Fontem paginae Physica electromagnetica inspicere

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[[Fasciculus:Ferrofluid poles.jpg|thumb|[[Ferrofluidus]] qui se congregat apud polos magnis potentis.]]
[[Fasciculus:Lightning3.jpg|thumb|[[Fulmen|Fulmina]] quae magnae sunt fluxiones electricae.]]
'''Physica electromagnetica''' de [[campus physicus|campo]] [[electromagnetismus|electromagnetico]] et effectu suo in particulas [[onus electricum]] habentes tractat. [[Aequationes Maxwellianae|Theoria Maxwelliana]] [[vis|vim]] [[electricitas|electricam]] et vim [[magnetismus|magneticam]] in formam [[relativitas specialis|theoriae relativitatis speciali]] congruentem unit. [[Aequationes Maxwellianae]] per se describunt campum electricum et campum magneticum et eorum causam imperfectam in particulis onus habentibus. [[Aequatio Lorentziana]] vim in particulas onus habentes a campis electricis magneticisque effectam describit. [[Aequationes Maxwellianae|Aequationes Maxwellianae in vacuo]] sunt basis [[doctrina]]e [[lux|lucis]] electromagneticae in quo [[celeritas lucis]] 

:::<math> c=2.99792458 \times 10^8 m/s </math>

in [[vacuum|vacuo]] esse praecinitur.

== Notiones fundamentales physicae electromagneticae ==
[[Fasciculus:Camposcargas.PNG|thumb|[[Campus physicus|Campus electricus]] lineis camporum repraesentatus a duobus particulis onus habentibus creatus.]]
* [[Aether (physica)|Aether physicus]]
* [[Campus physicus]]
* [[Celeritas luminis|Celeritas lucis]]
* [[Fluxus magneticus]]
* [[Fluxus oneris electrici]]
* [[Onus electricum]]
* [[Relativitas specialis|Principium relativitatis]]
* [[Productum interius]]
* [[Productum vectoriale]]
* [[Radiatio electromagnetica]]
* [[Systema coordinatarum]]
* [[Tensio electrica]]
* [[Vis physica|Vix motrix]]

== Historia ==
Theoria electromagnetica [[historia]]m longam ab antiquitate usque ad hodiernam diem habet. Ex perantiquitate totus [[tellus|mundus]] de [[fulmen|fulminibus]] scivit. [[Res Publica Populi Sinae|Seres]] antiqui circum [[400 a.C.n.]] de magnetismo in [[liber|libro]] ''Liber magistris vallis diaboli'' (鬼谷子) aiunt: "Magnes facit ferrum venire vel ferrum attrahit."<ref>Li Shu-hua, “Origine de la Boussole 11. Aimant et Boussole,” ''Isis'', Vol. 45, No. 2. (Iul., 1954), p. 175.</ref> Et circum annum [[1200]] notatur Seres [[pyxis nautica|pyxibus magneticis]] ad [[navigatio|navigandum]] uti.<ref>Ex pagina [[:en:Compass]] abstracta: Zhu Yu, ''Pingzhou Table Talks'' (Pingzhou Ke Tan) anno [[1117]] [[Anglice]] edita: "The navigator knows the geography, he watches the stars at night, watches the sun at day; when it is dark and cloudy, he watches the compass."</ref>

=== Opera Guilielmi Gilbert et Beniaminis Franklin ===
[[Fasciculus:William Gilbert.jpg|thumb|[[Gulielmus Gilbert]].]]
[[Gulielmus Gilbert]] anno [[1600]] in magna opera, ''De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure,''<ref>Vide etiam situm Anglice [[:en:De Magnete|"De Magnete"]] appellatum et paginam [http://www.phy6.org/earthmag/demagint.htm "400 Years of "De Magnete": Commemorating the 400th anniversary of "De Magnete" by William Gilbert of Colchester,"] a David P. Stern scriptam.</ref> 
imprimis fortiter disputabat magnetismum ab electricitate dissimile esse. Pro evidentia, Gilbertus monstrabat, cum temperatura augmentetur, quasdam attractiones electricas evanescere donec alias magneticas manere. Sua distinctio inter electricitatem et magnetismum 250 [[annus|annos]] progressus [[scientia (ratio)|scientiae]] maxime ingreditur. Gilbertus in eadem opera proposuit [[tellus (planeta)|tellurem]] propium esse magnem ingentem, quod efficit [[pyxis nautica|pyxes nauticas]] ad [[septentriones|borealem]] indicare. Antea vel [[stella]] [[Polaris]] vel [[insula]] magnetica boreale sita putabantur pyxes attrahere. Ipse quoque primitus verbum ''[[electricitas]]'' introduxit a [[vocabulum|verbo]] [[Graece|Graeco]] ''ήλεκτρον'' (''[[electron]]''), quae 'glaesum' (sive [[succinum]]) significat, materiem quod proprietates significativas electrostaticas habet.<ref>Verbum ''electricitas'' et sua origo in verbo Graeco '[[electron]]' pervestigata sunt in paginis 31–33 commentarii ''"Notes on the De Magnete of D. William Gilbert,"'' a Silvano P. Thompson et aliis scripti, Londoninii [[1901]] editi, et in ''"On the Magnet by William Gilbert,"' a Derek J. Price scripto (Novi Eboraci: Basic Books, 1958) iterum prolati.</ref> 

[[Beniaminus Franklin]] circum annum [[1750]] [[ele4ctricitas statica|elecricitatem staticam]] investigavit.<ref>"Experiments and Observations on Electricity made at Philadelphia in America by Benjamin Franklin, L. L. D. and F. R. S.", F. Newbery, London, M.DCC.LXXIV"; vide etiam commentarium [https://web.archive.org/web/20060110052254/http://www.physicstoday.org/vol-59/iss-1/p42.html "400 Years of "Benjamin Franklin and Lightning Rods,"] a E. Philip Krider scriptum.</ref> Sua experimenta milvis fulmina investigantia notitiam alteri physici attraxerunt. Franklin doctrinam proposuit notam in quo electricitas constat in fluido simplice qui est in materia aut in superfluo ''+,'' aut in carentia ''–''. Hi typi sunt origo hodierni usus signorum ''+'' et ''–'' ad onera electrica designanda.<ref>"Hence have arisen some new terms among us: we say B,(and bodies like circumstanced) is electrified ''positively''; A, ''negatively.'' Or rather, B. is electrified ''plus''; A, ''minus''." Beniaminus Franklin in alteris litteris ad Petro Collinson missis, ''Letter II from Benjamin Franklin, Esq.; in Philadelphia to Peter Collinson, Esq.; F. R. S. London, 1747.''</ref>

=== Opera Caroli Coulomb et Caroli Gauss ===
[[Fasciculus:Coulomb.jpg|thumb|175px|left|[[Carolus Coulomb]].]]
[[Fasciculus:Carl Friedrich Gauss.jpg|thumb|200px|[[Carolus Fridericus Gauss]].]]
Anno [[1785]], [[Carolus Coulomb]] suas tres operas experimentales de electricitate magnetismoque provulgavit,<ref>C.-A. Coulomb, "Premier Mémoire sur l’Electricité et le Magnétisme," Histoire de l’Académie Royale des Sciences, 569–577, 1785; "Sécond Mémoire sur l’Electricité et le Magnétisme," Histoire de l’Académie Royale des Sciences, 578–611, 1785; "Troisième Mémoire sur l’Electricité et le Magnétisme," Histoire de l’Académie Royale des Sciences, 612–638, 1785. Vide etiam [http://cnum.cnam.fr/CGI/redir.cgi?8CA121-1 "Collection de mémoires relatifs à la physique, . . . Tome I. Mémoires de Coulomb,"] p. 146, ubi Coulomb recapitulavit: "Que l'action, soit répulsive, soit attractive de deux globes électrisés et, par conséquent, de deux molécules électriques, est en raison composée des densités du fluide électrique des deux molécules électrisées et inverse du carré des distances."</ref> in quibus nuntiavit invenire vim electricam inter duas particulas onus electricum habentes esse vi gravitatis simile, reciproce ut quadrata distantiae inter particulas, proportionale quantitatibus eorum onerum electricorum in coniunctim, et directam secundum lineam inter particulas. Forma vectorali unitatibus [[Systema Internationale|MKSA]] scripta, [[lex Coulombiana]] est:

:::<math>\vec \mathbf{F}_{12} =  q_1 \vec \mathbf{E}_{2} = \frac {1} {4 \pi \epsilon_0} {q_1 q_2 \over r^2} 
\, \mathbf{\hat{r}}_{21}</math>

ubi

:<math>\vec \mathbf F_{12}</math> est vis electrica in particula 1 ob particulam 2,
:<math> \vec \mathbf E_{2}</math> est campus electricus in particulae 1 loco ob particulam 2,
:''q''<sub>1</sub> et ''q''<sub>2</sub> sunt onera electrica particularum 1 et 2,
:<math> r =|\vec \mathbf r_1 - \vec \mathbf r_2| </math> est distantia inter particulas 1 et 2, 
:<math> \mathbf{\hat{r}}_{21} \ \stackrel{\mathrm{def}}{=}\  \frac{\vec \mathbf{r}_1 - \vec \mathbf{r}_2}{\vert \vec \mathbf{r}_1 - \vec \mathbf{r}_2\vert} </math> est directio ad particulam 1 a particula 2, et 
:<math> \frac {1}{4 \pi \epsilon_o} =  8.988 \times 10^{9} \frac {N m^2}{C^2}</math> est constans electricus. 

[[Carolus Fridericus Gauss|Ioannes Carolus Fridericus Gauss]], [[mathematica|mathematicus]] et scientiarum doctus, anno [[1813]] [[theorema]] de campis [[lex quadratica inversa|legem quadraticam inversam]] habentibus formulavit,<ref>[[Carolus Fridericus Gauss]], "Theoria attractionis corporum sphaeroidicorum ellipticorum homogeneorum, Martii 1813, in "Werke Sammlung Mathematische Physik, ABHANDLUNGEN Band Bd. 5, paginis 3-24 apud [http://dz1.gdz-cms.de/index.php?id=toc&no_cache=1&IDDOC=38910 Universitaetsbibliothek Goettingen - Digitalisierungszentrum]
</ref> quae est casus proprii theorematis hodierni post [[Theorema Stokesianum|Georgium Stokes]] nominatae.<ref>"Theorema Stokes" dicitur vere a [[Gulielmus Thomson, baro Kelvin|Gulielmo Thomson]] repertus esse; vide etiam paginam [[lingua Anglica|Anglicam]] [[:en:Stokes' theorem]].</ref> Applicantes [[theorema Gauss]] ad legem Coulombianam, legem obtinemus Gaussianam electrostaticam forma differentiale hodierna:

:::<math>\nabla \cdot \vec \mathbf{E} = \rho/\epsilon_o</math>

ubi <math> \rho </math> est densitas oneris electrici ob varias particulas onus habentes complexas, et <math>\vec \mathbf E</math> est campus electricus universus ex illis particulis.

=== Opera Iohannis Oersted, Iohannis Baptiste Biot, Felicis Savart, Andreae Ampere ===
[[Fasciculus:Jean baptiste biot.jpg|thumb|200px|[[Ioannes Baptista Biot]].]]
[[Fasciculus:Ampere1.jpg|thumb|200px|[[Andreas Maria Ampère|Andreas Ampere]].]]
Circum annum [[1820]] [[Ioannes Christianus Ørsted|Ioannes Christianus Oersted]], [[Ioannes Baptista Biot]], [[Felix Savart]] et [[Andreas Maria Ampère|Andreas Marie Ampere]], vim magneticam in filis [[Fluxio electrica|fluxiones electricas]] habentibus ob fluxiones electricas in filis complexis investigantes, confirmaverunt legem magneticam legi Coulomb similem.<ref>Quamquam Biot, Savart, et Ampere omnes participaverunt ad hanc legem magneticam formulandam haec forma legis solum post Biot et Savart nominatus est; vide etiam nota 10 infra; et [http://www.ampere.cnrs.fr/oeuvresimp.php?lang=fr "Oeuvres imprimées d'AmpèreAndré-Marie Ampère," @.ampère et l'histoire de l'électricité]; et L. Pearce Williams, "Ampère, André-Marie", ''Dictionary of Scientific Biography'' 1:139-147 (Novi Eboraci: Charles Scribner's Sons, 1970); et paginam Anglicam [[:en:André-Marie Ampère]].</ref> Secundum hanc legem, forma vectorali unitatibus [[Systema Internationale|MKSA]] scriptam, vis magnetica <math> d \vec \mathbf F_{12} </math> in segmento fili 1 differentiale ob fluxiones in segmento fili 2 differentiale est:

:::<math>
d\vec \mathbf F_{12} = I_1 d\vec \mathbf L_1 \times \vec \mathbf B_2 = I_1 d\vec \mathbf L_1 \times \frac{\mu_0}{4\pi} \frac{I_2 d\vec \mathbf L_2 \times \mathbf{\hat r_{21}}}{r^2} 
</math>

ubi

:<math> d \vec \mathbf L_{1} = \hat I_1 dL_1 </math> est vector quod longitudinem segmenti fili 1 differentialem <math> dL_1 </math> et directionem fluxionis ipsius <math>\hat I_1</math> coniunctim dat,

:<math> \vec \mathbf B_{2}</math> est campus magneticus in segmenti 1 loco ob fluxionem electricum in segmento 2, 

:<math>I_1</math> et <math>I_2</math> sunt fluxiones electricae in quoque duorum segmentorum filorum,

:<math> r =|\vec \mathbf r_1 - \vec \mathbf r_2| </math> est distantia inter segmenta differentialia 1 et 2,

:<math> \mathbf{\hat{r}}_{21} \ \stackrel{\mathrm{def}}{=}\  \frac{\vec \mathbf{r}_1 - \vec \mathbf{r}_2}{\vert \vec \mathbf{r}_1 - \vec \mathbf{r}_2\vert} </math> est directio ad segmenti 1 positionem a segmenti 2 positione,

:<math> \times </math> est [[productum vectoriale]] sive productum crucis, et

:<math> \frac {\mu_o}{4 \pi} = 10^{-7} \frac {N}{A^2}</math> est constans magneticus. 

Circum annum [[1850]] ob labores [[Georgius Stokes|Georgii Stokes]] [[Gulielmus Thomson, baro Kelvin|Guilielmique Thomson]] [[theorema Stokesianum]] inventa fuit,<ref>Vide nota [9] supra.</ref> quae nos sinit transformare legem Biot-Savart ad legem formam differentialem hodiernam post [[Andreas Maria Ampère|Andream Ampere]] nominatam<ref>Haec aequatio legi Biot-Savart aequivalens nominata est post Andream Ampere. Sicut lex Biot-Savart lex Ampere exacta est solum quando fluxiones complexas sunt constantes. Posterius Iacobus Maxwell legem Ampere correxit pro casu fluxionibus variabilibus, ut videat infra.</ref>:

:::<math>\nabla \times \vec \mathbf B = \mu_o \vec \mathbf J</math>

ubi<math>\vec \mathbf J</math> est [[Fluxio electrica#Fluxionis electricae densitas|densitas fluxionis]] ob filos fluxionem habentes complexos et <math>\vec \mathbf B</math> est campus magneticus universus ex illis fluxionibus.

=== Opera Michaelis Faraday ===
[[Fasciculus:M Faraday Th Phillips oil 1842.jpg|thumb|175px|left|[[Michael Faraday]].]]
[[Fasciculus:M Faraday Lab H Moore.jpg|thumb|200px|[[Michael Faraday]] in suo laboratorio.]]
Quamquam ad leges Coulomb et Biot-Savart ascribendas campos magneticos electricosque utimur,
[[campus physicus|notio camporum]] per se primitus concepta est a [[Michael Faraday|Michaelo Faraday]], Professore Chemiae in Fulleriano Instituto Regali Britanniarum, qui annos [[1820]]-[[1873]] magnopere physicam electromagneticam chemiamque aggreditur.<ref>Historia Michaelis Faraday a L. Pearce Williams scripta est ''Michael Faraday: A Biography'' (Da Capo Press, 1987, ISBN 0-306-80299-6).</ref> Antea, vires electricas magneticasque putabantur esse [[actio trans distantiam|actiones trans distantias]] virium gravitatis Newtonianarum similes, sed Faraday theoriam protulit omnes vires esse ob campos qui spatium complent. Ad illos campos describendos, Faraday notionem ''lineae camporum'' comminiscit et postea demonstravit lineas magneticas, quae legi Amperi parent et fontes carent, solum per [[spatium]] circulare.<ref>Re vera Faraday ipse dicebat ''lineas viris'' quando exempli gratia de campo magnetico cogitabat. In suo opere "De natura lineae virium" ([[Anglice]]: [http://books.google.com/books?id=Q7sKAAAAIAAJ&pg=PA407&lpg=PA407&dq=on+the+physical+character+of+the+lines+of+force&source=web&ots=bk7DipWnwe&sig=mnAX-svCMRD3UKrYnx_XsWdhxpg#PPA414,M1|"On the physical character of the lines of force"]) nos certiores facit anno [[1852]]: "I cannot conceive curved lines of force without the conditions of ''a physical existence'' in that intermediate space" [emphasis additur].</ref> Applicantes igitur theorema Gauss ad campos magneticos fontes carentes obtinemus legem Gauss magneticam<ref>Vide notam [8] supra.</ref>:

:::<math>\nabla \cdot \vec \mathbf{B} = 0</math>

Faraday quoque theoriam protulit omnem campum esse idos uni campi universali. Ad hoc hypothesim arguendum quaesivit igitur quomodo transformare inter vires camposque gravitatis, electricitatis, et magnetismi. Et demum Faraday repperit quomodo vim magneticam ad electricam transformare. Campus magneticus commutatus campum electricum creat secundum legem Faraday, quae in forma vectorali-differentiali et in unitatibus [[Systema Internationale|MKSA]] est: 

:::<math>\nabla \times \vec \mathbf{E} = -\frac{\partial\vec \mathbf{B}} {\partial t}</math>

ubi <math>\vec \mathbf E</math> est portio campi electrici a campo magnetico commutante creata.<ref>In commentario laboratoriali, Faraday, die Augusti [[1831]] scripsit: "Have had an iron ring made (soft iron), iron round and 7/8 inches thick and ring 6 inches in external diameter. Wound many coils of copper wire round one half, the coils being separated by twine and calico. . . . Will call this side of the ring A . . . on the other side but separated by an interval was wound wire in two pieces together amounting to about 60 feet in length, the direction being as with the former coils; this side call B . . . continued the contact of A side [primary] with battery but broke and closed alternately contact of B side [secondary] with flat helix. No effect at such times on the needle [of a galvanometer connected to B side]—depends on the change at battery side. Hence is no permanent or peculiar state of wire from B but effect due to a wave of electricity caused at moments of breaking and completing contact at A side. Tried to perceive a spark with charcoal at flat helix junction B side but could find none. Wave apparently very short and sudden." (Qui scriptus adsumptus est ex fonte [13] supra, pag. 182.)</ref> Hoc [[inductantia electromagnetica|inductantiae electromagneticae]] principium utile est basis pro omnibus [[generatrum electricum|generatris]] et [[motrum electricum|motris electricis]].

=== Theoria Iacobi Maxwell et opera Henrici Hertz ===
[[Fasciculus:James-clerk-maxwell 1.jpg|thumb|175px|left|[[Iacobus Maxwell]].]]
[[Iacobus Maxwell]], qui Michaelem Faraday maxime miratus est,<ref>Maxwell Michaeli Faraday anno [[1857]] scripsit: "you are the first person in whom the idea of bodies acting at a distance by throwing the surrounding medium into a state of constraint has arisen, as a principle to be actually believed in . . . nothing is clearer than your description of all sources of force keeping up a state of energy in all that surrounds them."</ref> varias camporum electromagneticorum aequationes in systemate rationale postea ''[[aequationes Maxwellianae|aequationes Maxwellianas]]'' appellato ordinavit.<ref>J. C. Maxwell, "A Dynamical Theory Of The Electromagnetic Field", 1865,
[http://www.zpenergy.com/downloads/Maxwell_1864_1.pdf Pars 1],
[http://www.zpenergy.com/downloads/Maxwell_1864_2.pdf Pars 2],
[http://www.zpenergy.com/downloads/Maxwell_1864_3.pdf Pars 3],
[http://www.zpenergy.com/downloads/Maxwell_1864_4.pdf Pars 4],
[http://www.zpenergy.com/downloads/Maxwell_1864_5.pdf Pars 5],
[http://www.zpenergy.com/downloads/Maxwell_1864_6.pdf Pars 6]; Vide etiam analysim modernam ab
[http://www.zpenergy.com/modules.php?name=Downloads&d_op=getit&lid=60 Andre Waser, "On the Notation of Maxwell's Field Equations, 2000], et paginas Anglicas [http://www.victorianweb.org/science/maxwell/maxwell1.html Victorian Web: James Clerk Maxwell] et [[:en:James Clerk Maxwell]].</ref> In [[symmetria]]{{dubsig}} cum Faraday, Maxwell proposuit correctionem ad legem Amperianam necesse esse, in quo campus magneticus commutans campum electricum creat. Forma vectorali unitatibus [[Systemate Internationale|MKSA]] modo scripta, lex Amperiana a Maxwell correcta igitur est:

:::<math>\nabla \times \vec\mathbf{B} = \mu_0 \varepsilon_0 \frac{\partial \vec \mathbf{E}} {\partial t} +\mu_0 \vec \mathbf{J} </math>

Statim anno [[1861]], Maxwell agnovit hanc correctionem in aliarum aequationum electromagneticarum contextu [[unda electromagnetica|undas electromagneticas]] significare.<ref>Vide pagina 22 in parte III scriptarum suarum anni [[1861]] '[http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf J. C. Maxwell, "On Physical Lines of Force",The London, Edinburg and Dublin Philosophical Magazine and Journal of Science, Ser. 4, March, April, and May 1861]'.</ref> Quia ex [[Aequationes Maxwellianae|aequationibus Maxwellianis]] in vacuo lucis velocitas variaeque proprietates lucis undis similes praecinitur, Maxwell putabat undas electromagneticas ipsas esse lucem. Demum anno [[1887]], [[Heinrich Rudolf Hertz|Henricus Hertz]] per experimenta ingeniosa electromagneticam lucis naturam confirmavit.<ref>[http://historical.library.cornell.edu/cgi-bin/cul.cdl/docviewer?did=cdl334&view=50&frames=0&seq=5 "Electric waves: being researches on the propagation of electric action with finite velocity through space"] Heinrico Rudolph Hertz autore; obtimemus quoque opia per [http://www.amazon.com/dp/1429740361/ Cornell University Library Digital Collections].</ref>

=== Opera Iosephi Thomson et Hendrici Lorentz ===
[[Fasciculus:Hendrik Antoon Lorentz.jpg|thumb|200px|[[Hendricus Lorentz]].]]
Quamquam [[fulmen|fulminae]] et fluxiones prius investigatae erant, [[natura]] earum aliquanto in dubio manebat. Eratne electricitas fluidus vel particulae vel fluxio ex [[aether (physica)|aethere]]? Per experimenta radios cathodicos investigantes cum lagoenis evacuatis [[Iosephus Ioannes Thomson]] anno [[1897]] tandem indentificavit radios cathodicos et electricitatem compositos esse ex particulis minimis [[onus electricum|onus]] negativum [[massa]]mque habentibus quas hodie appellamus [[electron]]es,<ref>Vide [http://nobelprize.org/nobel_prizes/physics/laureates/1906/thomson-bio.html Lectura Praemii Nobeliani Iosephi Thomson] ubi describit suam identificationem existentiae electronis.</ref> nomen anno [[1881]] a Georgio Johnstone Stoney propositum pro minima onus electrici quantitate.<ref>G. Stoney, "On The Physical Units of Nature," Phil.Mag. 11, 381-391, 1881.</ref> Ad argumentum Iosephi Thomson confirmandum, [[Robertus A. Millikan]] anno [[1909]] onus electricum electronis diligenter metitur et determinavit:<ref>Vide [http://nobelprize.org/nobel_prizes/physics/laureates/1923/millikan-bio.html Lectura Praemii Nobeliani Roberti Millikin] ubi describit quomodo onus elecronis meditur.</ref>
:::<math>q_{electron} = -e = -1.6 \times 10 ^{-19} C</math>.

Antea, omnes leges physicae interpretatae erant ex perspectiva virium inter corpora tangibilia vel inter [[corpus|corpora]] et [[aether (physica)|aetherem]], sed annos [[1890]]-[[1905]] physici conantur leges interpretare ex perspectiva virium inter particulas ''elementarias'' vel ''subatomicas'' sicut electrones quae materiam tangibilem constituent. Eos annos [[Hendricus Lorentz]] hypothesim facit omnes fluxiones electricas esse ob particularum onus habentium motum et proposuit [[Aequatio Lorentziana|legem Lorentzianam]] vim electromagneticam dare in eas particulas elementarias.<ref>Vide [http://nobelprize.org/nobel_prizes/physics/laureates/1902/lorentz-bio.html Lectura Praemii Nobeliani Hendrici Lorentz].</ref> In unitatibus [[Systema Internationale|MKSA]], sua lex est:

:::<math>\vec \mathbf{F} = q (\vec \mathbf{E} + \vec \mathbf{v} \times \vec \mathbf{B})</math>

ubi <math>\vec \mathbf v</math> est particulae elementariae onus ''q'' habentis [[velocitas]] momentanea relativa [[aether (physica|aetheri]] immobili. Sua theoria electronica multas materiae proprietates fideliter praecinit inclusas eas ''relativisticas,'' e.g., inter alia, [[contractionem Fitzgerald-Lorentz]].<ref>G. F. Fitzgerald, "The ether and the earth's atmosphere," Science 13, 390, 1889; H. A. Lorentz, [http://www.historyofscience.nl/search/detail.cfm?pubid=615&view=image&startrow=1 "Electromagnetic phenomena in a system moving with any velocity smaller than that of light"], 6, 1903-1904, pp. 809-831, 1904.</ref>

=== Theoria relativitatis, effectum photoelectricum et opera Alberti Einstein ===
[[Fasciculus:Einstein1921 by F Schmutzer 2.jpg|thumb|[[Albertus Einstein]].]]
Hendricus Lorentz in sua theoria electromagnetica postulabat [[systema coordinatorum]] existere [[aether (physica)|aetheri immobili]] affixa, sed anno [[1903]] Lorentz invenit omnes [[transformationes Lorentzianae|transformationes coordinatorum]] inter [[systema coordinatorum|systemata inertialia]] asservare totas aequationes Maxwellianas sine quaquam commutatione.
<ref>Vide notae [24] et [25] supra.</ref> Sua theoria deprehensionem aetheris absolute vetabat. [[Celeritas luminis|Celeritas lucis]], exempli gratia, videtur identica{{dubsig}} in omnibus systematibus coordinatorum inertialibus.

Tandem anno [[1905]] [[Albertus Einstein]] comperit sola duo axiomata satis et necesse esse ad transformationes Lorentz derivandas<ref>[http://www.fourmilab.ch/etexts/einstein/specrel/www/ A. Einstein, "Zur Elektrodynamik bewegter Körper", Annalen der Physik 17, 891-921, 1905.]</ref>:
[[principium relativitatis]] a [[Galilaeus Galilaei|Galilaeo Galilaei]] primitus formulatum<ref>Galilaeus Galilei, "Discorsi e dimostrazioni matematiche intorno a due nuove scienze attenenti alla meccanica," Nederlandia, 1638; vide etiam paginam Anglice [[:en:Galileo's Ship.]]</ref> et constantia celeritatis lucis in omnibus systematibus coordinatorum inertialibus ab [[Experimentum Michelson-Morley|Alberto Michelson et Eduardo Morlei]] anno [[1887]] rescita.<ref>[https://web.archive.org/web/20150715063415/https://www.aip.org/history/gap/PDF/michelson.pdf A. A. Michelson and E.W. Morley, Philos. Mag. S.5, 24 (151), 449-463, 1887].</ref> Demum Einstein statuit [[relativitas specialis|theoriam relativitatis specialis]] demonstrando transformationes Lorentz fundamentaliores esse quam aequationes Maxwellianae et monstrando varias emendationes [[mechanica Newtoniana|mechanicae Newtonianae]] necesse esse.<ref> [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ A. Einstein, "Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?", Annalen der Physik 18, 639-641, 1905]; Et vide [http://nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-bio.html Lectura Praemii Nobeliani Alberti Einstein, "Fundamental Ideas and Problems of the Theory of Relativity."]</ref> Ex illa perspectiva relativistica campus magneticus ex campo electrico naturaliter oritur ob systematis coordinatorum motum.

Quia Lorentz monstraverat nemo aetherem deprehendere posse, Einstein abnuit postulare aetherem existire et potius demonstavit lucem compositum esse ex [[photon]]ibus quae particulae pro motu suo aetherem non requirunt.<ref>[https://web.archive.org/web/20080423195339/http://dbserv.ihep.su/~elan/src/einstein05/eng.pdf A. Einstein, "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt", Annalen der Physik 17, 132–148, 1905.]</ref> Secundum [[theoria photonica Einstein-Planck|theoriam Einstein photonicam]] [[energia]] ''E'' photonis est:

:::<math>E = h f</math>

ubi ''f'' est [[frequentia]] undae electromagneticae associatae et constans [[Maximilianus Planck|Planckis]] <math>h = 6.626 \times 10^{-34} Js</math>. Notio [[photon]]ium multas res explicabat, effectum photoelectricum ab [[Heinrich Rudolf Hertz|Hendrice Hertz]] et [[Philippus Lenard|Phillippe Lenard]] repertum inclusum.<ref>P. E. A. Lenard, Ann. Pkysik, 8, 149, 1902; vide etiam [http://nobelprize.org/nobel_prizes/physics/laureates/1905/lenard-bio.html lectura Praemii Nobeliani Phillippi Lenard].</ref>

=== Theoria camporum quantica ===
[[Fasciculus:Paul Dirac, 1933, head and shoulders portrait, bw.jpg|thumb|175px|left|[[Paulus Dirac]].]]
Imprimis Einstein negabat aetherem existire, sed mox circum annum [[1920]] Einstein ipse invenit ideam aetheris necesse esse pro una [[relativitas generalis|theoria relativitatis generalis]] satisfactoria cum interactionibus localibus et sine [[actiones trans distantias|actionibus trans distantias]]. 
<ref>[https://web.archive.org/web/20070419024649/http://www.tu-harburg.de/rzt/rzt/it/Ether.html A. Einstein, "Aether and the theory of Relativity" University of Leyden, Germany, 1920].</ref> Einsteini aether simpliciter erat sedes campi electromagnetici gravitatisque et compositum erat nec ex materia nec ex partibus positionem distinctam habentibus. Mox quoque post experimentum Geiger-Marsden,<ref>[https://web.archive.org/web/20080102232956/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/GM-1909.html H. Geiger and E. Marsden "On a Diffuse Reflection of the α-Particles," Proceedings of the Royal Society, Series A 82, 495–500, 1909.]</ref> physicus [[Ernestus Rutherford]] invenit theoriam Maxwellianam Lorentzianamque insatis esse ad electrones in atomos discribendam quia cum sola ea theoria electrones in [[nucleus atomi|nucleum]] cadendum sunt.<ref>[https://web.archive.org/web/20080114190208/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Rutherford-1911/Rutherford-1911.html E. Rutherford, "The Scattering of α and β Particles by Matter and the Structure of the Atom," Philosophical Magazine, Series 6 21: 669–688, 1911.]</ref> Ergo [[mechanica quantica]] nascitur ut nova principia reperiantur.<ref>[https://web.archive.org/web/20060201234749/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Bohr/Bohr-1913a.html N. Bohr, "On the Constitution of Atoms and Molecules," Philosophical Magazine, Series 6, Bol. 26. pg. 1-25, 1913]; Vide etiam [http://nobelprize.org/nobel_prizes/physics/laureates/1933/schrodinger-bio.html Lectura Praemii Nobeliani Ervinis Schrodinger].</ref>

[[Paulus Dirac]], cuius magnum opus ''Principia Mechanicae Quanticae'' ([[Anglice]] ''The Principles of Quantum Mechanics'') anno [[1930]] divulgatum est,<ref>P. A. M. Dirac, "The Principles of Quantum Mechanics," Oxford University Press, 1st edition 1930; quarta edition 1982. ISBN 0-19-852011-5; confer etiam theoriam photonicam Einsteinis citata in nota 31 supra.</ref> primam theoriam [[electrodynamica quantica|electrodynamicae quanticae]] creavit in quo photones repraesentant minimas quantitates energiae quas campus electromagneticus dat et capit. Qui, photonicam Einsteinis notionem per suam doctrinam explicans, comperit energias possibiles{{dubsig}} in campo electromagnetico esse:

:::<math>E_n = h f \left( n+\frac {1} {2} \right) </math>

ubi ''n'' est numerus integrus photonium in campo electromagnetico. Postmodo [[Ricardus Feynman|Richardus Feynman]], [[Freeman Dyson]], [[Julianus Schwinger]], et [[Sin-Itiro Tomonaga]] theoriam [[electrodynamica quantica|electrodynamicae quanticae]] annos [[1940]] magnopere promoverunt creando primam theoriam adusque satisfactoriam in quo [[electron]]es, [[positron]]es, et [[photon]]es ex [[aether (physica)|aethere]] (sive campo quantico) creantur et delentur.<ref>[http://nobelprize.org/nobel_prizes/physics/laureates/1965/ Lecturae Praemii Nobeliani Ricardi Feynman, Julianique Schwinger et Sin-Intiri Tomonagae.]</ref> Itaque physici inveniunt particulis opus esse et campi et aetheri ut eorum vires fiantur. Differentia inter suam aetherem et Lorentzianam in status motus non potendo constabat.

Dirac habetur conditor electrodynamicae quanticae, primus qui id vocabulo usus est. Notionem polarizationis vacui [[decennium 194|decennio 194]] ineunte introduxit.<!-- Suus [[liber]] ''Principles of Quantum Mechanics,'' ('Principia Mechanicae Quanticae'), anno 1930 editum, est lapis<!- -landmark- -> in [[historia scientiae]].<!- - It quickly became one of the standard textbooks on the subject and is still used today.- -> Anno 1931, Dirac probavit existentiam singuli monopoli magnetici in [[universum|universo]] satis esse ad explicandam observatam oneris electrici quantizationem.<!- -This proposal received much attention, but there is to date no convincing evidence for the existence of magnetic monopoles.- ->
[[Fasciculus:Niels Bohr.jpg|thumb|[[Nicolaus Bohr]].]]-->

== Unitates in aequationibus electromagneticis ==
Omnes [[mensura metrica|systemata mensurae metrica]] basim habent in unitatibus [[metrum|metri]], [[chiliogramma]]tis et [[secundum|secundi]], qui sunt usitati. Differentes autem systemata fieri possunt, in cuius definitione aequationes electromagneticae pars maior habent. 

=== Systema Unitatium Hodiernum MKSA ===
[[Systema Internationale|Systema metricum Internationale]] (sive SI sive MKSA) circum annum [[1960]] creata<ref>[http://www.bipm.org/en/si/ Bureau International des Poids et Mesures]; 
</ref> habet unitates cuius magnitudines pro mensura laboratoriale sunt utiles. 

Inter suas unitates principales sunt: [[metrum]] (m), [[chiliogramma]] (kg), [[secundum]] (s), et [[Amperium]] (A).<ref>Aliae unitates primarias sunt [[Kelvin]] (K), [[Moles (unitas)|Moles]] (mol), et [[Candela]] (cd). Unitates secundarias sunt, exempli gratia, de superficie metrum quadratum (m<sup>2</sup>), de volumine metrum cubicum (m<sup>3</sup>) de vire Newtonium (N = kg m/s<sup>2</sup>), et de tensio electrico Voltium (V = N m/A s).</ref> Fluxionis electricae unitas [[Amperium]] definitur postulando constantem magneticum in legem Biot-Savart esse accurate

:::<math> \frac {\mu_o}{4 \pi} = 10^{-7} \; \frac {kg \; m}{A^2 \; s^2}</math>. 

Oneris electrici unitas [[Coulomb (unitas)|Coulombium]] tunc ex fluxionis unitate Amperio definitur sicut quantum oneris electrici in unum secundum movet si fluxio electrica est unum Amperium, e. g. <math> C = A \cdot s </math>. Unitas campi magnetici ''Tesla'' (T) quoque definitur ut

:::<math>Tesla = \frac{N}{A \; m} = \frac{kg}{A \; s^2} </math>

et ut vis Lorentz scripta sit

:::<math>\vec \mathbf{F} = q (\vec \mathbf{E} + \vec \mathbf{v} \times \vec \mathbf{B})</math>.

=== Systema Unitatium Antiguum Gaussianum CGSF ===
[[Systema metricum Gaussianum]] (sive Gaussianum sive CGSF) est antiguum [[systema]] circum annum [[1874]] creatum.<ref>[http://www.bipm.org/en/si/history-si/ De historia Systematis Internationalis]
</ref> Multi physici etiam hodie systema Gaussianum malunt quia id habet unitates identicas{{dubsig}} pro campis magneticis et campis electris, quod est magis utile ad theoriam electromagneticam relativisticamque describendam. 

[[Systema metricum Gaussianum|Systema Gaussianum CGSF]] [[sex]] unitates primarias habet; 
<ref>Aliae primariae sunt [[Kelvin]] (K) et [[Moles (unitas)|Moles]] (mol). Unitates secundarias sunt, per exemplos, de superficie centimetrum quadratus (cm<sup>2</sup>), de volumine centimetrum cubicum (cm<sup>3</sup>), de vire [[dynium]] (dyn = gcm/s<sup>2</sup>), et de tensio electrico statvoltium (statV = dyn cm/Fr).</ref> inter principales earum sunt: [[centimetrum]] (cm), [[gramma]] (g), [[secundum]] (s), et [[Franklin]] (Fr). Oneris electrici unitas [[Franklin]] (appellata quoque ''esu'' pro "electrostatica unitate") definitur postulando constantem electricam in legem Coulomb esse accurate

:::<math> \frac {1}{4 \pi \epsilon_o} =  1 \; \frac {dyn \; cm^2}{Fr^2} 
= 1 \; \frac {g \; cm^3}{Fr^2 \; s^2}</math>

et unitas fluxionis est igitur ''Fr/s.'' Etiam unitas campi magnetici ''Gauss'' (G)

:::<math>Gauss = \frac{dyn}{Fr} = \frac{g \; cm}{Fr \; s^2}</math>

definitur ut campus electricus commensurabilis cum campo magnetico sit, et vis Lorentziana scripta sit

:::<math>\vec \mathbf{F} = q (\vec \mathbf{E} + \vec \frac {\mathbf{v}}{c} \times \vec \mathbf{B})</math>

ubi ''c'' est [[celeritas lucis]]. Ob eam definitionem, [[aequationes Maxwellianae]] in formam simpliorem tranformantur atque lex Ampere a Maxwell correcta simpliciter fit:

:::<math>\nabla \times \vec\mathbf{B} = \frac {1}{c} \frac{\partial \vec \mathbf{E}} {\partial t} + \frac {4 \pi} {c} \vec \mathbf{J} </math>

== Notae ==
<references />

== Fontes ==
* Gillispie, Charles C., ed. [[1970]]-[[1980]]. ''Dictionary of Scientific Biography.'' 16 vol. Novi Eboraci: Charles Scribner and Sons. ISBN 0-684-10114-9. + Supplement II, ed. Frederic Lawrence Holmes, 2 vols., 1990. ISBN 0-684-16962-2.
* Griffiths, David J. [[1998]]. ''Introduction to Electrodynamics.'' Ed. 3a. Prentice Hall. ISBN 0-13-805326-X.
* Jackson, John David. [[1975]] ''Classical Electrodynamics.'' Editio 2a. Novi Eboraci: John Wiley & Sons. ISBN 0-471-43132-X.
* Mottelay, Paul FLeury. [[1922]]. ''Bibiographical History of Electricity and Magnetism.'' Richard Clay & Sons, Ltd. ISBN 1-888262-54-0.
* Purcell, Edward M. [[1985]]. ''Electricity and Magnetism.'' Berkeley Physics Course Volume 2, Second Edition. Bostoniae: McGraw Hill. ISBN 0-07-004908-4.

== Nexus externi ==
* Paginae Anglice [[:en:Maxwell's Equations|"Maxwell's Equations"]] et [[:en:Electromagnetism|"Electromagnetism"]]
{{CommuniaCat|Electromagnetism|physicam electromagneticam}}

[[Categoria:Paginae mensis]]
[[Categoria:Physica]]