Fontem paginae Constans electrica inspicere

{{Capsa tabellaria
	|; Constans electrica
	| Dimensiones: {{Dimensiones|longitudo=-3|massa=-1|onus electricum=2|tempus=2}}
	| Magnitudo: {{val|8.8541878188|(14)|e=-12|u=[[coulomb (unitas)|C]]<sup>2</sup>&thinsp;[[chiliogramma|kg]]<sup>−1</sup>&thinsp;[[metrum|m]]<sup>−3</sup>&thinsp;[[secundum|s]]<sup>2</sup>}}
}}

{{Res|Constans electrica}} vel {{Res|permittivitas vacui}} vel {{Res|constans dielectrica vacui}} ({{mvar/epsilon_0}} notata) est [[quantitas constans|constans]] [[physica]] quae, dimensiones [[onus electricum|oneris electrici]], [[longitudo|longitudinis]] et [[vis|roboris]] inter eas nectendo, mētītur quam densus [[campus electricus]], propter quoddam onus, oriri possit<!-- indir. interr. --> (idcirco magnitudinem {{Creanda|en|Permittivity|d|Q211569|permittivitas electrica|permittivitatis electricae}} [[vacuum|vacui]] statuit).

Constans electrica sic definiri potest,

:<math>\varepsilon_{0}=\frac{1}{4\pi k_{e}}=\frac{1}{\mu_{0}c^{2}}=\frac{e^{2}}{2\alpha hc}=\frac{e^{2}}{4\pi\alpha\hbar c}</math>

ubi

* {{mvar/k_e}} est [[constans Coulombiana]]
* {{mvar/mu_0}} est {{Creanda|en|Vacuum permeability|d|Q1515261|constans magnetica}}
* {{mvar/c}} est [[celeritas lucis]] in vacuo
* {{mvar/Planck}} et {{mvar/hbar}} sunt [[constans Planckiana]] et [[constans Planckiana minuta]]
* {{mvar/phyalpha}} est [[constans structurae subtilis]]
* {{mvar/phye}} est onus electricum elementare ({{*ie}} onus [[proton]]is vel [[electron]]is)

Secundum unitates [[Systema internationale unitatum|Systematis internationalis unitatum]], constanti electricae congruunt {{val|8.8541878188|(14)|e=-12|u=[[coulomb (unitas)|C]]<sup>2</sup>&thinsp;[[chiliogramma|kg]]<sup>−1</sup>&thinsp;[[metrum|m]]<sup>−3</sup>&thinsp;[[secundum|s]]<sup>2</sup>}}.<ref>{{cite web
	| url = https://physics.nist.gov/cgi-bin/cuu/Value?ep0
	| title = 2022 CODATA Value: vacuum electric permittivity
	| date = [[Maius|Maio]] [[2024]]
	| work = The NIST Reference on Constants, Units, and Uncertainty
	| publisher = [[National Institute of Standards and Technology|NIST]]
}}</ref>

Exempli gratia, vis inter duo onera electrica punctiformia, secundum {{Creanda|en|Coulomb's law|d|Q83152|lex Coulombiana|legem Coulombianam}}, scribi potest,

:<math>F_\text{C} = \frac{1} {4 \pi \varepsilon_0} \frac{q_1 q_2} {r^2}</math>

ubi {{mvar|1=q<sub style="font-style: normal;">1</sub>}} et {{mvar|1=q<sub style="font-style: normal;">2</sub>}} sunt onera electrica, {{mvar|r}} est eorum mutua separatio, et {{math|{{vfrac|1|4{{mvar/pi}}{{mvar/epsilon_0}}}}}} est alius modus [[constans Coulombiana|constantem Coulombianam]] scribendi.

Eadem constans in [[aequationes Maxwellianae|aequationibus Maxwellianis]] quoque, quae faciem campi electrici [[campus magneticus|magnetici]]<nowiki />que et [[radiatio electromagnetica|radiationis electromagneticae]] describunt, incurritur.

In [[ars electrica|arte electrica]], constans {{mvar/epsilon_0}} saepe adhibetur unitas ad permittivitatem variarum {{Creanda|en|Dielectric|d|Q184996|materies dielectrica|dielectricarum materierum}} mētiendam.

== Historia ==
[[Fasciculus:Inverse square law.svg|thumb|upright=1|In hac imagine {{mvar|S}} est onus electricum punctiforme. Sive fons sive superficies [[sphaera]]rum quae fontem circumdant eandem quantitatem habent, sed quanto magis superficies a fonte distat, tanto magis eadem quantitas per maiorem [[area (geometria)|aream]] diluitur (secundum [[lex quadratica inversa|legem quadraticam inversam]]). Area sphaerae per aequationem {{math|1={{mvar|S}} = 4{{mvar/pi}}{{mvar|r}}<sup>2</sup>}} computatur.]]

[[Carolus de Coulomb]] primum intellexit vim inter duo onera electrica punctiformia ({{mvar|1=q<sub style="font-style: normal;">1</sub>}} et {{mvar|1=q<sub style="font-style: normal;">2</sub>}}), in spatio vacuo posita atque quoddam intervallum {{mvar|r}} inter se distantia, hanc formam habere:

: <math> F = k_{\text{e}} \frac{q_1 q_2}{r^2} </math>

Postea, intellectum est in condicionibus geometriae [[sphaera|sphaericae]] oportere factorem {{math|4{{mvar/pi}}}} in [[computatio]]ne includere, dehinc quandam constantem {{mvar|1=k<sub>e</sub><span style="font-style: normal;">′</span>}} in locum constantis Coulombianae ({{mvar/k_e}}) substituere, et eidem aequationi sequentem formam dare:

: <math> F = k'_{\text{e}} \frac{q_1 q_2}{4 \pi r^2} </math>

Haec ratio computandi appellatur “rationalizatio”, quia si novae constanti {{mvar|1=k<sub>e</sub><span style="font-style: normal;">′</span>}} eadem magnitudo constantis {{mvar/k_e}} assignatur, onera electrica cessant esse [[numerus irrationalis|numeri irrationales]].

In locum constantis {{mvar|1=k<sub>e</sub><span style="font-style: normal;">′</span>}} eius inversio {{math|1={{mvar/epsilon_0}} = {{vfrac|1|{{mvar|1=k<sub>e</sub><span style="font-style: normal;">′</span>}}}} = {{vfrac|1|4{{mvar/pi}}{{mvar/k_e}}}}}} postremo substituta est constans primaria suo iure, quae formam hodiernam legis Coulombianae gignit:

:<math>F=\frac{q_1 q_2}{4\pi r^2 \varepsilon_0}</math>

Sic anno [[1893]] {{Creanda|en|Oliver Heaviside|d|Q154345|Oliverius Heaviside}} in suo libro {{Op|Theoria electromagnetica}} talem methodum descripsit:<ref name="heaviside">{{cite book
	| last = Heaviside
	| first = Oliverius
	| author-link = Oliverius Heaviside
	| year = [[1893]]
	| title = Theoria electromagnetica
	| publisher = The D. van Nostrand Company
	| place = [[Londinium|Londinii]]
	| volume = 1
	| page = xi
	| url = https://books.google.com/books?id=_Zk3AAAAMAAJ
	| via = Google Books
}}. Alius fons eiusdem textūs: {{cite web
	| title = Heaviside [[1893]]: ''Electromagnetic Theory'' volume 1 ...
	| type = [[optical character recognition|OCR]] text
	| department = wiki
	| website = Open Source Ecology Germany (wiki.opensourceecology.de)
	| url = https://wiki.opensourceecology.de/Heaviside_1893
}}</ref>

{{Folium memoratum|
{{Barbarice|lingua=en|It is not long since it was taken for granted that the common electrical units were correct. That curious and obtrusive constant {{math|4{{mvar/pi}}}} was considered by some to be a sort of blessed dispensation, without which all electrical theory would fall to pieces. I believe that this view is now nearly extinct, and that it is well recognised that the {{math|4{{mvar/pi}}}} was an unfortunate and mischievous mistake, the source of many evils.}}

{{Barbarice|lingua=en|In plain English, the common system of electrical units involves an irrationality of the same kind as would be brought into the metric system of weights and measures, were we to define the unit area to be the area, not of a square with unit side, but of a circle of unit diameter. The constant {{mvar/pi}} would then obtrude itself into the area of a rectangle, and everywhere it should not be, and be a source of great confusion and inconvenience. So it is in the common electrical units, which are truly irrational.}}

{{Barbarice|lingua=en|Now, to make a mistake is easy and natural to man. But that is not enough. The next thing is to correct it: When a mistake has once been started, it is not necessary to go on repeating it for ever and ever with cumulative inconvenience.}}

{{Ast}}

Non pridem pro concesso sumebatur unitates oneris electrici esse rectas. Illa curiosa et molesta [[quantitas constans|constans]] {{math|4{{mvar/pi}}}} a multis putabatur quasi quaedam benedicta dispensatio, sine qua quaecumque theoria electrica dilapsura erat. Credo hodie hanc opinionem esse paene exstinctam, et constantem {{math|4{{mvar/pi}}}} bene agnosci esse infelix perniciosumque mendum ac fontem multorum malorum.

Id est, commune systema unitatum electricarum quandam irrationalitatem servat eodem genere quod introduceretur si in [[mensura metrica|systemate metrico ponderum et mensurarum]] unitatem [[area (geometria)|areae]] definiremus haud [[quadrum]] latere unius unitatis, sed [[circulus|circulum]] [[diametros|diametro]] unius unitatis. Ideo numerus {{mvar/pi}} se obtruderet in aream [[rectangulum|rectanguli]] et ubicumque esse non oporteat, atque fieret fons magnae confusionis et incommodi. Sic evenit in communibus unitatibus electricis, quae vere sunt [[numerus irrationalis|irrationales]].

Facile autem est, et naturale, [[Errare human est|homini errare]]. Sed postea error corrigendus est: Cum quidem semel occeptus sit error, non necesse est semper et semper, crescente incommodo, eum iterare.

}}

{{Norma dextra|
―[[Oliverius Heaviside]] (1893). {{Op|Theoria electromagnetica}}. Tom. 1.<ref name="heaviside" />
}}

== Notae ==
<references />

{{NexInt}}
* [[Ars electrica]]
* [[Constans gravitatis]]
* [[Constans Boltzmanniana]]
* [[Constans Coulombiana]]
* [[Constans Planckiana]]
* [[Carolus de Coulomb]]
* [[Electrificina]]
* [[Electricitas]]
* [[Electrochemia]]
* [[Electron]]
* [[Unitates Planckianae]]
* [[Unitates Stoneyanae]]

[[Categoria:Electricitas]]
[[Categoria:Notiones in physica]]
[[Categoria:Physica]]
[[Categoria:Quantitates constantes physicae]]