
777:
533:
173:
124:
2738:
2621:
2676:
2609:
2405:
2325:
2263:
NIST reference on constants, units, and uncertainty: Fundamental physical constants
2143:
2093:
1077:
free space, electromagnetic waves move with the speed of light. Understanding why
960:
518:
222:
161:
2417:
1019:
and even this usage is considered "obsolete" by some standards bodies in favor of
2197:
948:
214:
213:
is "permitted" to form in response to electric charges and relates the units for
2374:
2254:
1181:
depends on the units. If one is starting with no constraints, then the value of
218:
2680:
2173:
2138:
1726:
956:
514:
411:
407:
210:
2329:
340:
is the distance between their centres, and the value of the constant fraction
2790:
2354:(9th ed.), International Bureau of Weights and Measures, December 2022,
1498:{\displaystyle \ F={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q^{2}}{r^{2}}}.}
963:, each with exactly defined values. The relative uncertainty in the value of
2613:
2542:
1608:
and the value of the vacuum permittivity must be determined experimentally.
1023:. Hence, the term "dielectric constant of vacuum" for the electric constant
532:
is the parameter that international standards organizations refer to as the
2078:
826:
which in turn is determined by the experimentally determined dimensionless
544:
536:(also called vacuum permeability or the permeability of free space). Since
157:
130:
1580:{\displaystyle \ q_{\text{s}}={\frac {q}{\sqrt {4\pi \varepsilon _{0}}}}.}
172:, or the distributed capacitance of the vacuum. It is an ideal (baseline)
2703:
For an introduction to the subject of choices for independent units, see
2477:
2448:
1383:{\displaystyle F=k'_{\text{e}}{\frac {{q'_{\text{s}}}^{2}}{4\pi r^{2}}}.}
1286:
2230:
2595:"Glossary of terms used in photochemistry (IUPAC recommendations 2006)"
1786:{\displaystyle \mathbf {D} =\varepsilon _{0}\mathbf {E} +\mathbf {P} .}
998:
134:
2706:
2293:
CODATA recommended values of the fundamental physical constants: 2006"
1084:
has the value it does requires a brief understanding of the history.
156:(pronounced "epsilon nought" or "epsilon zero"), is the value of the
2169:
Sinusoidal plane-wave solutions of the electromagnetic wave equation
1104:
apart in free space, should be given by a formula that has the form
2153:
1407:′ are not the same as those in the older convention. Putting
98:
2312:
1052:
94:
1690:, as stated above. For a brief explanation of how the value of
1648:, then the relationship stated above is found to exist between
773:
418:, and relate them to their sources. In electrical engineering,
177:
106:
2288:
Table 1: Some exact quantities relevant to the 2006 adjustment
1519:
used in the old cgs esu system is related to the new quantity
2673:
IEEE Standard
Definitions of Terms for Radio Wave Propagation
2502:
2455:(Third ed.). New York: Wiley-Interscience. p. 788.
1048:
548:
102:
71:
67:
2766:
Fundamentals of the physics of solids: Electronic properties
1739:
of the medium. In general, this relationship has the form:
2668:
1290:
499:{\displaystyle \varepsilon _{0}={\frac {1}{\mu _{0}c^{2}}}}
2475:
2283:
2628:
1188:
may be chosen arbitrarily. For each different choice of
1058:
2482:(Third ed.). New York: Wiley. Inside front cover.
2422:
The NIST Reference on
Constants, Units, and Uncertainty
2202:
The NIST Reference on
Constants, Units, and Uncertainty
1033:
As for notation, the constant can be denoted by either
795:
is not exact. As before, it is defined by the equation
2159:
Mathematical descriptions of the electromagnetic field
1393:
This idea is called "rationalization". The quantities
1275:{\displaystyle F={\frac {{q_{\text{s}}}^{2}}{r^{2}}}.}
2015:
1813:
1748:
1532:
1433:
1313:
1229:
1160:{\displaystyle F=k_{\text{e}}{\frac {Q^{2}}{r^{2}}},}
1113:
842:
758:, and its value, are explained in more detail below.
585:
453:
346:
234:
2667:
970:
is therefore the same as that for the dimensionless
2233:. Geneva: International Electrotechnical Commission
1301:) electric charge and is not measured in coulombs.
2704:
2062:
1995:
1785:
1611:
1579:
1497:
1382:
1274:
1159:
924:
740:
498:
379:
311:
2341:
2339:
2284:PJ Mohr; BN Taylor; DB Newell (April–June 2008).
2198:"2022 CODATA Value: vacuum electric permittivity"
1424:, and to write Coulomb's law in its modern form:
1209:was taken equal to 1, and a quantity now called "
2788:
2713:(Third ed.). New York: Wiley. pp. 775
751:The historical origins of the electric constant
543:has an approximate value 4π × 10
2731:
2509:. Reading, Mass.: Addison-Wesley. p. 40.
2410:
2336:
16:Absolute dielectric permittivity of free space
2503:FW Sears, Zemansky MW & Young HD (1985).
2252:The approximate numerical value is found at:
2190:
1718:appears in the relationship that defines the
1706:
1633:In order to establish the numerical value of
2544:International Bureau of Weights and Measures
2418:"2022 CODATA Value: fine-structure constant"
2275:This formula determining the exact value of
2759:
2446:
1087:
2592:
2479:Device electronics for integrated circuits
2476:RS Muller, Kamins TI & Chan M (2003).
2311:
1195:there is a different "interpretation" of
815:, and is thus determined by the value of
705:
661:
632:
380:{\displaystyle 1/(4\pi \varepsilon _{0})}
2588:
2586:
2496:
2697:
2404:is provided in the 2006 CODATA Report:
2789:
2753:
2549:The International System of Units (SI)
1220:was defined by the resulting equation
2583:
2523:
2469:
1711:By convention, the electric constant
761:
2652:
2094:vacuum of classical electromagnetism
1594:, the elementary charge is fixed at
219:vacuum of classical electromagnetism
164:. It may also be referred to as the
1059:Historical origin of the parameter
788:a measured quantity. Consequently,
406:, which describe the properties of
209:It is a measure of how dense of an
13:
2707:"Appendix on units and dimensions"
2655:Fundamental Electromagnetic Theory
2440:
2246:
1850:
1069:As indicated above, the parameter
14:
2813:
2348:The International System of Units
1800:is assumed to be proportional to
1285:The unit of Gaussian charge, the
1096:and others showed that the force
2739:"9th edition of the SI Brochure"
2572:from the original on 4 June 2021
2529:B. E. A. Saleh and M. C. Teich,
2453:Physics of semiconductor devices
2386:A summary of the definitions of
2056:
2028:
2017:
1963:
1952:
1924:
1906:
1886:
1823:
1815:
1776:
1768:
1750:
576:can be expressed numerically as
158:absolute dielectric permittivity
2661:
2657:. New York: Dover. p. 139.
2646:
2536:
2282:is found in Table 1, p. 637 of
1676:is determined by the values of
23:. For the ordinal number ε
2380:
2367:
2220:
1836:
1819:
985:
776:was redefined by defining the
374:
355:
1:
2555:(8th ed.), p. 104,
2373:See the last sentence of the
2255:"–: Electric constant, ε
2149:Electromagnetic wave equation
1644:(and other ideas) to develop
1612:Determination of a value for
1047:, using either of the common
513:is the defined value for the
29:Epsilon numbers (mathematics)
2090:relative static permittivity
1021:relative static permittivity
990:Historically, the parameter
824:magnetic vacuum permeability
7:
2705:John David Jackson (1999).
2653:King, Ronold W. P. (1963).
2447:SM Sze & KK Ng (2007).
2132:
1720:electric displacement field
569: m⋅s, it follows that
10:
2818:
2681:10.1109/IEEESTD.1998.87897
2608:(3): 293–465, see p. 348.
2602:Pure and Applied Chemistry
1707:Permittivity of real media
765:
166:permittivity of free space
18:
2711:Classical electrodynamics
2593:Braslavsky, S.E. (2007).
2531:Fundamentals of Photonics
2375:NIST definition of ampere
2330:10.1103/RevModPhys.80.633
1796:For a linear dielectric,
1732:and classical electrical
416:electromagnetic radiation
2768:. Springer. p. 17.
2671:Standards Board (1997).
2640:Freie Universität Berlin
2184:
1211:Gaussian electric charge
1088:Rationalization of units
428:
2614:10.1351/pac200779030293
1592:2019 revision of the SI
972:fine-structure constant
828:fine-structure constant
768:2019 revision of the SI
2406:CODATA report, pp. 6–7
2064:
1997:
1787:
1581:
1499:
1384:
1276:
1161:
926:
742:
500:
381:
313:
2802:Fundamental constants
2227:"electric constant".
2164:Relative permittivity
2065:
1998:
1788:
1582:
1500:
1385:
1297:and subsequently the
1277:
1162:
1007:relative permittivity
927:
743:
501:
382:
314:
2760:Jenö Sólyom (2008).
2013:
1811:
1746:
1734:polarization density
1530:
1431:
1311:
1227:
1111:
840:
583:
451:
344:
232:
2322:2008RvMP...80..633M
2179:Vacuum permeability
2096:, the polarization
1859:
1700:Vacuum permeability
1646:Maxwell's equations
1349:
1332:
1092:The experiments of
404:Maxwell's equations
145:, commonly denoted
143:Vacuum permittivity
21:Vacuum permeability
2762:"Equation 16.1.50"
2060:
1993:
1842:
1783:
1642:Ampère's force law
1577:
1495:
1380:
1337:
1320:
1272:
1157:
922:
762:Revision of the SI
738:
496:
377:
309:
2775:978-3-540-85315-2
2724:978-0-471-30932-1
2690:978-0-7381-0580-2
2636:"Naturkonstanten"
2516:978-0-201-07836-7
2489:978-0-471-59398-0
2462:978-0-471-14323-9
2361:978-92-822-2272-0
2042:
1976:
1937:
1915:
1896:
1832:
1572:
1571:
1543:
1535:
1490:
1466:
1436:
1375:
1344:
1327:
1267:
1247:
1152:
1127:
941:elementary charge
918:
914:
883:
778:elementary charge
723:
710:
681:
666:
638:
534:magnetic constant
494:
387:is approximately
336:are the charges,
307:
271:
242:
190: =
174:physical constant
170:electric constant
140:
139:
2809:
2797:Electromagnetism
2780:
2779:
2757:
2751:
2750:
2748:
2746:
2735:
2729:
2728:
2701:
2695:
2694:
2665:
2659:
2658:
2650:
2644:
2643:
2632:
2626:
2625:
2599:
2590:
2581:
2580:
2579:
2577:
2571:
2554:
2540:
2534:
2527:
2521:
2520:
2500:
2494:
2493:
2473:
2467:
2466:
2444:
2438:
2437:
2435:
2433:
2414:
2408:
2384:
2378:
2371:
2365:
2364:
2353:
2343:
2334:
2333:
2315:
2297:
2274:
2272:
2270:
2250:
2244:
2242:
2240:
2238:
2224:
2218:
2217:
2215:
2213:
2194:
2128:
2115:
2105:
2069:
2067:
2066:
2061:
2059:
2054:
2053:
2044:
2043:
2040:
2031:
2020:
2002:
2000:
1999:
1994:
1989:
1985:
1984:
1974:
1970:
1966:
1955:
1950:
1946:
1945:
1935:
1931:
1927:
1913:
1909:
1894:
1893:
1889:
1883:
1882:
1870:
1858:
1853:
1830:
1826:
1818:
1792:
1790:
1789:
1784:
1779:
1771:
1766:
1765:
1753:
1725:in terms of the
1697:is decided, see
1607:
1605:
1602:
1599:
1586:
1584:
1583:
1578:
1573:
1570:
1569:
1554:
1550:
1545:
1544:
1541:
1533:
1504:
1502:
1501:
1496:
1491:
1489:
1488:
1479:
1478:
1469:
1467:
1465:
1464:
1463:
1444:
1434:
1416:
1389:
1387:
1386:
1381:
1376:
1374:
1373:
1372:
1356:
1355:
1350:
1345:
1342:
1334:
1328:
1325:
1281:
1279:
1278:
1273:
1268:
1266:
1265:
1256:
1255:
1250:
1249:
1248:
1245:
1237:
1166:
1164:
1163:
1158:
1153:
1151:
1150:
1141:
1140:
1131:
1129:
1128:
1125:
981:
979:
931:
929:
928:
923:
916:
915:
913:
899:
898:
889:
884:
882:
881:
880:
871:
870:
857:
852:
851:
814:
747:
745:
744:
739:
734:
733:
725:
724:
721:
717:
712:
711:
708:
704:
703:
682:
680:
679:
678:
673:
669:
668:
667:
664:
651:
647:
646:
645:
640:
639:
636:
631:
630:
600:
595:
594:
568:
567:
564:
519:classical vacuum
505:
503:
502:
497:
495:
493:
492:
491:
482:
481:
468:
463:
462:
394:
392:
386:
384:
383:
378:
373:
372:
354:
318:
316:
315:
310:
308:
306:
305:
296:
295:
294:
285:
284:
274:
272:
270:
269:
268:
249:
244:
243:
240:
204:
202:
198:
195:
162:classical vacuum
155:
121:
120:
117:
91:
89:
85:
82:
64:
62:
58:
55:
34:
33:
2817:
2816:
2812:
2811:
2810:
2808:
2807:
2806:
2787:
2786:
2783:
2776:
2758:
2754:
2744:
2742:
2737:
2736:
2732:
2725:
2702:
2698:
2691:
2666:
2662:
2651:
2647:
2634:
2633:
2629:
2597:
2591:
2584:
2575:
2573:
2569:
2563:
2552:
2541:
2537:
2528:
2524:
2517:
2506:College physics
2501:
2497:
2490:
2474:
2470:
2463:
2445:
2441:
2431:
2429:
2416:
2415:
2411:
2403:
2396:
2385:
2381:
2372:
2368:
2362:
2351:
2345:
2344:
2337:
2295:
2281:
2268:
2266:
2258:
2253:
2251:
2247:
2236:
2234:
2226:
2225:
2221:
2211:
2209:
2196:
2195:
2191:
2187:
2135:
2127:
2117:
2113:
2107:
2097:
2087:
2055:
2049:
2045:
2039:
2035:
2027:
2016:
2014:
2011:
2010:
1977:
1962:
1961:
1960:
1956:
1951:
1938:
1923:
1922:
1905:
1904:
1900:
1885:
1884:
1878:
1874:
1863:
1854:
1846:
1822:
1814:
1812:
1809:
1808:
1775:
1767:
1761:
1757:
1749:
1747:
1744:
1743:
1717:
1709:
1696:
1689:
1682:
1675:
1668:
1661:
1654:
1639:
1629:
1620:
1618:
1603:
1600:
1597:
1595:
1565:
1561:
1549:
1540:
1536:
1531:
1528:
1527:
1518:
1484:
1480:
1474:
1470:
1468:
1459:
1455:
1448:
1443:
1432:
1429:
1428:
1414:
1408:
1406:
1399:
1368:
1364:
1357:
1351:
1341:
1336:
1335:
1333:
1324:
1312:
1309:
1308:
1261:
1257:
1251:
1244:
1240:
1239:
1238:
1236:
1228:
1225:
1224:
1219:
1208:
1194:
1187:
1180:
1146:
1142:
1136:
1132:
1130:
1124:
1120:
1112:
1109:
1108:
1090:
1083:
1075:
1067:
1065:
1051:for the letter
1046:
1039:
1029:
1018:
996:
988:
977:
975:
969:
949:Planck constant
900:
894:
890:
888:
876:
872:
866:
862:
861:
856:
847:
843:
841:
838:
837:
821:
809:
802:
796:
794:
787:
770:
764:
757:
726:
720:
719:
718:
713:
707:
706:
696:
692:
674:
663:
662:
657:
653:
652:
641:
635:
634:
633:
623:
619:
609:
605:
604:
599:
590:
586:
584:
581:
580:
575:
565:
562:
560:
542:
531:
487:
483:
477:
473:
472:
467:
458:
454:
452:
449:
448:
444:by the formula
439:
431:
424:
401:
390:
388:
368:
364:
350:
345:
342:
341:
335:
328:
301:
297:
290:
286:
280:
276:
275:
273:
264:
260:
253:
248:
239:
235:
233:
230:
229:
215:electric charge
200:
196:
193:
191:
189:
153:
146:
118:
115:
113:
87:
83:
80:
78:
60:
56:
53:
51:
43:
32:
26:
17:
12:
11:
5:
2815:
2805:
2804:
2799:
2782:
2781:
2774:
2752:
2730:
2723:
2696:
2689:
2660:
2645:
2627:
2582:
2561:
2535:
2522:
2515:
2495:
2488:
2468:
2461:
2439:
2409:
2401:
2394:
2379:
2366:
2360:
2335:
2306:(2): 633–729.
2279:
2256:
2245:
2219:
2188:
2186:
2183:
2182:
2181:
2176:
2174:Wave impedance
2171:
2166:
2161:
2156:
2151:
2146:
2141:
2139:Casimir effect
2134:
2131:
2125:
2111:
2085:
2071:
2070:
2058:
2052:
2048:
2038:
2034:
2030:
2026:
2023:
2019:
2004:
2003:
1992:
1988:
1983:
1980:
1973:
1969:
1965:
1959:
1954:
1949:
1944:
1941:
1934:
1930:
1926:
1921:
1918:
1912:
1908:
1903:
1899:
1892:
1888:
1881:
1877:
1873:
1869:
1866:
1862:
1857:
1852:
1849:
1845:
1841:
1838:
1835:
1829:
1825:
1821:
1817:
1794:
1793:
1782:
1778:
1774:
1770:
1764:
1760:
1756:
1752:
1727:electric field
1715:
1708:
1705:
1694:
1687:
1680:
1673:
1666:
1659:
1652:
1637:
1627:
1619:
1616:
1610:
1588:
1587:
1576:
1568:
1564:
1560:
1557:
1553:
1548:
1539:
1516:
1506:
1505:
1494:
1487:
1483:
1477:
1473:
1462:
1458:
1454:
1451:
1447:
1442:
1439:
1412:
1404:
1397:
1391:
1390:
1379:
1371:
1367:
1363:
1360:
1354:
1348:
1340:
1331:
1323:
1319:
1316:
1283:
1282:
1271:
1264:
1260:
1254:
1243:
1235:
1232:
1217:
1206:
1192:
1185:
1178:
1168:
1167:
1156:
1149:
1145:
1139:
1135:
1123:
1119:
1116:
1089:
1086:
1081:
1073:
1066:
1063:
1057:
1044:
1037:
1027:
1016:
994:
987:
984:
967:
957:speed of light
933:
932:
921:
912:
909:
906:
903:
897:
893:
887:
879:
875:
869:
865:
860:
855:
850:
846:
819:
807:
800:
792:
785:
766:Main article:
763:
760:
755:
749:
748:
737:
732:
729:
716:
702:
699:
695:
691:
688:
685:
677:
672:
660:
656:
650:
644:
629:
626:
622:
618:
615:
612:
608:
603:
598:
593:
589:
573:
540:
529:
515:speed of light
507:
506:
490:
486:
480:
476:
471:
466:
461:
457:
437:
430:
427:
422:
399:
376:
371:
367:
363:
360:
357:
353:
349:
333:
326:
320:
319:
304:
300:
293:
289:
283:
279:
267:
263:
259:
256:
252:
247:
238:
221:) is given by
211:electric field
207:
206:
187:
151:
138:
137:
122:
110:
109:
92:
75:
74:
65:
48:
47:
44:
41:
24:
15:
9:
6:
4:
3:
2:
2814:
2803:
2800:
2798:
2795:
2794:
2792:
2785:
2777:
2771:
2767:
2763:
2756:
2740:
2734:
2726:
2720:
2716:
2712:
2708:
2700:
2692:
2686:
2682:
2678:
2675:. p. 6.
2674:
2670:
2664:
2656:
2649:
2641:
2637:
2631:
2623:
2619:
2615:
2611:
2607:
2603:
2596:
2589:
2587:
2568:
2564:
2562:92-822-2213-6
2558:
2551:
2550:
2545:
2539:
2533:(Wiley, 1991)
2532:
2526:
2518:
2512:
2508:
2507:
2499:
2491:
2485:
2481:
2480:
2472:
2464:
2458:
2454:
2450:
2443:
2427:
2423:
2419:
2413:
2407:
2400:
2393:
2389:
2383:
2376:
2370:
2363:
2357:
2350:
2349:
2342:
2340:
2331:
2327:
2323:
2319:
2314:
2309:
2305:
2301:
2294:
2292:
2289:
2278:
2264:
2260:
2249:
2232:
2231:
2223:
2207:
2203:
2199:
2193:
2189:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2162:
2160:
2157:
2155:
2152:
2150:
2147:
2145:
2144:Coulomb's law
2142:
2140:
2137:
2136:
2130:
2124:
2120:
2110:
2104:
2100:
2095:
2091:
2084:
2080:
2076:
2050:
2046:
2036:
2032:
2024:
2021:
2009:
2008:
2007:
1990:
1986:
1981:
1978:
1971:
1967:
1957:
1947:
1942:
1939:
1932:
1928:
1919:
1916:
1910:
1901:
1897:
1890:
1879:
1875:
1871:
1867:
1864:
1860:
1855:
1847:
1843:
1839:
1833:
1827:
1807:
1806:
1805:
1803:
1799:
1780:
1772:
1762:
1758:
1754:
1742:
1741:
1740:
1738:
1735:
1731:
1728:
1724:
1721:
1714:
1704:
1702:
1701:
1693:
1686:
1679:
1672:
1665:
1658:
1651:
1647:
1643:
1636:
1631:
1626:
1615:
1609:
1593:
1574:
1566:
1562:
1558:
1555:
1551:
1546:
1537:
1526:
1525:
1524:
1522:
1515:
1511:
1492:
1485:
1481:
1475:
1471:
1460:
1456:
1452:
1449:
1445:
1440:
1437:
1427:
1426:
1425:
1423:
1418:
1411:
1403:
1396:
1377:
1369:
1365:
1361:
1358:
1352:
1346:
1338:
1329:
1321:
1317:
1314:
1307:
1306:
1305:
1302:
1300:
1296:
1292:
1288:
1269:
1262:
1258:
1252:
1241:
1233:
1230:
1223:
1222:
1221:
1216:
1212:
1205:
1200:
1198:
1191:
1184:
1177:
1173:
1154:
1147:
1143:
1137:
1133:
1121:
1117:
1114:
1107:
1106:
1105:
1103:
1099:
1095:
1085:
1080:
1072:
1062:
1056:
1054:
1050:
1043:
1036:
1031:
1026:
1022:
1015:
1011:
1008:
1002:
1000:
993:
983:
973:
966:
962:
958:
954:
950:
946:
942:
938:
919:
910:
907:
904:
901:
895:
891:
885:
877:
873:
867:
863:
858:
853:
848:
844:
836:
835:
834:
832:
829:
825:
818:
812:
806:
799:
791:
784:
779:
775:
769:
759:
754:
735:
730:
727:
714:
700:
697:
693:
689:
686:
683:
675:
670:
658:
654:
648:
642:
627:
624:
620:
616:
613:
610:
606:
601:
596:
591:
587:
579:
578:
577:
572:
558:
554:
550:
546:
539:
535:
528:
524:
520:
516:
512:
488:
484:
478:
474:
469:
464:
459:
455:
447:
446:
445:
443:
436:
433:The value of
426:
421:
417:
413:
409:
405:
398:
393:10 N⋅m⋅C
369:
365:
361:
358:
351:
347:
339:
332:
325:
302:
298:
291:
287:
281:
277:
265:
261:
257:
254:
250:
245:
236:
228:
227:
226:
224:
223:Coulomb's law
220:
216:
212:
186:
183:
182:
181:
179:
175:
171:
167:
163:
159:
154:
150:
144:
136:
132:
128:
127:
123:
112:
111:
108:
104:
100:
96:
93:
77:
76:
73:
69:
66:
50:
49:
45:
40:
36:
35:
30:
22:
2784:
2765:
2755:
2743:. Retrieved
2741:. BIPM. 2019
2733:
2714:
2710:
2699:
2672:
2663:
2654:
2648:
2630:
2605:
2601:
2574:, retrieved
2548:
2538:
2530:
2525:
2505:
2498:
2478:
2471:
2452:
2449:"Appendix E"
2442:
2430:. Retrieved
2421:
2412:
2398:
2391:
2387:
2382:
2369:
2347:
2303:
2300:Rev Mod Phys
2299:
2290:
2287:
2276:
2267:. Retrieved
2262:
2248:
2235:. Retrieved
2229:
2222:
2210:. Retrieved
2201:
2192:
2122:
2118:
2108:
2102:
2098:
2082:
2079:permittivity
2074:
2072:
2005:
1801:
1797:
1795:
1736:
1729:
1722:
1712:
1710:
1698:
1691:
1684:
1677:
1670:
1663:
1656:
1649:
1634:
1632:
1624:
1621:
1613:
1589:
1520:
1513:
1509:
1507:
1421:
1419:
1409:
1401:
1400:′ and
1394:
1392:
1303:
1284:
1214:
1203:
1201:
1196:
1189:
1182:
1175:
1171:
1169:
1101:
1097:
1091:
1078:
1070:
1068:
1060:
1041:
1034:
1032:
1024:
1013:
1009:
1003:
991:
989:
964:
952:
944:
936:
934:
830:
816:
810:
804:
797:
789:
782:
771:
752:
750:
687:8.8541878176
570:
556:
552:
537:
526:
510:
508:
441:
434:
432:
419:
396:
395:. Likewise,
337:
330:
323:
321:
208:
184:
169:
165:
148:
147:
142:
141:
125:
38:
2576:16 December
1415:′ = 1
1287:statcoulomb
986:Terminology
414:fields and
402:appears in
203:10 F⋅m
2791:Categories
2428:. May 2024
2269:22 January
2208:. May 2024
999:free space
955:being the
947:being the
939:being the
180:value is:
2313:0801.0028
2092:. In the
2047:ε
2037:ε
2025:ε
1898:ε
1872:∫
1851:∞
1848:−
1844:∫
1759:ε
1606:10 C
1563:ε
1559:π
1457:ε
1453:π
1362:π
974:, namely
905:α
864:μ
845:ε
728:−
715:⋅
698:−
690:×
684:≈
659:299792458
625:−
617:×
614:π
597:≈
588:ε
475:μ
456:ε
366:ε
362:π
262:ε
258:π
37:Value of
2622:96601716
2567:archived
2546:(2006),
2237:26 March
2154:ISO 31-5
2133:See also
1982:′
1968:′
1943:′
1929:′
1891:′
1868:′
1347:′
1330:′
555:has the
523:SI units
412:magnetic
408:electric
2318:Bibcode
2077:is the
1590:In the
1094:Coulomb
1053:epsilon
1042:ϵ
557:defined
442:defined
2772:
2745:20 May
2721:
2715:et seq
2687:
2620:
2559:
2513:
2486:
2459:
2432:18 May
2358:
2265:. NIST
2212:18 May
2073:where
1975:
1936:
1914:
1895:
1831:
1534:
1435:
1170:where
1049:glyphs
1035:ε
961:vacuum
951:, and
917:
822:, the
774:ampere
559:value
551:, and
525:, and
509:where
322:Here,
185:ε
178:CODATA
176:. Its
168:, the
114:55.263
27:, see
2618:S2CID
2598:(PDF)
2570:(PDF)
2553:(PDF)
2352:(PDF)
2308:arXiv
2296:(PDF)
2185:Notes
2106:, so
1596:1.602
935:with
803:= 1/(
429:Value
192:8.854
79:8.854
52:8.854
46:Unit
2770:ISBN
2747:2019
2719:ISBN
2685:ISBN
2669:IEEE
2578:2021
2557:ISBN
2511:ISBN
2484:ISBN
2457:ISBN
2434:2024
2426:NIST
2397:and
2356:ISBN
2271:2012
2239:2015
2214:2024
2206:NIST
2116:and
2088:the
2081:and
1683:and
1662:and
1523:by:
1291:dyne
772:The
410:and
329:and
199:(14)
197:8188
86:(14)
84:8188
59:(14)
57:8188
2677:doi
2610:doi
2326:doi
2291:in
2114:= 1
1601:634
1598:176
1295:MKS
1040:or
976:1.6
959:in
665:m/s
637:N/A
566:458
563:792
561:299
521:in
517:in
440:is
194:187
160:of
116:494
81:187
54:187
2793::
2764:.
2717:.
2709:.
2683:.
2638:.
2616:.
2606:79
2604:.
2600:.
2585:^
2565:,
2451:.
2424:.
2420:.
2390:,
2338:^
2324:.
2316:.
2304:80
2302:.
2298:.
2261:.
2204:.
2200:.
2129:.
2121:=
2101:=
1703:.
1655:,
1299:SI
1213:"
1055:.
982:.
980:10
943:,
833::
701:12
694:10
621:10
225::
135:μm
131:eV
119:06
99:kg
90:10
63:10
2778:.
2749:.
2727:.
2693:.
2679::
2642:.
2624:.
2612::
2519:.
2492:.
2465:.
2436:.
2402:0
2399:ε
2395:0
2392:μ
2388:c
2377:.
2332:.
2328::
2320::
2310::
2286:"
2280:0
2277:ε
2273:.
2259:"
2257:0
2243:.
2241:.
2216:.
2126:0
2123:ε
2119:ε
2112:r
2109:ε
2103:0
2099:P
2086:r
2083:ε
2075:ε
2057:E
2051:0
2041:r
2033:=
2029:E
2022:=
2018:D
1991:.
1987:)
1979:t
1972:,
1964:r
1958:(
1953:E
1948:)
1940:t
1933:,
1925:r
1920:;
1917:t
1911:,
1907:r
1902:(
1887:r
1880:3
1876:d
1865:t
1861:d
1856:t
1840:=
1837:)
1834:t
1828:,
1824:r
1820:(
1816:D
1802:E
1798:P
1781:.
1777:P
1773:+
1769:E
1763:0
1755:=
1751:D
1737:P
1730:E
1723:D
1716:0
1713:ε
1695:0
1692:μ
1688:0
1685:μ
1681:0
1678:c
1674:0
1671:ε
1667:0
1664:c
1660:0
1657:μ
1653:0
1650:ε
1638:0
1635:ε
1628:0
1625:ε
1617:0
1614:ε
1604:×
1575:.
1567:0
1556:4
1552:q
1547:=
1542:s
1538:q
1521:q
1517:s
1514:q
1510:q
1493:.
1486:2
1482:r
1476:2
1472:q
1461:0
1450:4
1446:1
1441:=
1438:F
1422:q
1413:e
1410:k
1405:e
1402:k
1398:s
1395:q
1378:.
1370:2
1366:r
1359:4
1353:2
1343:s
1339:q
1326:e
1322:k
1318:=
1315:F
1270:.
1263:2
1259:r
1253:2
1246:s
1242:q
1234:=
1231:F
1218:s
1215:q
1207:e
1204:k
1197:Q
1193:e
1190:k
1186:e
1183:k
1179:e
1176:k
1172:Q
1155:,
1148:2
1144:r
1138:2
1134:Q
1126:e
1122:k
1118:=
1115:F
1102:r
1098:F
1082:0
1079:ε
1074:0
1071:ε
1064:0
1061:ε
1045:0
1038:0
1028:0
1025:ε
1017:0
1014:ε
1012:/
1010:ε
995:0
992:ε
978:×
968:0
965:ε
953:c
945:h
937:e
920:,
911:c
908:h
902:2
896:2
892:e
886:=
878:2
874:c
868:0
859:1
854:=
849:0
831:α
820:0
817:μ
813:)
811:c
808:0
805:μ
801:0
798:ε
793:0
790:ε
786:0
783:μ
756:0
753:ε
736:.
731:1
722:m
709:F
676:2
671:)
655:(
649:)
643:2
628:7
611:4
607:(
602:1
592:0
574:0
571:ε
553:c
549:m
547:/
545:H
541:0
538:μ
530:0
527:μ
511:c
489:2
485:c
479:0
470:1
465:=
460:0
438:0
435:ε
423:0
420:ε
400:0
397:ε
391:×
389:9
375:)
370:0
359:4
356:(
352:/
348:1
338:r
334:2
331:q
327:1
324:q
303:2
299:r
292:2
288:q
282:1
278:q
266:0
255:4
251:1
246:=
241:C
237:F
205:.
201:×
188:0
152:0
149:ε
133:⋅
129:⋅
126:e
107:s
105:⋅
103:m
101:⋅
97:⋅
95:C
88:×
72:m
70:⋅
68:F
61:×
42:0
39:ε
31:.
25:0
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.