2611:, twelve general equations of the electromagnetic field are listed and these include the eight that are listed in the 1865 paper. His theoretical investigations of the electromagnetic field was guided by the notions of work, energy, potential, the principle of conservation of energy, and Lagrangian dynamics. All the principal equations concerning Maxwell's electromagnetic theory are recapitulated in Chapter IX of Part IV. At the end of this chapter, all the equations are listed and set in quaternion form. The first two equations
1817:
42:
1622:
5780:
1825:
936:. In these papers, he used mechanical models, such as rotating vortex tubes, to model the electromagnetic field. He also modeled the vacuum as a kind of insulating elastic medium to account for the stress of the magnetic lines of force given by Faraday. These works had already laid the basis of the formulation of the Maxwell's equations. Moreover, the 1862 paper already derived the
849:
1485:) that Maxwell had used as the central concepts in his equations; this effort was somewhat controversial, though it was understood by 1884 that the potentials must propagate at the speed of light like the fields, unlike the concept of instantaneous action-at-a-distance like the then conception of gravitational potential.
972:
1625:
Figure of
Maxwell's molecular vortex model. For a uniform magnetic field, the field lines point outward from the display screen, as can be observed from the black dots in the middle of the hexagons. The vortex of each hexagonal molecule rotates counter-clockwise. The small green circles are clockwise
1188:, Maxwell travelled from Scotland to London and looked up Weber and Kohlrausch's results. He converted them into a format which was compatible with his own writings, and in doing so he established the connection to the speed of light and concluded that light is a form of electromagnetic radiation.
4195:
in the absence of motion. Presciently, Maxwell also mentions that although some of the equations could be combined to eliminate some quantities, the objective of his list was to express every relation of which there was any knowledge of, rather than to obtain compactness of mathematical formulae.
1459:
The precise formulation of the time-space laws was the work of
Maxwell. Imagine his feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarized waves, and at the speed of light! To few men in the world has such an experience
1081:
The left-hand side is the speed of light and the right-hand side is a quantity related to the constants that appear in the equations governing electricity and magnetism. Although the right-hand side has units of velocity, it can be inferred from measurements of electric and magnetic forces, which
1552:
Equation (54) expresses what Oliver
Heaviside referred to as 'Faraday's law', which addresses the time-variant aspect of electromagnetic induction, but not the one induced by motion; Faraday's original flux law accounted for both. Maxwell deals with the motion-related aspect of electromagnetic
1541:
in 1857 without using displacement current, but he did use
Poisson's equation and the equation of continuity, which are the mathematical ingredients of the displacement current. Nevertheless, believing his equations to be applicable only inside an electric wire, he cannot be credited with the
1451:
predicted that, "From a long view of the history of mankind, seen from, say, ten thousand years from now, there can be little doubt that the most significant event of the 19th century will be judged as
Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into
2121:
902:
wrote down the equation to calculate the induced force by change of magnetic flux. However, these experimental results and rules were not well organized and sometimes confusing to scientists. A comprehensive summary of the electrodynamic principles was needed.
1853:", entitled "General equations of the electromagnetic field", and this confusion is compounded by the writing of six of those eight equations as three separate equations (one for each of the Cartesian axes), resulting in twenty equations and twenty unknowns.
1536:
in his 1865 paper A Dynamical Theory of the
Electromagnetic Field, showing that light is an electromagnetic wave. This lent the equations their full significance with respect to understanding the nature of the phenomena he elucidated. (Kirchhoff derived the
1934:
975:
Maxwell's differential gear model for induction. Flywheels P and Q represent the primary and secondary circuits. An increase of the moment of inertia of the flywheel in the middle illustrates the effect of placing an iron core between the two
1849:" in which he showed that light was an electromagnetic phenomenon. Confusion over the term "Maxwell's equations" sometimes arises because it has been used for a set of eight equations that appeared in Part III of Maxwell's 1865 paper "
2996:
1215:, grouped the twenty equations together into a set of only four, via vector notation. This group of four equations was known variously as the HertzâHeaviside equations and the MaxwellâHertz equations, but are now universally known as
3130:
2931:
3067:
1219:. Heaviside's equations, which are taught in textbooks and universities as Maxwell's equations are not exactly the same as the ones due to Maxwell, and, in fact, the latter are more easily made to conform to quantum physics.
4261:
of the velocity of the observer. He applied the FitzGeraldâLorentz transformation to kinematics, and not just
Maxwell's equations. Maxwell's equations played a key role in Einstein's groundbreaking 1905 scientific paper on
2313:
1222:
This very subtle and paradoxical sounding situation can perhaps be most easily understood in terms of the similar situation that exists with respect to Newton's second law of motion: In textbooks and in classrooms the law
2036:
1093:
determined that there was a quantity related to electricity and magnetism, "the ratio of the absolute electromagnetic unit of charge to the absolute electrostatic unit of charge" (in modern language, the value
2167:
1076:
3596:
3548:
2629:
Here the twelve
Maxwell's equations have been given, respecting the original notations used by Maxwell. The only difference is that the vectors have been denoted using bold typeface instead of the original
4139:
2213:
4227:", and that the speed of light has to be respective to the reference frame of this aether. Measurements designed to measure the speed of the Earth through the aether conflicted with this notion, though.
3495:
3446:
3319:
2365:
3225:
3180:
1979:
3276:
2822:
4193:
1460:
been vouchsafed ... it took physicists some decades to grasp the full significance of
Maxwell's discovery, so bold was the leap that his genius forced upon the conceptions of his fellow workers.
1141:
2746:
2051:
4254:
property of the
Lorentz transformation (PoincarĂ© 1905). Sometimes this transformation is called the FitzGeraldâLorentz transformation or even the FitzGeraldâLorentzâEinstein transformation.
2253:
957:
as a summary of his work on electromagnetism. In summary, Maxwell's equations successfully unified theories of light and electromagnetism, which is one of the great unifications in physics.
4584:
3669:
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4084:
4047:
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1742:
that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the
599:
5526:
572:
1869:
5590:
1412:
1328:
1285:
4911:
5263:
4313:
4250:) as one under which Maxwell's equations were invariant. Poincaré (1900) analyzed the coordination of moving clocks by exchanging light signals. He also established the
1357:
584:
5625:
5307:
2937:
930:
where he actually came into regular contact with Faraday, and became life-long friends. From 1861 to 1862, Maxwell published a series of 4 papers under the title of
5557:
1850:
1846:
1840:
1439:
947:
1250:
6046:
2682:
2659:
1614:. The paper presented a simplified model of Faraday's work, and how the two phenomena were related. He reduced all of the current knowledge into a linked set of
945:
from the expression of the velocity of the electromagnetic wave in relation to the vacuum constants. The final form of Maxwell's equations was published in 1865
5816:
3073:
2869:
1377:
4561:
Maxwell, James C. (1862). "On physical lines of force. Part 4. The theory of electrical vortices applied to the action of magnetism on polarized light".
1182:
in 1850. However, Weber and Kohlrausch did not make the connection to the speed of light. Towards the end of 1861 while working on Part III of his paper
5341:
5216:
6135:
5229:
3007:
835:
4205:
1563:, in equation (77), which is the same as equation (D) in Maxwell's original equations as listed below. It is expressed today as the force law equation,
604:
4141:
is obtained which relates magnetic potential with current. Elsewhere in the Part I of the book, the electric potential is related to charge density as
5290:
4996:
2264:
614:
5600:
5514:
4216:
Maxwell's equations were an essential inspiration for the development of special relativity. Possibly the most important aspect was their denial of
1082:
involve no physical velocities. Therefore, establishing this relationship provided convincing evidence that light is an electromagnetic phenomenon.
5735:
5661:
5186:
2590:
1143:), and determined that it should have units of velocity. They then measured this ratio by an experiment which involved charging and discharging a
986:
953:
1199:
The four modern Maxwell's equations can be found individually throughout his 1861 paper, derived theoretically using a molecular vortex model of
4086:, which, Maxwell points out, is true only if the total current includes the variation of electric displacement. Lastly, combining equation
994:
to synthesize Maxwell's over 20 equations into the 4 recognizable ones which modern physicists use. Maxwell's equations also inspired
6014:
439:
1990:
5656:
5063:
5033:
5006:
4875:
1828:
Boltzmann's Bicykel model of electromagnetic induction. It is a more complicated model than Maxwell's, to model further details of induction.
454:
76:
5053:
5668:
5413:
5380:
5725:
5758:
4865:
4540:
Maxwell, James C. (1862). "On physical lines of force. Part 3. The theory of electrical vortices applied to statical electricity".
4267:
2132:
1023:
5531:
4519:
Maxwell, James C. (1861). "On physical lines of force. Part 2. The theory of electrical vortices applied to electric currents".
4498:
Maxwell, James C. (1861). "On physical lines of force. Part 1. The theory of molecular vortices applied to magnetic phenomena".
3554:
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334:
5809:
5428:
5403:
5268:
5258:
5120:
4808:
4318:
66:
4095:
2178:
4342:
As noted above, this terminology is not common: Modern use of the term "Maxwell's equations" refer to the Heaviside reformulation.
3452:
3403:
3282:
2321:
5608:
5319:
5209:
3186:
3141:
1945:
6166:
4397:
5564:
5502:
5336:
5302:
4625:
1611:
249:
5962:
5433:
5331:
5023:
4976:(November 1888). "Sketch of the electrical papers in Section A, at the recent Bath Meeting of the British Association".
3236:
2791:
828:
594:
71:
4826:
4257:
Albert Einstein also dismissed the notion of the aether, and relied on Lorentz's conclusion about the fixed speed of light,
2617:
relates the electric scalar potential and magnetic vector potential to the electric and magnetic fields. The third equation
5079:
4680:
4144:
2491:
is nowadays used for voltage, but it is clear from the context that Maxwell's meaning corresponded more to the modern term
1203:'s "lines of force" and in conjunction with the experimental result of Weber and Kohlrausch. But it wasn't until 1884 that
926:. He tried to use the analogy of incompressible fluid flow to model the magnetic lines of forces. Later, Maxwell moved to
5740:
5521:
5487:
5440:
4211:
2563:
which is used in modern textbooks. (Faraday's law itself does not appear among his equations.) However, Maxwell drops the
2560:
1533:
1434:
1097:
609:
314:
2116:{\displaystyle \mathbf {E} =\mu \mathbf {v} \times \mathbf {H} -{\frac {\partial \mathbf {A} }{\partial t}}-\nabla \phi }
5802:
5509:
5482:
5460:
5418:
5314:
4278:
4223:
Maxwell's original equations are based on the idea that light travels through a sea of molecular vortices known as the "
2712:
1510:
474:
464:
449:
214:
81:
1525:
1422:
514:
204:
6161:
6099:
5783:
5753:
5536:
5497:
5445:
5202:
2430:
861:
767:
642:
539:
4400:
in 1887 failed to show that the aether moved against the Earth. While other experiments, such as measurements of the
2626:
relates the electromagnetic field to material data: the current and charge densities as well as the material medium.
2224:
434:
1856:
The eight original Maxwell's equations can be written in the modern form of Heaviside's vector notation as follows:
5930:
5903:
5613:
5475:
5365:
5285:
3641:
3607:
1538:
1496:
1292:
1184:
1017:
The relationships amongst electricity, magnetism, and the speed of light can be summarized by the modern equation:
932:
267:
5720:
3871:
3836:
5689:
5569:
5465:
5360:
4235:
4055:
4018:
3796:
3718:
2828:
2466:
1482:
885:
821:
782:
309:
299:
239:
234:
174:
3364:
3330:
6156:
6036:
5745:
5618:
5574:
5492:
5470:
5324:
4300:. This strategy of using additional dimensions to unify different forces remains an active area of research in
4220:. Rather, according to them, forces are propagated at the velocity of light through the electromagnetic field.
2579:
when he is deriving the electromagnetic wave equation, as he considers the situation only from the rest frame.
2389:
4289:
971:
927:
922:, a physicist that impacted Maxwell's work as well. In 1856, he published his 1st paper in electromagnetism:
877:
873:
752:
632:
319:
4266:. For example, in the opening paragraph of his paper, he began his theory by noting that a description of an
3758:
3680:
2752:
1009:
in a series of experiments in the 1890s. After that, Maxwell's equations were fully accepted by scientists.
5651:
5353:
5295:
5273:
2524:
911:
757:
727:
159:
149:
144:
968:") based on Maxwell's flywheel model, which he used for lecture demonstrations. Figures are at the end of.
910:
through a series of papers published from the 1850s to the 1870s. In the 1850s, Maxwell was working at the
6120:
5982:
4563:
4542:
4521:
4500:
4243:
919:
579:
349:
124:
19:
6125:
6094:
5957:
5878:
5646:
5641:
5595:
5452:
5251:
2042:
Electromotive force created by convection, induction, and by static electricity. (This is in effect the
1748:
vector. The magnetic inductive current represents lines of force. In particular, it represents lines of
1647:
1615:
677:
364:
354:
304:
294:
41:
1929:{\displaystyle \mathbf {J} _{\mathrm {tot} }=\mathbf {J} +{\frac {\partial \mathbf {D} }{\partial t}}}
6084:
5908:
5868:
5246:
4973:
4642:"Gearing up for Lagrangian dynamics: The flywheel analogy in Maxwell's 1865 paper on electrodynamics"
4217:
1529:
1444:
1430:
1208:
1086:
802:
702:
667:
419:
284:
184:
169:
104:
5098:
209:
6059:
5918:
5913:
5898:
5873:
5850:
5826:
5699:
5049:
4401:
4224:
2608:
2488:
1630:
It is later clarified in his concept of a sea of molecular vortices that appears in his 1861 paper
899:
762:
742:
737:
544:
529:
414:
384:
279:
2553:
term, is effectively the Lorentz force, similarly to equation (77) of his 1861 paper (see above).
1777:, then it necessarily follows from Gauss's law and from the equation of continuity of charge that
1452:
provincial insignificance in comparison with this important scientific event of the same decade."
1382:
1298:
1255:
6115:
5992:
5987:
5940:
5694:
5375:
5225:
5154:
4725:
4601:
4293:
4263:
4251:
2506:
1749:
1646:
was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered
1478:
1421:
Maxwell's contribution to science in producing these equations lies in the correction he made to
1415:
999:
637:
377:
179:
139:
2556:
When Maxwell derives the electromagnetic wave equation in his 1865 paper, he uses equation
1333:
951:, in which the theory is formulated in strictly mathematical form. In 1873, Maxwell published
4430:"Znanstveno-filozofski aspekti BoĆĄkoviÄeva djela i utjecaj na razvoj klasiÄne i moderne fizike"
2991:{\displaystyle \mathbf {E} =\mathbf {G} \times \mathbf {B} -{\dot {\mathbf {A} }}-\nabla \Psi }
6130:
6079:
6024:
6004:
5890:
5765:
5684:
5370:
5348:
5238:
5116:
5059:
5029:
5002:
4954:
4871:
4804:
4792:
4717:
4661:
4441:
4270:
must generate a consistent set of fields regardless of whether the force is calculated in the
4247:
1090:
697:
5152:
Original German language text from "Zur Elektrodynamik bewegter Körper", (30 June 1905)
1532:. This may be the most remarkable contribution of Maxwell's work, enabling him to derive the
6069:
6009:
5935:
5704:
4946:
4896:
4709:
4653:
4593:
2604:
1204:
1179:
1174:
1164:
981:
961:
907:
865:
857:
797:
712:
672:
662:
549:
504:
487:
404:
339:
109:
33:
1824:
1816:
6089:
5999:
5945:
5845:
5136:
4934:
4843:
4323:
4231:
3125:{\displaystyle \mathbf {F} =\mathbf {C} \times \mathbf {B} -e\nabla \Psi -m\nabla \Omega }
2926:{\displaystyle \mathbf {E} =V.\mathbf {G} \mathbf {B} -{\dot {\mathbf {A} }}-\nabla \Psi }
2407:
1739:
1465:
1448:
1226:
1200:
995:
991:
881:
732:
657:
652:
519:
394:
359:
254:
219:
119:
772:
4867:
Oliver Heaviside: The life, work, and times of an electrical genius of the Victorian age
4381:
would be better. But even then the mathematicians would still use the large-letter name
2664:
2641:
1447:. This fact was later confirmed experimentally by Heinrich Hertz in 1887. The physicist
6019:
5974:
5952:
5840:
5730:
5392:
5140:
4768:
4743:
4282:
2492:
1725:
1700:
was seen as a kind of magnetic current of vortices aligned in their axial planes, with
1621:
1546:
1455:
The concept of fields was introduced by, among others, Faraday. Albert Einstein wrote:
1362:
1212:
1006:
937:
869:
692:
687:
509:
399:
324:
274:
224:
197:
154:
129:
99:
92:
2620:
relates the electromagnetic field to electromagnetic force. The rest of the equations
6150:
4861:
4641:
4605:
4239:
3062:{\displaystyle \mathbf {F} =V.\mathbf {C} \mathbf {B} -e\nabla \Psi -m\nabla \Omega }
2043:
1587:
890:
807:
792:
777:
717:
429:
344:
329:
244:
229:
134:
4242:. Both Larmor (1897) and Lorentz (1899, 1904) ignored aether motion and derived the
6054:
1288:
848:
787:
682:
647:
589:
524:
409:
289:
164:
444:
4620:
1672:
was essentially a rotational analogy to the linear electric current relationship,
5194:
4950:
4924:
The re-formulated equations published by Heaviside are now universally known as
4286:
2532:
2448:
707:
559:
389:
51:
2308:{\displaystyle \nabla \cdot \mathbf {J} =-{\frac {\partial \rho }{\partial t}}}
1147:
and measuring the magnetic force from the discharge current, and found a value
6074:
6064:
4657:
4484:
4271:
4012:
In the same chapter, Maxwell points out that the consequence of equation
2685:
2635:
1155:, remarkably close to the speed of light, which had recently been measured at
1144:
424:
4721:
4665:
4582:
Maxwell, James C. (1865). "A dynamical theory of the electromagnetic field".
4445:
1501:
The four equations we use today appeared separately in Maxwell's 1861 paper,
5925:
5794:
4297:
895:
747:
722:
534:
459:
56:
4958:
4912:
The Great Equations: Breakthroughs in Science from Pythagoras to Heisenberg
4597:
5181:
1655:
to be a measure of the density of the vortex sea. Hence the relationship,
860:
had improved through many experiments and theoretical work. In the 1780s,
4281:
has also had a close relationship with Maxwell's equations. For example,
2600:
499:
494:
114:
4476:
2031:{\displaystyle \nabla \times \mathbf {H} =\mathbf {J} _{\mathrm {tot} }}
4301:
2631:
1738:
The electric current equation can be viewed as a convective current of
469:
5162:, p 891. English translations by W. Perrett and G.B. Jeffery for
4729:
4697:
6029:
4998:
The Creation of Scientific Effects: Heinrich Hertz and electric waves
4682:
Ableitung der Grundgleichungen fĂŒr ruhende, homogene, isotrope Körper
554:
61:
1590:, even though Maxwell derived it when Lorentz was still a young boy.
4870:. Baltimore, MD: Johns Hopkins University Press. pp. 108â112.
4713:
4375:. So for the electric current density, a name with small letters,
4366:
2162:{\displaystyle \mathbf {E} ={\frac {1}{\varepsilon }}\mathbf {D} }
1823:
1815:
1620:
1433:
term to AmpĂšre's circuital law and this enabled him to derive the
1252:
is attributed to Newton, but Newton in fact wrote his second law
1071:{\displaystyle c={\frac {1}{\sqrt {\mu _{0}\varepsilon _{0}}}}\ .}
1013:
Relationships among electricity, magnetism, and the speed of light
1005:
The experimental proof of Maxwell's equations was demonstrated by
970:
847:
4794:
The Story of Electrical and Magnetic Measurements: From 500
4408:, seemed to show that the aether is moving relative to the Earth.
4405:
1586:, which sits adjacent to Maxwell's equations and bears the name
5798:
5198:
3591:{\displaystyle \mathbf {C} =\mathbf {K} +{\dot {\mathbf {D} }}}
3543:{\displaystyle \mathbf {C} =\mathbf {K} +{\dot {\mathbf {D} }}}
2634:
typeface. For comparison Maxwell's equations in their original
960:
Maxwell built a simple flywheel model of electromagnetism, and
4459:
Maxwell, James C. (1855â1856). "On Faraday's Lines of Force".
4429:
1755:
The extension of the above considerations confirms that where
4134:{\displaystyle \nabla ^{2}\mathbf {A} =4\pi \mu \mathbf {C} }
2208:{\displaystyle \mathbf {E} ={\frac {1}{\sigma }}\mathbf {J} }
1626:
rotating particles sandwiched between the molecular vortices.
1295:, where Newton's manuscript is open to the relevant page. as
3490:{\displaystyle \mathbf {D} ={\frac {1}{4\pi }}K\mathbf {E} }
3441:{\displaystyle \mathbf {D} ={\frac {1}{4\pi }}K\mathbf {E} }
3314:{\displaystyle 4\pi \mathbf {C} =\nabla \times \mathbf {H} }
2360:{\displaystyle \nabla \cdot \mathbf {J} _{\mathrm {tot} }=0}
1712:
representing vortex density, it follows that the product of
1606:
vectors can be traced back to Maxwell's 1855 paper entitled
856:
By the first half of the 19th century, the understanding of
3220:{\displaystyle \mathbf {B} =\mathbf {H} +4\pi \mathbf {J} }
3175:{\displaystyle \mathbf {B} =\mathbf {H} +4\pi \mathbf {J} }
1974:{\displaystyle \mu \mathbf {H} =\nabla \times \mathbf {A} }
5111:
Flood, Raymond; McCartney, Mark; Whitaker, Andrew (2014).
5022:
la Lanne, J.R.; Carmona, F.; Servant, L. (November 1999).
4937:(24 May 1940). "The Fundamentals of Theoretical Physics".
1379:. This seems a trivial enough fact until you realize that
898:
solved the problem of the direction of the induction, and
4585:
Philosophical Transactions of the Royal Society of London
1706:
being the circumferential velocity of the vortices. With
1085:
The discovery of this relationship started in 1855, when
2419:
being the total current including displacement current).
4856:
4854:
4292:
that Maxwell's equations could be derived by extending
3271:{\displaystyle 4\pi \mathbf {C} =V.\nabla \mathbf {H} }
2817:{\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }
918:
concept. Faraday created this concept by impression of
5113:
James Clerk Maxwell: Perspectives on his Life and Work
4428:
Poljak, Dragan; SokoliÄ, Franjo; JakiÄ, Mirko (2011).
4351:
Here it is noted that a quite different quantity, the
5115:(1st ed.). Oxford, GB: Oxford University Press.
4188:{\displaystyle \nabla ^{2}\Psi =-{\frac {4\pi }{K}}e}
4147:
4098:
4058:
4021:
3874:
3839:
3799:
3761:
3721:
3683:
3644:
3610:
3557:
3509:
3455:
3406:
3367:
3333:
3285:
3239:
3189:
3144:
3076:
3010:
2940:
2872:
2831:
2794:
2755:
2715:
2667:
2644:
2324:
2267:
2227:
2181:
2135:
2054:
1993:
1948:
1872:
1385:
1365:
1336:
1301:
1258:
1229:
1100:
1026:
4475:
3831:
When magnetic force can be derived from a potential
1136:{\displaystyle 1/{\sqrt {\mu _{0}\varepsilon _{0}}}}
6108:
6045:
5973:
5889:
5861:
5833:
5713:
5677:
5634:
5583:
5547:
5391:
5237:
4387:
for the corresponding current two-form (see below).
2559:to cater for electromagnetic induction rather than
4268:electric conductor moving with respect to a magnet
4187:
4133:
4078:
4041:
3894:
3859:
3819:
3784:
3741:
3706:
3663:
3629:
3602:When magnetization arises from magnetic induction
3590:
3542:
3489:
3440:
3386:
3352:
3313:
3270:
3219:
3174:
3124:
3061:
2990:
2925:
2851:
2816:
2778:
2741:{\displaystyle \mathbf {B} =V.\nabla \mathbf {A} }
2740:
2676:
2653:
2359:
2307:
2247:
2207:
2161:
2115:
2030:
1973:
1928:
1406:
1371:
1351:
1322:
1279:
1244:
1135:
1070:
4314:Classical electromagnetism and special relativity
1542:discovery that light is an electromagnetic wave).
18:For current versions of Maxwell's equations, see
4049:. Similarly, taking divergence of equation
2638:form and their vector form have been given. The
2527:(Maxwell called the inverse of conductivity the
5081:A dynamical theory of the electromagnetic field
5025:Optical spectroscopies of electronic absorption
4893:The Topological Foundations of Electromagnetism
2248:{\displaystyle \nabla \cdot \mathbf {D} =\rho }
1851:A dynamical theory of the electromagnetic field
1847:A dynamical theory of the electromagnetic field
1841:A Dynamical Theory of the Electromagnetic Field
1834:A Dynamical Theory of the Electromagnetic Field
1457:
1440:A Dynamical Theory of the Electromagnetic Field
948:A Dynamical Theory of the Electromagnetic Field
5058:. Courier Dover Publications. pp. 49â56.
4434:MetodiÄki ogledi: Äasopis za filozofiju odgoja
1477:Heaviside worked to eliminate the potentials (
5810:
5210:
4230:A more theoretical approach was suggested by
3664:{\displaystyle \mathbf {B} =\mu \mathbf {H} }
3630:{\displaystyle \mathbf {B} =\mu \mathbf {H} }
2686:scalar and vector parts of quaternion product
1443:and to demonstrate the fact that light is an
829:
8:
5001:. University of Chicago Press. p. 194.
4461:Cambridge Philosophical Society Transactions
3895:{\displaystyle \mathbf {H} =-\nabla \Omega }
3860:{\displaystyle \mathbf {H} =-\nabla \Omega }
5055:Introduction to Electromagnetic Engineering
4786:
4784:
4782:
4079:{\displaystyle \nabla \cdot \mathbf {C} =0}
4042:{\displaystyle \nabla \cdot \mathbf {B} =0}
3820:{\displaystyle m=\nabla \cdot \mathbf {J} }
3742:{\displaystyle e=\nabla \cdot \mathbf {D} }
2852:{\displaystyle \nabla \cdot \mathbf {A} =0}
1820:Engineering diagram of Boltzmann's Bicykel.
1640:represented pure vorticity (spin), whereas
5817:
5803:
5795:
5217:
5203:
5195:
5166:, (1922) 4th ed., published in English as
3387:{\displaystyle \mathbf {K} =C\mathbf {E} }
3353:{\displaystyle \mathbf {K} =C\mathbf {E} }
1287:is clearly visible in a glass case in the
836:
822:
40:
24:
5180:Turnbull, Graham, ed. (29 October 2019).
5141:"On the electrodynamics of moving bodies"
4640:Lazaroff-Puck, Cameron (September 2015).
4167:
4152:
4146:
4126:
4109:
4103:
4097:
4065:
4057:
4028:
4020:
3875:
3873:
3840:
3838:
3812:
3798:
3777:
3760:
3734:
3720:
3699:
3682:
3656:
3645:
3643:
3622:
3611:
3609:
3577:
3575:
3574:
3566:
3558:
3556:
3529:
3527:
3526:
3518:
3510:
3508:
3482:
3464:
3456:
3454:
3433:
3415:
3407:
3405:
3379:
3368:
3366:
3345:
3334:
3332:
3306:
3292:
3284:
3263:
3246:
3238:
3212:
3198:
3190:
3188:
3167:
3153:
3145:
3143:
3093:
3085:
3077:
3075:
3030:
3025:
3011:
3009:
2968:
2966:
2965:
2957:
2949:
2941:
2939:
2903:
2901:
2900:
2892:
2887:
2873:
2871:
2838:
2830:
2809:
2795:
2793:
2765:
2754:
2733:
2716:
2714:
2666:
2643:
2338:
2337:
2332:
2323:
2285:
2274:
2266:
2234:
2226:
2200:
2190:
2182:
2180:
2154:
2144:
2136:
2134:
2088:
2082:
2074:
2066:
2055:
2053:
2015:
2014:
2009:
2000:
1992:
1966:
1952:
1947:
1910:
1904:
1896:
1880:
1879:
1874:
1871:
1509:Equation (56) in Maxwell's 1861 paper is
1393:
1392:
1384:
1364:
1338:
1337:
1335:
1309:
1308:
1300:
1266:
1265:
1257:
1228:
1125:
1115:
1109:
1104:
1099:
1053:
1043:
1033:
1025:
4748:Famous Scientists (famousscientists.org)
4698:"Maxwell and the Origins of Cybernetics"
4369:commission has been given the same name
4274:of the magnet or that of the conductor.
2692:
1860:
5187:Engineering and Technology History Wiki
4928:; for example, A. Einstein called them
4420:
4335:
4206:Maxwell's equations in curved spacetime
4052:gives conservation of electric charge,
3785:{\displaystyle m=S.\nabla \mathbf {J} }
3707:{\displaystyle e=S.\nabla \mathbf {D} }
2779:{\displaystyle S.\nabla \mathbf {A} =0}
2597:A Treatise on Electricity and Magnetism
2591:A Treatise on Electricity and Magnetism
2584:A Treatise on Electricity and Magnetism
1359:is the time derivative of the momentum
987:A Treatise on Electricity and Magnetism
954:A Treatise on Electricity and Magnetism
585:Electromagnetism and special relativity
32:
6015:Atomic, molecular, and optical physics
4827:The Dictionary of Scientific Biography
4803:. John Wiley & Sons. p. 115.
964:built an elaborate mechanical model ("
888:through his experiments, and proposed
5101:from Technische Universitat Darmstadt
4646:Archive for History of Exact Sciences
1866:
1863:
605:Maxwell equations in curved spacetime
7:
5669:Noisy intermediate-scale quantum era
4791:Keithley, Joseph F. (January 1999).
4685:(in German). Johann Ambrosius Barth.
1207:, concurrently with similar work by
914:where he was impressed by Faraday's
4824:Gillispie, Charles Coulston (ed.).
4218:instantaneous action at a distance
4158:
4149:
4100:
4059:
4022:
3942:is the intensity of magnetization.
3889:
3886:
3854:
3851:
3806:
3774:
3728:
3696:
3300:
3260:
3119:
3116:
3107:
3104:
3056:
3053:
3044:
3041:
2985:
2982:
2920:
2917:
2832:
2803:
2762:
2730:
2345:
2342:
2339:
2325:
2296:
2288:
2268:
2228:
2107:
2095:
2085:
2022:
2019:
2016:
1994:
1960:
1917:
1907:
1887:
1884:
1881:
1662:causes a magnetic current density
14:
4319:History of electromagnetic theory
2684:notations are used to denote the
2127:The electric elasticity equation
5779:
5778:
4365:by decision of an international
4127:
4110:
4066:
4029:
3876:
3841:
3813:
3778:
3735:
3700:
3657:
3646:
3623:
3612:
3578:
3567:
3559:
3530:
3519:
3511:
3483:
3457:
3434:
3408:
3380:
3369:
3346:
3335:
3307:
3293:
3264:
3247:
3213:
3199:
3191:
3168:
3154:
3146:
3094:
3086:
3078:
3031:
3026:
3012:
2969:
2958:
2950:
2942:
2904:
2893:
2888:
2874:
2839:
2810:
2796:
2766:
2734:
2717:
2333:
2275:
2235:
2201:
2183:
2155:
2137:
2089:
2075:
2067:
2056:
2010:
2001:
1967:
1953:
1911:
1897:
1875:
6136:Timeline of physics discoveries
5028:. World Scientific. p. 8.
4626:The Feynman Lectures on Physics
1940:The equation of magnetic force
1612:Cambridge Philosophical Society
1:
5087:. wikimedia.org. p. 480.
4212:History of special relativity
3952:is the current of conduction.
1534:electromagnetic wave equation
1528:, with Maxwell's addition of
1435:electromagnetic wave equation
610:Relativistic electromagnetism
5168:The Principles of Relativity
4891:Barrett, Terence W. (2008).
4279:general theory of relativity
2453:quantity of free electricity
1694:is electric charge density.
1407:{\displaystyle F={\dot {p}}}
1323:{\displaystyle F={\dot {p}}}
1280:{\displaystyle F={\dot {p}}}
1000:theory of special relativity
6100:Quantum information science
5591:Cosmic microwave background
4951:10.1126/science.91.2369.487
4398:MichelsonâMorley experiment
4008:is magnetic charge density.
3998:is electric charge density.
3988:is electrical conductivity.
3978:is the dielectric constant.
3922:is the velocity of a point.
2509:(which Maxwell also called
2392:, which Maxwell called the
1845:In 1865 Maxwell published "
1676:Electric convection current
1608:On Faraday's Lines of Force
1594:The difference between the
924:On Faraday's Lines of Force
862:Charles-Augustin de Coulomb
6183:
5931:Classical electromagnetism
4775:. New York, NY: Macmillan.
4679:Boltzmann, Ludwig (1891).
4478:On Physical Lines of Force
4474:Maxwell, James C. (1861).
4209:
4203:
3968:is the magnetic potential.
3960:is the electric potential.
2588:
2561:Faraday's law of induction
1864:The law of total currents
1838:
1660:Magnetic induction current
1632:On Physical Lines of Force
1503:On Physical Lines of Force
1497:On Physical Lines of Force
1494:
1490:On Physical Lines of Force
1427:On Physical Lines of Force
1352:{\displaystyle {\dot {p}}}
1293:Trinity College, Cambridge
1185:On Physical Lines of Force
933:On Physical Lines of Force
335:LiĂ©nardâWiechert potential
17:
5774:
4995:Buchwald, Jed Z. (1994).
4658:10.1007/s00407-015-0157-9
2701:
2698:
2695:
2531:, what is now called the
1511:Gauss's law for magnetism
1191:
894:to describe it. In 1834,
886:electromagnetic induction
600:Mathematical descriptions
310:Electromagnetic radiation
300:Electromagnetic induction
240:Magnetic vector potential
235:Magnetic scalar potential
6037:Condensed matter physics
4015:is (in vector notation)
3753:Magnetic volume density
3675:Electric volume density
2576:term from equation
1437:in his later 1865 paper
1418:, without modification.
5726:ChandrasekharâEddington
5652:Golden age of cosmology
5584:On specific discoveries
5532:Lorentz transformations
5099:Die Maxwell-Gleichungen
4841:Hunt, Bruce J. (1991).
2525:electrical conductivity
2259:Equation of continuity
1985:AmpĂšre's circuital law
1634:. Within that context,
1539:telegrapher's equations
912:University of Cambridge
150:Electrostatic induction
145:Electrostatic discharge
6121:Nobel Prize in Physics
5983:Relativistic mechanics
5657:Medieval Islamic world
5400:Computational physics
5342:Variational principles
5269:Electrical engineering
4909:Crease, Robert (2008)
4598:10.1098/rstl.1865.0008
4564:Philosophical Magazine
4543:Philosophical Magazine
4522:Philosophical Magazine
4501:Philosophical Magazine
4244:Lorentz transformation
4189:
4135:
4080:
4043:
3896:
3861:
3821:
3786:
3743:
3708:
3665:
3631:
3592:
3544:
3491:
3442:
3398:Electric displacement
3388:
3354:
3315:
3272:
3221:
3176:
3126:
3063:
2992:
2927:
2853:
2818:
2780:
2742:
2678:
2655:
2361:
2309:
2249:
2209:
2163:
2117:
2032:
1975:
1930:
1829:
1821:
1627:
1616:differential equations
1610:which was read to the
1526:AmpĂšre's circuital law
1475:
1423:AmpĂšre's circuital law
1408:
1373:
1353:
1324:
1281:
1246:
1137:
1072:
977:
906:This work was done by
853:
580:Electromagnetic tensor
6126:Philosophy of physics
5647:Golden age of physics
5642:Copernican Revolution
5182:"Maxwell's Equations"
5164:Das Relativatsprinzip
4744:"James Clerk Maxwell"
4396:Experiments like the
4353:magnetic polarization
4190:
4136:
4081:
4044:
3897:
3862:
3822:
3787:
3744:
3709:
3666:
3632:
3593:
3545:
3492:
3443:
3389:
3355:
3316:
3273:
3222:
3177:
3127:
3064:
2993:
2928:
2854:
2819:
2781:
2743:
2679:
2656:
2487:by Maxwell. The term
2435:electric displacement
2362:
2310:
2250:
2210:
2164:
2118:
2033:
1976:
1931:
1827:
1819:
1648:magnetic permeability
1624:
1409:
1374:
1354:
1325:
1282:
1247:
1138:
1073:
974:
928:King's College London
851:
573:Covariant formulation
365:Synchrotron radiation
305:Electromagnetic pulse
295:Electromagnetic field
6085:Mathematical physics
5750:Relativity priority
5605:Subatomic particles
5565:Loop quantum gravity
5554:Quantum information
5503:Quantum field theory
5303:Gravitational theory
5050:Harrington, Roger F.
4864:(13 November 2002).
4145:
4096:
4056:
4019:
3872:
3837:
3797:
3759:
3719:
3681:
3642:
3608:
3555:
3507:
3453:
3404:
3365:
3331:
3283:
3237:
3187:
3142:
3074:
3008:
2938:
2870:
2864:Electromotive force
2829:
2792:
2753:
2713:
2665:
2642:
2451:density (called the
2322:
2265:
2225:
2179:
2133:
2052:
1991:
1946:
1870:
1530:displacement current
1445:electromagnetic wave
1431:displacement current
1383:
1363:
1334:
1299:
1256:
1245:{\displaystyle F=ma}
1227:
1209:Josiah Willard Gibbs
1098:
1087:Wilhelm Eduard Weber
1024:
615:Stressâenergy tensor
540:Reluctance (complex)
285:Displacement current
6167:Maxwell's equations
6060:Atmospheric physics
5899:Classical mechanics
5827:branches of physics
5714:Scientific disputes
5700:Via Panisperna boys
5601:Gravitational waves
5548:Recent developments
5279:Maxwell's equations
4978:Electrical Engineer
4930:Maxwell's equations
4926:Maxwell's equations
4696:Mayr, Otto (1971).
4402:aberration of light
4296:into five physical
4290:in the 1920s showed
4225:luminiferous aether
3910:Unfamiliar notation
2707:Magnetic induction
2609:James Clerk Maxwell
2529:specific resistance
2489:electromotive force
2485:electromotive force
1217:Maxwell's equations
1194:Maxwell's equations
900:Franz Ernst Neumann
852:James Clerk Maxwell
530:Magnetomotive force
415:Electromotive force
385:Alternating current
320:Jefimenko equations
280:Cyclotron radiation
20:Maxwell's equations
6162:History of physics
6116:History of physics
5759:General relativity
5754:Special relativity
5695:Oxford Calculators
5522:Special relativity
5441:General relativity
5226:History of physics
5155:Annalen der Physik
4619:Feynman, Richard.
4294:general relativity
4264:special relativity
4252:mathematical group
4185:
4131:
4089:and equation
4076:
4039:
3892:
3857:
3817:
3782:
3739:
3704:
3661:
3627:
3588:
3540:
3487:
3438:
3384:
3350:
3311:
3268:
3231:Electric currents
3217:
3172:
3122:
3059:
2988:
2923:
2849:
2814:
2776:
2738:
2677:{\displaystyle V.}
2674:
2654:{\displaystyle S.}
2651:
2511:electric potential
2507:electric potential
2467:magnetic potential
2431:displacement field
2394:magnetic intensity
2357:
2305:
2245:
2205:
2159:
2113:
2028:
1971:
1926:
1830:
1822:
1750:inverse-square law
1628:
1545:Equation (115) is
1524:Equation (112) is
1483:magnetic potential
1479:electric potential
1425:in his 1861 paper
1416:special relativity
1404:
1369:
1349:
1320:
1277:
1242:
1133:
1068:
998:in developing the
984:studied Maxwell's
978:
874:André-Marie AmpÚre
854:
378:Electrical network
215:Gauss magnetic law
180:Static electricity
140:Electric potential
6144:
6143:
6131:Physics education
6080:Materials science
6047:Interdisciplinary
6005:Quantum mechanics
5792:
5791:
5766:Transfermium Wars
5685:Harvard Computers
5510:Subatomic physics
5483:Quantum mechanics
5419:Superconductivity
5410:Condensed matter
5239:Classical physics
5097:Gerhard W. Bruhn
5065:978-0-486-43241-0
5035:978-981-02-3861-2
5008:978-0-226-07888-5
4945:(2369): 487â492.
4877:978-0-8018-6909-9
4621:"Chapter 18"
4236:George FitzGerald
4180:
3932:is total current.
3905:
3904:
3585:
3537:
3477:
3428:
3002:Mechanical force
2976:
2911:
2390:magnetizing field
2371:
2370:
2303:
2198:
2152:
2102:
1924:
1401:
1372:{\displaystyle p}
1346:
1317:
1274:
1131:
1091:Rudolf Kohlrausch
1064:
1060:
1059:
846:
845:
545:Reluctance (real)
515:Gyratorâcapacitor
460:Resonant cavities
350:Maxwell equations
6174:
6070:Chemical physics
6010:Particle physics
5936:Classical optics
5819:
5812:
5805:
5796:
5782:
5781:
5705:Women in physics
5457:Nuclear physics
5381:Perpetual motion
5315:Material science
5259:Electromagnetism
5219:
5212:
5205:
5196:
5191:
5173:
5172:
5149:
5148:
5139:(30 June 1905).
5133:
5127:
5126:
5108:
5102:
5095:
5089:
5088:
5086:
5076:
5070:
5069:
5046:
5040:
5039:
5019:
5013:
5012:
4992:
4986:
4985:
4974:Lodge, Oliver J.
4970:
4964:
4962:
4922:
4916:
4907:
4901:
4900:
4897:World Scientific
4888:
4882:
4881:
4858:
4849:
4848:
4838:
4832:
4831:
4821:
4815:
4814:
4799:
4798:
4788:
4777:
4776:
4765:
4759:
4758:
4756:
4755:
4740:
4734:
4733:
4693:
4687:
4686:
4676:
4670:
4669:
4637:
4631:
4630:
4616:
4610:
4609:
4579:
4573:
4572:
4558:
4552:
4551:
4537:
4531:
4530:
4516:
4510:
4509:
4495:
4489:
4488:
4482:
4471:
4465:
4464:
4456:
4450:
4449:
4425:
4409:
4394:
4388:
4386:
4380:
4374:
4364:
4349:
4343:
4340:
4194:
4192:
4191:
4186:
4181:
4176:
4168:
4157:
4156:
4140:
4138:
4137:
4132:
4130:
4113:
4108:
4107:
4085:
4083:
4082:
4077:
4069:
4048:
4046:
4045:
4040:
4032:
4007:
3997:
3987:
3977:
3967:
3959:
3951:
3941:
3931:
3921:
3901:
3899:
3898:
3893:
3879:
3866:
3864:
3863:
3858:
3844:
3826:
3824:
3823:
3818:
3816:
3791:
3789:
3788:
3783:
3781:
3748:
3746:
3745:
3740:
3738:
3713:
3711:
3710:
3705:
3703:
3670:
3668:
3667:
3662:
3660:
3649:
3636:
3634:
3633:
3628:
3626:
3615:
3597:
3595:
3594:
3589:
3587:
3586:
3581:
3576:
3570:
3562:
3549:
3547:
3546:
3541:
3539:
3538:
3533:
3528:
3522:
3514:
3496:
3494:
3493:
3488:
3486:
3478:
3476:
3465:
3460:
3447:
3445:
3444:
3439:
3437:
3429:
3427:
3416:
3411:
3393:
3391:
3390:
3385:
3383:
3372:
3359:
3357:
3356:
3351:
3349:
3338:
3320:
3318:
3317:
3312:
3310:
3296:
3277:
3275:
3274:
3269:
3267:
3250:
3226:
3224:
3223:
3218:
3216:
3202:
3194:
3181:
3179:
3178:
3173:
3171:
3157:
3149:
3131:
3129:
3128:
3123:
3097:
3089:
3081:
3068:
3066:
3065:
3060:
3034:
3029:
3015:
2997:
2995:
2994:
2989:
2978:
2977:
2972:
2967:
2961:
2953:
2945:
2932:
2930:
2929:
2924:
2913:
2912:
2907:
2902:
2896:
2891:
2877:
2858:
2856:
2855:
2850:
2842:
2823:
2821:
2820:
2815:
2813:
2799:
2785:
2783:
2782:
2777:
2769:
2747:
2745:
2744:
2739:
2737:
2720:
2699:Quaternion Form
2693:
2683:
2681:
2680:
2675:
2660:
2658:
2657:
2652:
2605:electromagnetism
2575:
2552:
2522:
2504:
2482:
2464:
2446:
2428:
2418:
2405:
2387:
2366:
2364:
2363:
2358:
2350:
2349:
2348:
2336:
2314:
2312:
2311:
2306:
2304:
2302:
2294:
2286:
2278:
2254:
2252:
2251:
2246:
2238:
2214:
2212:
2211:
2206:
2204:
2199:
2191:
2186:
2168:
2166:
2165:
2160:
2158:
2153:
2145:
2140:
2122:
2120:
2119:
2114:
2103:
2101:
2093:
2092:
2083:
2078:
2070:
2059:
2037:
2035:
2034:
2029:
2027:
2026:
2025:
2013:
2004:
1980:
1978:
1977:
1972:
1970:
1956:
1935:
1933:
1932:
1927:
1925:
1923:
1915:
1914:
1905:
1900:
1892:
1891:
1890:
1878:
1861:
1812:
1806:
1800:
1794:
1788:
1782:
1776:
1772:
1766:
1760:
1747:
1733:
1723:
1717:
1711:
1705:
1699:
1689:
1671:
1654:
1645:
1639:
1605:
1599:
1585:
1562:
1520:
1473:
1414:remains true in
1413:
1411:
1410:
1405:
1403:
1402:
1394:
1378:
1376:
1375:
1370:
1358:
1356:
1355:
1350:
1348:
1347:
1339:
1329:
1327:
1326:
1321:
1319:
1318:
1310:
1286:
1284:
1283:
1278:
1276:
1275:
1267:
1251:
1249:
1248:
1243:
1205:Oliver Heaviside
1177:
1172:
1165:Hippolyte Fizeau
1162:
1160:
1154:
1152:
1142:
1140:
1139:
1134:
1132:
1130:
1129:
1120:
1119:
1110:
1108:
1077:
1075:
1074:
1069:
1062:
1061:
1058:
1057:
1048:
1047:
1038:
1034:
982:Oliver Heaviside
944:
908:James C. Maxwell
864:established his
858:electromagnetics
838:
831:
824:
505:Electric machine
488:Magnetic circuit
450:Parallel circuit
440:Network analysis
405:Electric current
340:London equations
185:Triboelectricity
175:Potential energy
44:
34:Electromagnetism
25:
6182:
6181:
6177:
6176:
6175:
6173:
6172:
6171:
6157:Electrodynamics
6147:
6146:
6145:
6140:
6104:
6090:Medical physics
6041:
6000:Nuclear physics
5969:
5963:Non-equilibrium
5885:
5857:
5829:
5823:
5793:
5788:
5770:
5741:Jouleâvon Mayer
5709:
5673:
5630:
5579:
5543:
5434:Big Bang theory
5387:
5286:Fluid mechanics
5233:
5223:
5179:
5176:
5146:
5144:
5135:
5134:
5130:
5123:
5110:
5109:
5105:
5096:
5092:
5084:
5078:
5077:
5073:
5066:
5048:
5047:
5043:
5036:
5021:
5020:
5016:
5009:
4994:
4993:
4989:
4972:
4971:
4967:
4933:
4923:
4919:
4908:
4904:
4890:
4889:
4885:
4878:
4860:
4859:
4852:
4844:The Maxwellians
4840:
4839:
4835:
4823:
4822:
4818:
4811:
4796:
4795:
4790:
4789:
4780:
4769:Hertz, Heinrich
4767:
4766:
4762:
4753:
4751:
4742:
4741:
4737:
4695:
4694:
4690:
4678:
4677:
4673:
4639:
4638:
4634:
4629:. Vol. II.
4618:
4617:
4613:
4581:
4580:
4576:
4560:
4559:
4555:
4539:
4538:
4534:
4518:
4517:
4513:
4497:
4496:
4492:
4473:
4472:
4468:
4458:
4457:
4453:
4436:(in Croatian).
4427:
4426:
4422:
4418:
4413:
4412:
4395:
4391:
4382:
4376:
4370:
4360:
4356:
4350:
4346:
4341:
4337:
4332:
4324:The Maxwellians
4310:
4232:Hendrik Lorentz
4214:
4208:
4202:
4169:
4148:
4143:
4142:
4099:
4094:
4093:
4054:
4053:
4017:
4016:
4003:
3993:
3983:
3973:
3965:
3957:
3947:
3937:
3927:
3917:
3870:
3869:
3835:
3834:
3795:
3794:
3757:
3756:
3717:
3716:
3679:
3678:
3640:
3639:
3606:
3605:
3553:
3552:
3505:
3504:
3469:
3451:
3450:
3420:
3402:
3401:
3363:
3362:
3329:
3328:
3281:
3280:
3235:
3234:
3185:
3184:
3140:
3139:
3072:
3071:
3006:
3005:
2936:
2935:
2868:
2867:
2827:
2826:
2790:
2789:
2751:
2750:
2711:
2710:
2663:
2662:
2640:
2639:
2593:
2587:
2564:
2543:
2518:
2500:
2478:
2471:angular impulse
2460:
2442:
2424:
2417:
2411:
2408:current density
2401:
2383:
2331:
2320:
2319:
2295:
2287:
2263:
2262:
2223:
2222:
2177:
2176:
2131:
2130:
2094:
2084:
2050:
2049:
2008:
1989:
1988:
1944:
1943:
1916:
1906:
1873:
1868:
1867:
1843:
1837:
1808:
1807:parallels with
1802:
1796:
1795:parallels with
1790:
1784:
1778:
1774:
1768:
1762:
1756:
1743:
1740:electric charge
1729:
1719:
1718:with vorticity
1713:
1707:
1701:
1695:
1678:
1663:
1650:
1641:
1635:
1601:
1595:
1564:
1554:
1514:
1499:
1493:
1474:
1464:
1449:Richard Feynman
1429:. He added the
1381:
1380:
1361:
1360:
1332:
1331:
1297:
1296:
1254:
1253:
1225:
1224:
1201:Michael Faraday
1197:
1170:
1168:
1167:in 1848 and at
1158:
1156:
1150:
1148:
1121:
1111:
1096:
1095:
1049:
1039:
1022:
1021:
1015:
996:Albert Einstein
992:vector calculus
940:
920:Roger Boscovich
916:lines of forces
891:lines of forces
882:Michael Faraday
842:
813:
812:
628:
620:
619:
575:
565:
564:
520:Induction motor
490:
480:
479:
395:Current density
380:
370:
369:
360:Poynting vector
270:
268:Electrodynamics
260:
259:
255:Right-hand rule
220:Magnetic dipole
210:BiotâSavart law
200:
190:
189:
125:Electric dipole
120:Electric charge
95:
23:
12:
11:
5:
6180:
6178:
6170:
6169:
6164:
6159:
6149:
6148:
6142:
6141:
6139:
6138:
6133:
6128:
6123:
6118:
6112:
6110:
6106:
6105:
6103:
6102:
6097:
6092:
6087:
6082:
6077:
6072:
6067:
6062:
6057:
6051:
6049:
6043:
6042:
6040:
6039:
6034:
6033:
6032:
6027:
6022:
6012:
6007:
6002:
5997:
5996:
5995:
5990:
5979:
5977:
5971:
5970:
5968:
5967:
5966:
5965:
5960:
5953:Thermodynamics
5950:
5949:
5948:
5943:
5933:
5928:
5923:
5922:
5921:
5916:
5911:
5906:
5895:
5893:
5887:
5886:
5884:
5883:
5882:
5881:
5871:
5865:
5863:
5859:
5858:
5856:
5855:
5854:
5853:
5843:
5837:
5835:
5831:
5830:
5824:
5822:
5821:
5814:
5807:
5799:
5790:
5789:
5787:
5786:
5775:
5772:
5771:
5769:
5768:
5763:
5762:
5761:
5756:
5748:
5746:ShapleyâCurtis
5743:
5738:
5736:LeibnizâNewton
5733:
5731:Galileo affair
5728:
5723:
5717:
5715:
5711:
5710:
5708:
5707:
5702:
5697:
5692:
5687:
5681:
5679:
5675:
5674:
5672:
5671:
5666:
5665:
5664:
5654:
5649:
5644:
5638:
5636:
5632:
5631:
5629:
5628:
5626:Speed of light
5623:
5622:
5621:
5616:
5611:
5603:
5598:
5593:
5587:
5585:
5581:
5580:
5578:
5577:
5572:
5570:Nanotechnology
5567:
5562:
5561:
5560:
5551:
5549:
5545:
5544:
5542:
5541:
5540:
5539:
5534:
5529:
5519:
5518:
5517:
5507:
5506:
5505:
5500:
5495:
5490:
5480:
5479:
5478:
5473:
5468:
5463:
5455:
5450:
5449:
5448:
5438:
5437:
5436:
5431:
5423:
5422:
5421:
5416:
5408:
5407:
5406:
5397:
5395:
5393:Modern physics
5389:
5388:
5386:
5385:
5384:
5383:
5378:
5373:
5368:
5361:Thermodynamics
5358:
5357:
5356:
5346:
5345:
5344:
5339:
5329:
5328:
5327:
5322:
5312:
5311:
5310:
5300:
5299:
5298:
5293:
5283:
5282:
5281:
5276:
5271:
5266:
5256:
5255:
5254:
5243:
5241:
5235:
5234:
5224:
5222:
5221:
5214:
5207:
5199:
5193:
5192:
5175:
5174:
5143:. Fourmilab.ch
5128:
5121:
5103:
5090:
5071:
5064:
5052:(2003-10-17).
5041:
5034:
5014:
5007:
4987:
4965:
4917:
4902:
4883:
4876:
4862:Nahin, Paul J.
4850:
4833:
4816:
4809:
4778:
4773:Electric waves
4760:
4735:
4714:10.1086/350788
4708:(4): 425â444.
4688:
4671:
4652:(5): 455â490.
4632:
4611:
4574:
4553:
4532:
4511:
4490:
4466:
4451:
4419:
4417:
4414:
4411:
4410:
4389:
4358:
4344:
4334:
4333:
4331:
4328:
4327:
4326:
4321:
4316:
4309:
4306:
4283:Theodor Kaluza
4248:Henri Poincaré
4204:Main article:
4201:
4198:
4184:
4179:
4175:
4172:
4166:
4163:
4160:
4155:
4151:
4129:
4125:
4122:
4119:
4116:
4112:
4106:
4102:
4092:, the formula
4075:
4072:
4068:
4064:
4061:
4038:
4035:
4031:
4027:
4024:
4010:
4009:
4001:
3999:
3991:
3989:
3981:
3979:
3971:
3969:
3963:
3961:
3955:
3953:
3945:
3943:
3935:
3933:
3925:
3923:
3915:
3913:
3911:
3907:
3906:
3903:
3902:
3891:
3888:
3885:
3882:
3878:
3867:
3856:
3853:
3850:
3847:
3843:
3832:
3828:
3827:
3815:
3811:
3808:
3805:
3802:
3792:
3780:
3776:
3773:
3770:
3767:
3764:
3754:
3750:
3749:
3737:
3733:
3730:
3727:
3724:
3714:
3702:
3698:
3695:
3692:
3689:
3686:
3676:
3672:
3671:
3659:
3655:
3652:
3648:
3637:
3625:
3621:
3618:
3614:
3603:
3599:
3598:
3584:
3580:
3573:
3569:
3565:
3561:
3550:
3536:
3532:
3525:
3521:
3517:
3513:
3502:
3501:Total current
3498:
3497:
3485:
3481:
3475:
3472:
3468:
3463:
3459:
3448:
3436:
3432:
3426:
3423:
3419:
3414:
3410:
3399:
3395:
3394:
3382:
3378:
3375:
3371:
3360:
3348:
3344:
3341:
3337:
3326:
3322:
3321:
3309:
3305:
3302:
3299:
3295:
3291:
3288:
3278:
3266:
3262:
3259:
3256:
3253:
3249:
3245:
3242:
3232:
3228:
3227:
3215:
3211:
3208:
3205:
3201:
3197:
3193:
3182:
3170:
3166:
3163:
3160:
3156:
3152:
3148:
3137:
3136:Magnetization
3133:
3132:
3121:
3118:
3115:
3112:
3109:
3106:
3103:
3100:
3096:
3092:
3088:
3084:
3080:
3069:
3058:
3055:
3052:
3049:
3046:
3043:
3040:
3037:
3033:
3028:
3024:
3021:
3018:
3014:
3003:
2999:
2998:
2987:
2984:
2981:
2975:
2971:
2964:
2960:
2956:
2952:
2948:
2944:
2933:
2922:
2919:
2916:
2910:
2906:
2899:
2895:
2890:
2886:
2883:
2880:
2876:
2865:
2861:
2860:
2848:
2845:
2841:
2837:
2834:
2812:
2808:
2805:
2802:
2798:
2787:
2775:
2772:
2768:
2764:
2761:
2758:
2736:
2732:
2729:
2726:
2723:
2719:
2708:
2704:
2703:
2700:
2697:
2673:
2670:
2650:
2647:
2589:Main article:
2586:
2581:
2539:Equation
2537:
2536:
2516:
2514:
2498:
2496:
2493:electric field
2483:is called the
2476:
2474:
2458:
2456:
2440:
2438:
2422:
2420:
2415:
2399:
2397:
2381:
2379:
2377:
2373:
2372:
2369:
2368:
2356:
2353:
2347:
2344:
2341:
2335:
2330:
2327:
2301:
2298:
2293:
2290:
2284:
2281:
2277:
2273:
2270:
2260:
2256:
2255:
2244:
2241:
2237:
2233:
2230:
2220:
2216:
2215:
2203:
2197:
2194:
2189:
2185:
2174:
2170:
2169:
2157:
2151:
2148:
2143:
2139:
2128:
2124:
2123:
2112:
2109:
2106:
2100:
2097:
2091:
2087:
2081:
2077:
2073:
2069:
2065:
2062:
2058:
2047:
2039:
2038:
2024:
2021:
2018:
2012:
2007:
2003:
1999:
1996:
1986:
1982:
1981:
1969:
1965:
1962:
1959:
1955:
1951:
1941:
1937:
1936:
1922:
1919:
1913:
1909:
1903:
1899:
1895:
1889:
1886:
1883:
1877:
1865:
1839:Main article:
1836:
1831:
1736:
1735:
1726:magnetic field
1673:
1592:
1591:
1550:
1543:
1522:
1495:Main article:
1492:
1487:
1472:, 24 May 1940)
1462:
1400:
1397:
1391:
1388:
1368:
1345:
1342:
1316:
1313:
1307:
1304:
1273:
1270:
1264:
1261:
1241:
1238:
1235:
1232:
1213:Heinrich Hertz
1196:
1190:
1128:
1124:
1118:
1114:
1107:
1103:
1079:
1078:
1067:
1056:
1052:
1046:
1042:
1037:
1032:
1029:
1014:
1011:
1007:Heinrich Hertz
938:speed of light
876:published his
870:electrostatics
844:
843:
841:
840:
833:
826:
818:
815:
814:
811:
810:
805:
800:
795:
790:
785:
780:
775:
770:
765:
760:
755:
750:
745:
740:
735:
730:
725:
720:
715:
710:
705:
700:
695:
690:
685:
680:
675:
670:
665:
660:
655:
650:
645:
640:
635:
629:
626:
625:
622:
621:
618:
617:
612:
607:
602:
597:
595:Four-potential
592:
587:
582:
576:
571:
570:
567:
566:
563:
562:
557:
552:
547:
542:
537:
532:
527:
522:
517:
512:
510:Electric motor
507:
502:
497:
491:
486:
485:
482:
481:
478:
477:
472:
467:
465:Series circuit
462:
457:
452:
447:
442:
437:
435:Kirchhoff laws
432:
427:
422:
417:
412:
407:
402:
400:Direct current
397:
392:
387:
381:
376:
375:
372:
371:
368:
367:
362:
357:
355:Maxwell tensor
352:
347:
342:
337:
332:
327:
325:Larmor formula
322:
317:
312:
307:
302:
297:
292:
287:
282:
277:
275:Bremsstrahlung
271:
266:
265:
262:
261:
258:
257:
252:
247:
242:
237:
232:
227:
225:Magnetic field
222:
217:
212:
207:
201:
198:Magnetostatics
196:
195:
192:
191:
188:
187:
182:
177:
172:
167:
162:
157:
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142:
137:
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130:Electric field
127:
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117:
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100:Charge density
96:
93:Electrostatics
91:
90:
87:
86:
85:
84:
79:
74:
69:
64:
59:
54:
46:
45:
37:
36:
30:
29:
28:Articles about
13:
10:
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6:
4:
3:
2:
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6119:
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6107:
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6098:
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6095:Ocean physics
6093:
6091:
6088:
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6083:
6081:
6078:
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6071:
6068:
6066:
6063:
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6058:
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6030:Modern optics
6028:
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5879:Computational
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5721:BohrâEinstein
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5575:String theory
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5325:Metamaterials
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4806:
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4750:. 1 July 2014
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4255:
4253:
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4246:(so named by
4245:
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4240:Joseph Larmor
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2187:
2175:
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2149:
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2129:
2126:
2125:
2110:
2104:
2098:
2079:
2071:
2063:
2060:
2048:
2045:
2044:Lorentz force
2041:
2040:
2005:
1997:
1987:
1984:
1983:
1963:
1957:
1949:
1942:
1939:
1938:
1920:
1901:
1893:
1862:
1859:
1858:
1857:
1854:
1852:
1848:
1842:
1835:
1832:
1826:
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1814:
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1793:
1787:
1781:
1771:
1765:
1759:
1753:
1751:
1746:
1741:
1732:
1727:
1724:leads to the
1722:
1716:
1710:
1704:
1698:
1693:
1688:
1685:
1681:
1677:
1674:
1670:
1666:
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1649:
1644:
1638:
1633:
1623:
1619:
1617:
1613:
1609:
1604:
1598:
1589:
1588:Lorentz force
1583:
1579:
1575:
1571:
1567:
1561:
1557:
1551:
1548:
1544:
1540:
1535:
1531:
1527:
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1518:
1512:
1508:
1507:
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1504:
1498:
1491:
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1480:
1471:
1467:
1461:
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1450:
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1441:
1436:
1432:
1428:
1424:
1419:
1417:
1398:
1395:
1389:
1386:
1366:
1343:
1340:
1314:
1311:
1305:
1302:
1294:
1290:
1271:
1268:
1262:
1259:
1239:
1236:
1233:
1230:
1220:
1218:
1214:
1210:
1206:
1202:
1195:
1189:
1187:
1186:
1181:
1180:LĂ©on Foucault
1176:
1166:
1146:
1126:
1122:
1116:
1112:
1105:
1101:
1092:
1088:
1083:
1065:
1054:
1050:
1044:
1040:
1035:
1030:
1027:
1020:
1019:
1018:
1012:
1010:
1008:
1003:
1001:
997:
993:
990:and employed
989:
988:
983:
973:
969:
967:
963:
958:
956:
955:
950:
949:
943:
939:
935:
934:
929:
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921:
917:
913:
909:
904:
901:
897:
893:
892:
887:
883:
879:
875:
871:
867:
863:
859:
850:
839:
834:
832:
827:
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820:
819:
817:
816:
809:
806:
804:
801:
799:
796:
794:
791:
789:
786:
784:
781:
779:
776:
774:
771:
769:
766:
764:
761:
759:
756:
754:
751:
749:
746:
744:
741:
739:
736:
734:
731:
729:
726:
724:
721:
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631:
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623:
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586:
583:
581:
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569:
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561:
558:
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553:
551:
548:
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543:
541:
538:
536:
533:
531:
528:
526:
523:
521:
518:
516:
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511:
508:
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503:
501:
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492:
489:
484:
483:
476:
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471:
468:
466:
463:
461:
458:
456:
453:
451:
448:
446:
443:
441:
438:
436:
433:
431:
430:Joule heating
428:
426:
423:
421:
418:
416:
413:
411:
408:
406:
403:
401:
398:
396:
393:
391:
388:
386:
383:
382:
379:
374:
373:
366:
363:
361:
358:
356:
353:
351:
348:
346:
345:Lorentz force
343:
341:
338:
336:
333:
331:
328:
326:
323:
321:
318:
316:
313:
311:
308:
306:
303:
301:
298:
296:
293:
291:
288:
286:
283:
281:
278:
276:
273:
272:
269:
264:
263:
256:
253:
251:
248:
246:
245:Magnetization
243:
241:
238:
236:
233:
231:
230:Magnetic flux
228:
226:
223:
221:
218:
216:
213:
211:
208:
206:
203:
202:
199:
194:
193:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
161:
158:
156:
153:
151:
148:
146:
143:
141:
138:
136:
135:Electric flux
133:
131:
128:
126:
123:
121:
118:
116:
113:
111:
108:
106:
103:
101:
98:
97:
94:
89:
88:
83:
80:
78:
75:
73:
72:Computational
70:
68:
65:
63:
60:
58:
55:
53:
50:
49:
48:
47:
43:
39:
38:
35:
31:
27:
26:
21:
16:
6055:Astrophysics
5869:Experimental
5690:The Martians
5354:Spectroscopy
5296:Aerodynamics
5278:
5274:Field theory
5185:
5167:
5163:
5159:
5153:
5151:
5145:. Retrieved
5137:Einstein, A.
5131:
5112:
5106:
5093:
5080:
5074:
5054:
5044:
5024:
5017:
4997:
4990:
4981:
4977:
4968:
4942:
4938:
4935:Einstein, A.
4929:
4925:
4920:
4910:
4905:
4892:
4886:
4866:
4842:
4836:
4825:
4819:
4800:to the 1940s
4793:
4772:
4763:
4752:. Retrieved
4747:
4738:
4705:
4701:
4691:
4681:
4674:
4649:
4645:
4635:
4624:
4614:
4589:
4583:
4577:
4568:
4562:
4556:
4547:
4541:
4535:
4526:
4520:
4514:
4505:
4499:
4493:
4483:– via
4477:
4469:
4460:
4454:
4440:(1): 11â34.
4437:
4433:
4423:
4392:
4383:
4377:
4371:
4361:
4352:
4347:
4338:
4276:
4258:
4256:
4229:
4222:
4215:
4090:
4087:
4050:
4013:
4011:
4004:
3994:
3984:
3974:
3948:
3938:
3928:
3918:
2825:
2749:
2702:Vector Form
2628:
2624:
2621:
2618:
2615:
2612:
2596:
2594:
2583:
2577:
2572:
2568:
2565:
2557:
2555:
2549:
2545:
2542:, with the
2540:
2538:
2528:
2519:
2510:
2501:
2484:
2479:
2473:by Maxwell).
2470:
2469:(called the
2461:
2455:by Maxwell).
2452:
2443:
2437:by Maxwell).
2434:
2433:(called the
2425:
2412:
2402:
2393:
2384:
2318:
2315:
2219:Gauss's law
1855:
1844:
1833:
1809:
1803:
1797:
1791:
1785:
1779:
1769:
1767:, and where
1763:
1757:
1754:
1744:
1737:
1730:
1720:
1714:
1708:
1702:
1696:
1691:
1686:
1683:
1679:
1675:
1668:
1664:
1659:
1651:
1642:
1636:
1631:
1629:
1607:
1602:
1596:
1593:
1581:
1577:
1573:
1569:
1565:
1559:
1555:
1516:
1502:
1500:
1489:
1476:
1469:
1458:
1454:
1438:
1426:
1420:
1289:Wren Library
1221:
1216:
1198:
1193:
1183:
1084:
1080:
1016:
1004:
985:
979:
965:
959:
952:
946:
941:
931:
923:
915:
905:
889:
855:
590:Four-current
525:Linear motor
410:Electrolysis
290:Eddy current
250:Permeability
170:Polarization
165:Permittivity
15:
5958:Statistical
5874:Theoretical
5851:Engineering
5614:Higgs boson
4592:: 459â512.
4287:Oskar Klein
4259:independent
4234:along with
2607:written by
2533:resistivity
2449:free charge
1728:denoted as
1553:induction,
1547:Gauss's law
1161:10 m/s
1153:10 m/s
884:discovered
880:. In 1831,
872:. In 1825,
560:Transformer
390:Capacitance
315:Faraday law
110:Coulomb law
52:Electricity
6151:Categories
6075:Geophysics
6065:Biophysics
5909:Analytical
5862:Approaches
5635:By periods
5453:Geophysics
5425:Cosmology
5170:by Tuebner
5147:2008-10-19
4915:, page 133
4754:2020-02-17
4529:: 281â291.
4508:: 161â175.
4485:Wikisource
4416:References
4298:dimensions
4272:rest frame
4210:See also:
4200:Relativity
3325:Ohm's law
2636:quaternion
2599:, an 1873
2173:Ohm's law
1801:, whereas
1145:Leyden jar
627:Scientists
475:Waveguides
455:Resistance
425:Inductance
205:AmpĂšre law
6025:Molecular
5926:Acoustics
5919:Continuum
5914:Celestial
5904:Newtonian
5891:Classical
5834:Divisions
5678:By groups
5662:Astronomy
5498:Molecules
5332:Mechanics
5247:Astronomy
4963:cited in.
4722:0021-1753
4666:0003-9519
4606:186207827
4446:0353-765X
4404:from the
4174:π
4165:−
4159:Ψ
4150:∇
4124:μ
4121:π
4101:∇
4063:⋅
4060:∇
4026:⋅
4023:∇
3890:Ω
3887:∇
3884:−
3855:Ω
3852:∇
3849:−
3810:⋅
3807:∇
3775:∇
3732:⋅
3729:∇
3697:∇
3654:μ
3620:μ
3583:˙
3535:˙
3474:π
3425:π
3304:×
3301:∇
3290:π
3261:∇
3244:π
3210:π
3165:π
3120:Ω
3117:∇
3111:−
3108:Ψ
3105:∇
3099:−
3091:×
3057:Ω
3054:∇
3048:−
3045:Ψ
3042:∇
3036:−
2986:Ψ
2983:∇
2980:−
2974:˙
2963:−
2955:×
2921:Ψ
2918:∇
2915:−
2909:˙
2898:−
2836:⋅
2833:∇
2807:×
2804:∇
2763:∇
2731:∇
2329:⋅
2326:∇
2297:∂
2292:ρ
2289:∂
2283:−
2272:⋅
2269:∇
2243:ρ
2232:⋅
2229:∇
2196:σ
2150:ε
2111:ϕ
2108:∇
2105:−
2096:∂
2086:∂
2080:−
2072:×
2064:μ
1998:×
1995:∇
1964:×
1961:∇
1950:μ
1918:∂
1908:∂
1399:˙
1344:˙
1315:˙
1272:˙
1192:The term
1123:ε
1113:μ
1051:ε
1041:μ
976:circuits.
962:Boltzmann
896:Emil Lenz
878:force law
783:Steinmetz
713:Kirchhoff
698:Jefimenko
693:Hopkinson
678:Helmholtz
673:Heaviside
535:Permeance
420:Impedance
160:Insulator
155:Gauss law
105:Conductor
82:Phenomena
77:Textbooks
57:Magnetism
5784:Category
5609:timeline
5596:Graphene
5558:timeline
5527:timeline
5515:timeline
5488:timeline
5429:timeline
5414:timeline
5404:timeline
5366:timeline
5337:timeline
5320:timeline
5308:timeline
5291:timeline
5264:timeline
5252:timeline
5230:timeline
4959:17847438
4771:(1893).
4571:: 85â95.
4550:: 12â24.
4463:: 27â83.
4308:See also
2601:treatise
2376:Notation
1600:and the
1466:Einstein
1463:â
1330:, where
1173:10
808:Wiechert
763:Poynting
653:Einstein
500:DC motor
495:AC motor
330:Lenz law
115:Electret
6109:Related
5993:General
5988:Special
5846:Applied
5619:Neutron
5476:Weapons
5461:Fission
5376:Entropy
4939:Science
4302:physics
2632:Fraktur
2523:is the
2505:is the
2465:is the
2447:is the
2429:is the
2406:is the
2388:is the
1752:force.
1470:Science
980:Later,
966:Bicykel
793:Thomson
768:Ritchie
758:Poisson
743:Neumann
738:Maxwell
733:Lorentz
728:Liénard
658:Faraday
643:Coulomb
470:Voltage
445:Ohm law
67:History
6020:Atomic
5975:Modern
5825:Major
5466:Fusion
5371:Energy
5349:Optics
5119:
5062:
5032:
5005:
4984:: 535.
4957:
4874:
4807:
4730:229816
4728:
4720:
4664:
4604:
4480:
4444:
2410:(with
1783:is to
1773:is to
1761:is to
1690:where
1063:
778:Singer
773:Savart
753:Ărsted
718:Larmor
708:Kelvin
663:Fizeau
633:AmpĂšre
555:Stator
62:Optics
5537:tests
5493:Atoms
5471:Power
5446:tests
5085:(PDF)
4726:JSTOR
4602:S2CID
4569:XXIII
4548:XXIII
4406:stars
4367:IUPAP
4330:Notes
2696:Name
1789:i.e.
1149:3.107
803:Weber
798:Volta
788:Tesla
703:Joule
688:Hertz
683:Henry
668:Gauss
550:Rotor
5946:Wave
5841:Pure
5117:ISBN
5060:ISBN
5030:ISBN
5003:ISBN
4955:PMID
4872:ISBN
4805:ISBN
4797:B.C.
4718:ISSN
4702:Isis
4662:ISSN
4442:ISSN
4285:and
4277:The
4238:and
2661:and
2614:and
1667:= Ό
1515:â âą
1481:and
1211:and
1169:2.98
1157:3.14
1089:and
723:Lenz
648:Davy
638:Biot
5941:Ray
4947:doi
4932:in
4710:doi
4654:doi
4594:doi
4590:155
4527:XXI
4506:XXI
2688:.
2623:to
2603:on
2595:In
2416:tot
2316:or
1519:= 0
1291:of
1178:by
1175:m/s
1163:by
868:of
866:law
748:Ohm
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5158:,
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4943:91
4941:.
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4706:62
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2513:).
2046:)
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1618:.
1580:Ă
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1568:=
1566:F
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4162:=
4154:2
4128:C
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4115:=
4111:A
4105:2
4074:0
4071:=
4067:C
4037:0
4034:=
4030:B
4005:m
3995:e
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3975:K
3966:Ω
3958:Κ
3949:K
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3804:=
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2061:=
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2020:o
2017:t
2011:J
2006:=
2002:H
1968:A
1958:=
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