1395:
O. F. Mossotti, Discussione analitica sull'influenza che l'azione di un mezzo dielettrico ha sulla distribuzione dell'elettricità alla superficie di più corpi electrici disseminati in esso, Memorie di
Mathematica e di Fisica della Società Italiana della Scienza Residente in Modena, vol. 24,
407:
174:
564:
gas up to 1000 atm between 25 °C and 125 °C. Moreover, the
Clausius–Mossotti relation may be applicable to substances if the applied electric field is at a sufficiently high frequencies such that any permanent dipole modes are inactive.
687:
297:
287:
In the case that the material consists of a mixture of two or more species, the right hand side of the above equation would consist of the sum of the molecular polarizability contribution from each species, indexed by
228:
474:
88:
823:
879:
952:
727:
763:
519:
494:
524:
The
Clausius–Mossotti relation assumes only an induced dipole relevant to its polarizability and is thus inapplicable for substances with a significant permanent
602:
577:
is similar to the
Clausius–Mossotti relation, except that it relates the refractive index (rather than the dielectric constant) of a substance to its
1419:
184:
412:
402:{\displaystyle {\frac {\varepsilon _{\mathrm {r} }-1}{\varepsilon _{\mathrm {r} }+2}}=\sum _{i}{\frac {N_{i}\alpha _{i}}{3\varepsilon _{0}}}}
17:
424:
1307:
Lorenz, Ludvig, "Experimentale og theoretiske
Undersogelser over Legemernes Brydningsforhold", Vidensk Slsk. Sckrifter 8,205 (1870)
1424:
771:
476:
which has units of volume . Confusion may arise from the practice of using the shorter name "molecular polarizability" for both
1262:
1235:
1200:
1169:
1033:
834:
901:
169:{\displaystyle {\frac {\varepsilon _{\mathrm {r} }-1}{\varepsilon _{\mathrm {r} }+2}}={\frac {N\alpha }{3\varepsilon _{0}}}}
280:
729:
is the mean polarizability. This equation is approximately valid for homogeneous solids as well as liquids and gases.
1290:
703:
560:
at sufficiently low densities and pressures. For example, the
Clausius–Mossotti relation is accurate for N
39:
260:
1112:
1414:
735:
83:(rather than the dielectric constant) of a substance to its polarizability. It may be expressed as:
1409:
1282:
Principles of Optics: Electromagnetic Theory of
Propagation, Interference and Diffraction of Light
1308:
966:
499:
479:
1151:
1368:
1327:
1281:
416:
8:
231:
72:
47:
1372:
1331:
889:
1128:
1384:
1343:
1296:
1286:
1258:
1231:
1206:
1196:
1165:
1132:
1113:"Dielectric constant of nitrogen up to 1000 atms. Between 25 °C and 150 °C"
1093:
1054:
1029:
994:
Rysselberghe, P. V. (January 1932). "Remarks concerning the
Clausius–Mossotti Law".
682:{\displaystyle {\frac {n^{2}-1}{n^{2}+2}}={\frac {4\pi }{3}}N\alpha _{\mathrm {m} }}
581:. The Lorentz–Lorenz equation is named after the Danish mathematician and scientist
1376:
1335:
1250:
1223:
1157:
1124:
1085:
1003:
245:
80:
31:
1190:
1073:
586:
43:
1074:"The Dependence of the Dielectric Constants of Gases on Temperature and Density"
1357:"Ueber die Anwendung des Satzes vom Virial in der kinetischen Theorie der Gase"
593:
578:
270:
64:
1254:
27:
Equation for a material's dielectric constant given its atomic polarizability
1403:
1388:
1380:
1347:
1339:
1136:
1097:
582:
1300:
1227:
1210:
1161:
973:
is the (absolute) temperature, which together determine the number density
51:
1058:
223:{\displaystyle \varepsilon _{r}={\tfrac {\varepsilon }{\varepsilon _{0}}}}
1007:
1089:
1276:
1356:
1315:
1272:
553:
530:
884:
This applies to gases at ordinary pressures. The refractive index
469:{\displaystyle \alpha '={\tfrac {\alpha }{4\pi \varepsilon _{0}}}}
415:
the
Clausius–Mossotti relation is typically rewritten to show the
1285:(7th ed.). Cambridge New York: Cambridge University Press.
525:
1309:
https://www.biodiversitylibrary.org/item/48423#page/5/mode/1up
234:
of the material, which for non-magnetic materials is equal to
71:, of the material's constituent atoms and/or molecules, or a
592:
The most general form of the
Lorentz–Lorenz equation is (in
818:{\displaystyle n^{2}-1\approx 4\pi N\alpha _{\mathrm {m} }}
521:
within literature intended for the respective unit system.
1195:. Bellingham, Wash., USA: SPIE Optical Engineering Press.
544:
537:
874:{\displaystyle n-1\approx 2\pi N\alpha _{\mathrm {m} }}
947:{\displaystyle n\approx {\sqrt {1+{\frac {3Ap}{RT}}}}}
440:
202:
1192:
Selected papers on linear optical composite materials
1110:
1024:
Atkins, Peter; de Paula, Julio (2010). "Chapter 17".
904:
837:
774:
738:
706:
605:
502:
482:
427:
300:
187:
91:
1111:
Michels, A.; Jaspers, A.; Sanders, P. (1934-05-01).
765:, as it is for many gases, the equation reduces to:
585:, who published it in 1869, and the Dutch physicist
946:
873:
817:
757:
721:
681:
513:
488:
468:
401:
222:
168:
888:of the gas can then be expressed in terms of the
1401:
1051:Introduction to electromagnetic fields and waves
700:is the number of molecules per unit volume, and
1023:
1048:
1028:. Oxford University Press. pp. 622–629.
1053:. San Francisco: W.H. Freeman. p. 116.
993:
1247:Die Mechanische Behandlung der Electricität
732:When the square of the refractive index is
589:, who discovered it independently in 1878.
1071:
568:
273:of the molecules (number per cubic meter);
1188:
1072:Uhlig, H. H.; Keyes, F. G. (1933-02-01).
1271:
1244:
1217:
1149:
1019:
1017:
1354:
63:) of a material in terms of the atomic
14:
1420:Electric and magnetic fields in matter
1402:
1313:
1049:Corson, Dale R; Lorrain, Paul (1962).
722:{\displaystyle \alpha _{\mathrm {m} }}
1014:
1249:. Wiesbaden: Vieweg+Teubner Verlag.
528:. It is applicable to gases such as
24:
865:
809:
713:
673:
330:
310:
121:
101:
25:
1436:
75:thereof. It is equivalent to the
1316:"Ueber die Refractionsconstante"
1220:Theory of Electric Polarization
1182:
1153:Theory of Electric Polarization
1078:The Journal of Chemical Physics
1425:Eponymous equations of physics
1143:
1104:
1065:
1042:
987:
758:{\displaystyle n^{2}\approx 1}
13:
1:
1320:Annalen der Physik und Chemie
1129:10.1016/S0031-8914(34)80250-9
980:
961:is the pressure of the gas,
7:
10:
1441:
1222:(2nd ed.). Elsevier.
1026:Atkins' Physical Chemistry
261:permittivity of free space
36:Clausius–Mossotti relation
1279:(1999). "section 2.3.3".
1255:10.1007/978-3-663-20232-5
1218:Böttcher, C.J.F. (1973).
1150:Böttcher, C.J.F. (1973).
696:is the refractive index,
417:molecular polarizability
1381:10.1002/andp.18812480110
1340:10.1002/andp.18802470905
514:{\displaystyle \alpha '}
281:molecular polarizability
1355:Lorentz, H. A. (1881).
1228:10.1016/c2009-0-15579-4
1162:10.1016/c2009-0-15579-4
575:Lorentz–Lorenz equation
569:Lorentz–Lorenz equation
489:{\displaystyle \alpha }
292:in the following form:
77:Lorentz–Lorenz equation
18:Lorentz–Lorenz equation
967:universal gas constant
948:
875:
819:
759:
723:
683:
515:
490:
470:
403:
224:
170:
1396:p. 49-74 (1850).
1367:(1). Wiley: 127–136.
1245:Clausius, R. (1879).
1189:Lakhtakia, A (1996).
949:
876:
820:
760:
724:
684:
516:
491:
471:
404:
225:
171:
1326:(9). Wiley: 70–103.
902:
835:
772:
736:
704:
603:
500:
480:
425:
298:
185:
89:
79:, which relates the
1373:1881AnP...248..127L
1332:1880AnP...247...70L
1314:Lorenz, L. (1880).
1008:10.1021/j150334a007
413:CGS system of units
232:dielectric constant
73:homogeneous mixture
48:dielectric constant
1361:Annalen der Physik
944:
890:molar refractivity
871:
815:
755:
719:
679:
511:
486:
466:
464:
399:
357:
220:
218:
166:
1264:978-3-663-19891-8
1237:978-0-444-41019-1
1202:978-0-8194-2152-4
1171:978-0-444-41019-1
1090:10.1063/1.3247827
1035:978-0-19-954337-3
942:
940:
662:
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463:
397:
348:
343:
217:
164:
134:
16:(Redirected from
1432:
1415:Electromagnetism
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1021:
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1002:(4): 1152–1155.
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81:refractive index
70:
62:
46:, expresses the
32:electromagnetism
21:
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1410:Electrodynamics
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44:Rudolf Clausius
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1215:
1201:
1184:
1181:
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1177:
1170:
1142:
1123:(7): 627–633.
1103:
1084:(2): 155–159.
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579:polarizability
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271:number density
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65:polarizability
59:
40:O. F. Mossotti
26:
9:
6:
4:
3:
2:
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1378:
1374:
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1366:
1363:(in German).
1362:
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1349:
1345:
1341:
1337:
1333:
1329:
1325:
1322:(in German).
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1292:0-521-64222-1
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1020:
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1005:
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997:
996:J. Phys. Chem
990:
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978:
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584:
583:Ludvig Lorenz
580:
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283:in SI-units .
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33:
19:
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1319:
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1219:
1191:
1183:Bibliography
1156:. Elsevier.
1152:
1145:
1120:
1116:
1106:
1081:
1077:
1067:
1050:
1044:
1025:
999:
995:
989:
956:
883:
827:
731:
691:
594:Gaussian-CGS
591:
574:
572:
523:
418:
410:
294:
286:
252:
236:
177:
85:
76:
56:
52:permittivity
38:, named for
35:
29:
1404:Categories
1277:Wolf, Emil
981:References
828:or simply
50:(relative
1389:0003-3804
1348:0003-3804
1273:Born, Max
1137:0031-8914
1098:0021-9606
909:≈
861:α
854:π
848:≈
842:−
805:α
798:π
792:≈
786:−
750:≈
709:α
669:α
656:π
620:−
505:α
484:α
454:ε
450:π
443:α
430:α
388:ε
373:α
350:∑
326:ε
317:−
306:ε
209:ε
205:ε
190:ε
155:ε
146:α
117:ε
108:−
97:ε
1301:40200160
1211:34046175
508:′
433:′
240:, where
1369:Bibcode
1328:Bibcode
1117:Physica
965:is the
596:units)
411:In the
279:is the
269:is the
259:is the
244:is the
230:is the
1387:
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1261:
1234:
1209:
1199:
1168:
1135:
1096:
1059:398313
1057:
1032:
969:, and
957:where
692:where
526:dipole
419:volume
277:α
253:ε
178:where
34:, the
1385:ISSN
1344:ISSN
1297:OCLC
1287:ISBN
1259:ISBN
1232:ISBN
1207:OCLC
1197:ISBN
1166:ISBN
1133:ISSN
1094:ISSN
1055:OCLC
1030:ISBN
895:as:
573:The
551:and
496:and
42:and
1377:doi
1365:248
1336:doi
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1251:doi
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1158:doi
1125:doi
1086:doi
1004:doi
30:In
1406::
1383:.
1375:.
1359:.
1342:.
1334:.
1318:.
1295:.
1275:;
1257:.
1230:.
1205:.
1164:.
1131:.
1119:.
1115:.
1092:.
1080:.
1076:.
1016:^
1000:36
998:.
977:.
545:CH
543:,
538:CO
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1379::
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1338::
1330::
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1267:.
1253::
1240:.
1226::
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1174:.
1160::
1139:.
1127::
1121:1
1100:.
1088::
1082:1
1061:.
1038:.
1010:.
1006::
975:N
971:T
963:R
959:p
937:T
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929:p
926:A
923:3
917:+
914:1
906:n
893:A
886:n
866:m
857:N
851:2
845:1
839:n
810:m
801:N
795:4
789:1
781:2
777:n
753:1
745:2
741:n
714:m
698:N
694:n
674:m
665:N
660:3
653:4
647:=
641:2
638:+
633:2
629:n
623:1
615:2
611:n
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547:4
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437:=
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354:i
346:=
340:2
337:+
331:r
320:1
311:r
290:i
267:N
263:;
256:0
248:;
242:n
237:n
213:0
199:=
194:r
159:0
151:3
143:N
137:=
131:2
128:+
122:r
111:1
102:r
69:α
60:r
57:ε
20:)
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