Qada elektrîkê (Electric field)

Qadeke elektrîkî (ku wekî E-qad jî tê zanîn) qadeke fîzîkî ye ku keriyên barkirî yên elektrîkî, wekî elektronan, dorpêç dike. Di elektromanyetîzma klasîk de, qada elektrîkî ya ku ji hêla barekî yekane an komek bajaran ve tê çêkirin, kapasîteya wan a ku li ser tiştekî din ê barkirî Hêzên kişandin an dûrxistinê bi kar bînin, diyar dike. Keriyên barkirî Hêzên kişandinê bi kar tînin dema ku barên wan nîşanên dijber hebin (yek erênî, yek neyînî), û dema ku barên wan nîşana heman parve bikin, dûr dikevin. Wekî encam, hebûna du bajaran ji bo derketina van Hêzên hevdu pêwîst e. Van Hêzan ji hêla yasaya Coulomb ve têne vegotin, ku destnîşan dike ku Hêz bi Mezinahiya bajaran zêde dibe û bi zêdebûna dûrahiya di navbera wan de kêm dibe. Di warê têgehî de, hêza qada elektrîkî ya tiştekî rasterast bi Mezinahiya barê wê ve têkildar e, nêzîkî tiştên barkirî xurtir dibe û bi dûrahiyê re qels dibe. Qadên elektrîkî hem ji barên elektrîkî yên Rawestayî hem jî ji herikînên elektrîkî yên Dînamîk û bi demê re diguherin derdikevin. Hem qadên elektrîkî hem jî yên manyetîk xuyangkirinên qada elektromanyetîk a yekbûyî ne, ku elektromanyetîzm yek ji çar têkiliyên Bingehîn ên di xwezayê de pêk tîne.

Qadên elektrîkî di gelek warên Fîzîkê de JGirîng in û Bi berfirehî di endezyariya elektrîkê de têne bikaranîn. Mînak, di Fîzîka atomî û kîmyayê de, têkiliya elektrostatîk a di navbera Sîsika Atomê û elektronan de Hêza Bingehîn pêk tîne ku van keriyan Di nav de atoman de girêdide. Bi heman awayî, têkiliya qada elektrîkî ya di navbera atoman de pêvajoyên girêdana kîmyewî dimeşîne ku molekulan Form dikin.

Qada elektrîkî bi fermî wekî qadeke vektorî tê pênasekirin ku ji her xala fezayî re Hêza per yekîneya barê destnîşan dike ku ji hêla barekî ceribandinê yê bêdawî piçûk, Rawestayî, erênî ve tê hîskirin ku li wê xalê hatiye bicihkirin. Yekîneya wê ya SI volt per metre (V/m) ye, ku ji aliyê pîvanê ve wekhevî newton per coulomb (N/C) ye.

Danasîn

Qada elektrîkî li her koordînata fezayî wekî Hêza ku li ser barekî ceribandinê yê bêdawî piçûk, Rawestayî, erênî li wê cihê tê sepandin, ku bi Mezinahiya wî barî ve tê normalîzekirin, tê têgihîştin. Ji ber ku qada elektrîkî Bi Bingehîn ji hêla Hêzê ve tê pênasekirin, Pîvaneke vektorî ku hem Mezinahî hem jî alî heye, Wekî encam, wekî qadeke vektorî tê temsîlkirin. Têkiliya di navbera du bajaran de bi riya qada elektrîkî wekî têkiliya gravîtasyonê ya di navbera du girseyan de ye, ku her du jî yasaya berevajî-çarçikî ya li ser dûrahiyê dişopînin. Ev prensîb bingeha yasaya Coulomb pêk tîne, ku destnîşan dike ku, ji bo barên Rawestayî, hêza qada elektrîkî rasterast bi barê Çavkaniyê ve têkildar e û berevajî bi çarçika dûrahiya ji wê ve têkildar e. Wekî encam, du qatkirina barê Çavkaniyê dibe sedema zêdebûnek du qat di qada elektrîkî de, dema ku çûna du qat dûrahiya ji Çavkaniyê hêza qadê li wê xalê dadixe çaryeka nirxa wê ya destpêkê.

Qada elektrîkê bi gelemperî bi karanîna xêzên qadê tê xuyakirin, ev konsepta ku ji aliyê Michael Faraday ve hatiye pêşxistin, û navlêkirina wî ya orîjînal 'xêzên hêzê' carinan hîn jî tê bikaranîn. Aliyê van xêzan li her xalekê, aliyê qadê nîşan dide. Ev nîşandana grafîkî taybetmendiyeke bikêr pêşkêş dike ku, dema her xêzek mîqdarek wekhev a herikînê nîşan dide, ziravbûna qadê rasterast bi tîrbûna xêzan re rêjeyî ye. Ji bo barên rawestayî, xêzên qada elektrîkê çend taybetmendiyên bingehîn nîşan didin: ew her dem ji barên pozîtîf derdikevin û di barên negatîf de diqedin, ew rûxarên konduktorên baş bi awayekî perpendîkular dibirin, û ew ne hevdu dibirin û ne jî xelekên girtî çêdikin. Pêwîst e ku were zanîn ku xêzên qadê amûrek têgînî ne; qada elektrîkê bi xwe bi berdewamî hemû feza dagir dike, tevî herêmên di navbera xêzên xêzkirî de. Hejmara xêzên nîşandî dikare were sererastkirin da ku reng bide asta xwestî ya rastbûna nîşandanê. Şaxa fîzîkê ya ku ji bo lêkolîna qadên elektrîkê yên ku ji aliyê barên rawestayî ve têne çêkirin hatiye veqetandin, wekî elektrostatîk tê binavkirin.

Qanûna Faraday têkiliya di navbera qada manyetîk a bi demê ve girêdayî û qada elektrîkê de zelal dike. Bi taybetî, yek ji formûlasyonên Qanûna Faraday destnîşan dike ku curl a qada elektrîkê wekhev e bi derîvatîfa demkî ya negatîf a qada manyetîk. Wekî encam, di nebûna qada manyetîk a bi demê ve diguhere de, qada elektrîkê wekî parastî tê pênasekirin, ango, ew bê-curl e. Ev cudahî hebûna du kategoriyên sereke yên qadên elektrîkê pêşniyar dike: qadên elektrostatîk û yên ku ji aliyê qadên manyetîk ên bi demê ve diguherin ve têne çêkirin. Her çend taybetmendiya bê-curl a xwerû ya qadên elektrîkê yên rawestayî analîzek hêsantir di nav elektrostatîkê de hêsan dike jî, qadên manyetîk ên bi demê ve diguherin bi gelemperî wekî beşek bingehîn a qada elektromanyetîk a yekbûyî têne têgînkirin. Dîsîplîna akademîk a ku ji bo lêkolîna qadên manyetîk û elektrîkê yên ku guhertoya demkî nîşan didin hatiye veqetandin, wekî elektrodînamîk tê zanîn.

Formûlasyona Matematîkî

Qadên elektrîkê ji du çavkaniyên sereke derdikevin: barên elektrîkê, wekî ku ji aliyê qanûna Gauss ve hatiye diyar kirin, û qadên manyetîk ên bi demê ve diguherin, wekî ku ji aliyê qanûna biderxistinê ya Faraday ve hatiye vegotin. Bi hev re, ev qanûnên bingehîn bi têra xwe tevgera qada elektrîkê taybetmendî dikin. Lêbelê, ji ber ku qada manyetîk bi xwe wekî fonksiyona qada elektrîkê tê îfadekirin, hevkêşeyên ku her du qadan birêve dibin bi awayekî hundirîn girêdayî ne. Ev hevkêşeyên girêdayî bi hev re hevkêşeyên Maxwell pêk tînin, ku her du qadan bi awayekî berfireh di warê bar û herikan de vedibêjin.

Elektrostatîk

Di şertên rewşa domdar de, ku bi barên û herikînên rawestayî tê diyar kirin, bandora biderxistinê ya Maxwell-Faraday tune ye. Wekî encam, her du hevkêşeyên encamdar—qanûna Gauss ∇<!-- ∇ --> ⋅<!-- ⋅ --> E = ρ<!-- ρ --> ε<!-- ε -->28 {\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}} û qanûna Faraday bêyî terma wê ya biderxistinê ∇<!-- ∇ --> ×<!-- × --> E =60 {\displaystyle \nabla \times \mathbf {E} =0} —bi hev re qanûna Coulomb pêk tînin. Ev qanûn Hêz (mandatory) ku ji hêla barekî elektrîkî q80 {\displaystyle q_{1}} li pozîsyona r104 {\displaystyle \mathbf {r} _{1}} li ser barekî din q126 {\displaystyle q_{0}} ku li pozîsyona r150 {\displaystyle \mathbf {r} _{0}} ye, bi vî awayî pîvan dike:

• Terma ${\displaystyle \mathbf {F} _{01}}$ Hêz (mandatory) ku ji hêla keriyeke barkirî q56{\displaystyle q_{1}} ve li ser keriyeke barkirî q34{\displaystyle q_{0}} tê sepandin, nîşan dide.
• ε3 permîtîvîteya Feza (mandatory) vala nîşan dide.
• Sembol (mandatory) ${\displaystyle {\hat {\mathbf {r} }}_{01}}$ vektoreke yekîne destnîşan dike ku ji r45{\displaystyle \mathbf {r} _{1}} derdikeve û ber bi r69{\displaystyle \mathbf {r} _{0}} ve nîşan dide.
• Nîşankirina ${\displaystyle \mathbf {r} _{01}}$ behsa vektora jicîhûwarkirinê dike ku ji r36{\displaystyle \mathbf {r} _{1}} heta r60{\displaystyle \mathbf {r} _{0}} dirêj dibe.

JGirîng (mandatory) e ku Nota (mandatory) were girtin ku ε<!-- ε -->11{\displaystyle \varepsilon _{0}}, ku permîtîvîteya Feza (mandatory) vala temsîl dike, divê bi ${\displaystyle \varepsilon }$, ku permîtîvîteya Navgîn (mandatory) nîşan dide, were guhertin, dema bar Di nav de (mandatory) Navgîn (mandatory)ên ne-vala de cih digirin.

Ev qada elektrîkê li cihê r14 {\displaystyle \mathbf {r} _{0}} temsîl dike, ku ji aliyê barê xalî yê ${\displaystyle q_{1}}$ ve tê çêkirin. Ev Fonksiyon-a vektorî Hêza Coulombê ya ser yekîneya barê diyar dike, ku barekî ceribandinê yê pozîtîf dê pê re rû bi rû bimîne li cihê r §6061§ {\displaystyle \mathbf {r} _{0}} . Ji ber ku ev formula hem Mezinahî û hem jî aliyê qada elektrîkê li her xalek cîhî r §8485§ {\displaystyle \mathbf {r} _{0}} diyar dike (ji bilî cihê barê bi xwe, ${\displaystyle \mathbf {r} _{1}}$, ku li wir qad dibe Bêdawî), ew bi xwezayî qadek vektorî pênase dike. Formula jorîn nîşan dide ku qada elektrîkê ya ku ji barekî xalî derdikeve, her dem ji bar dûr dikeve heke ew pozîtîf be, û ber bi wê ve diçe heke ew negatîf be. Herwiha, Mezinahîya wê bi rêjeyî bi çargoşeya berevajî ya dûrahiya ji bar kêm dibe.

Hêza Coulombê ya ku li ser barekî bi Mezinahî ${\displaystyle q}$ li her xalek cîhî ya diyarkirî tê sepandin, bi berhema bar û qada elektrîkê ya Niha li wê cihê taybetî tê diyarkirin, wekî ku bi hevkêşeya $${\displaystyle \mathbf {F} =q\mathbf {E} .}$$ tê îfadekirin. Pergala Navneteweyî ya Yekîneyan (SI) yekîneya qada elektrîkê wekî newton per coulomb (N/C) an jî, bi heman awayî, volt per metre (V/m) diyar dike. Dema ku bi yekîneyên Baz ên SI ve tê îfadekirin, ev bi kg⋅m⋅s⁻³⋅A⁻¹ re têkildar e.

Prensîba Superpozîsyonê

Xêzîtiya ku di hevkêşeyên Maxwell de heye destnîşan dike ku zeviyên elektrîkê li gorî prensîba superpozîsyonê tevdigerin. Ev prensîb diyar dike ku tevahiya zeviya elektrîkê li her xalek diyarkirî, ku ji gelek baran derdikeve, wekhev e bi kombûna vektorî ya zeviyên elektrîkê yên ku ji her barekî takekesî li heman xalê têne hilberandin. Ev prensîba Bingehîn ji bo diyarkirina zeviya elektrîkê ya ku ji komek barên xalî tê hilberandin, pir bi qîmet e. Bi texmîna ku barên q10 , q 20 , … , q n {\displaystyle q_{1},q_{2},\dots ,q_{n}} li Koordînatên fezayî R59 , R 71 , … , R n {\displaystyle \mathbf {R} _{1},\mathbf {R} _{2},\dots ,\mathbf {R} _{n}} Rawestayî ne, û di nebûna herikînan de, prensîba superpozîsyonê destnîşan dike ku zeviya elektrîkê ya encam kombûna zeviyên ku ji her perçeyek takekesî têne hilberandin e, wekî ku ji hêla qanûna Coulomb ve hatî pênasekirin.

• Têgîna ${\displaystyle {\hat {\mathbf {r} }}_{i}}$ vektora yekîneyê nîşan dide ku ji xala ${\displaystyle \mathbf {R} _{i}}$ ber bi xala ${\displaystyle \mathbf {r} }$ ve ye.
• Têgîna ${\displaystyle \mathbf {r} _{i}}$ vektora jicîhûwarkirinê nîşan dide ku ji xala ${\displaystyle \mathbf {R} _{i}}$ derdikeve û li xala ${\displaystyle \mathbf {r} }$ diqede.

Belavkirinên Barê Berdewam

Prensîba superpozîsyonê diyarkirina qada elektrîkê ya ku ji hêla belavbûna tîrbûna barê ve tê hilberandin, ku wekî ${\displaystyle \rho (\mathbf {r} )}$ tê nîşankirin, hêsan dike. Bi têgihîştina barê ${\displaystyle \rho (\mathbf {r} ')dv}$ di nav her elementa qebareyê ya bêsînor biçûk ${\displaystyle dv}$ de li xalek çavkaniyê ${\displaystyle \mathbf {r} '}$ wekî barek xalî yê takekesî, qada elektrîkê ya bêsînor biçûk a encamdar, ku wekî ${\displaystyle d\mathbf {E} (\mathbf {r} )}$ tê destnîşankirin, li xalek çavdêriyê ${\displaystyle \mathbf {r} }$, dikare bi vê hevkêşeya jêrîn were îfadekirin: dv=ρ(r′)274πε§284285§r′|r′|320dv{\displaystyle d\mathbf {E} (\mathbf {r} )={\frac {\rho (\mathbf {r} ')}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}' \over {|\mathbf {r} '|}^{2}}dv={\frac {\rho (\mathbf {r} ')}{4\pi \varepsilon _{0}}}{\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}dv}, li vir

• ${\displaystyle {\hat {\mathbf {r} }}'}$ vektora yekîneyê nîşan dide ku ji ${\displaystyle \mathbf {r} '}$ derdikeve û ber bi ${\displaystyle \mathbf {r} }$ ve tê rêvebirin.
• ${\displaystyle \mathbf {r} '}$ vektora jicîhûwarkirinê nîşan dide ku ji ${\displaystyle \mathbf {r} '}$ ber bi ${\displaystyle \mathbf {r} }$ ve dirêj dibe.

Qada giştî bi berhevkirina beşdariyên ji hemî zêdebûnên qebareyên pir biçûk tê diyarkirin, ku ev yek bi rêya Entegrasyona tîrbûna barê li seranserê tevahiya qebareyê ${\displaystyle V}$ tê bidestxistin, wekî ku bi vê hevkêşeya jêrîn tê îfadekirin: E(r)=38§4142§πε§5152§∭Vρ(r′)r′|r′|113dv{\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\iiint _{V}\,\rho (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}dv}

Hevkêşeyên mîna wan ji bo barekî rûxarê têne derxistin, ku bi tîrbûna barê rûxarê ${\displaystyle \sigma (\mathbf {r} ')}$ ku li ser rûxarekê ${\displaystyle S}$ belavbûyî ye, tê taybetmendîkirin: E ( r ) =67 §7071§ π ε §8081§ ∬ S σ ( r ′ ) r ′ | r ′ | 143 d a , {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\iint _{S}\,\sigma (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}da,} Herwiha, ji bo barên xêzê yên ku xwedî tîrbûna barê xêzî ${\displaystyle \lambda (\mathbf {r} ')}$ li ser xêzekê ${\displaystyle L}$ ne, ev hevkêşeya jêrîn derbasdar e: E ( r ) =230 §233234§ π ε §243244§ ∫ L λ ( r ′ ) r ′ | r ′ | 306 d ℓ . {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\int _{L}\,\lambda (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}d\ell .}

Potansiyela elektrîkî

Di pergala Rawestayî de, ku tê de qadên magnetîkî guhertoyîya demkî nîşan nadin, zagona Faraday destnîşan dike ku qada elektrîkê bêdor e. Wekî encam, potansiyela elektrîkê, ku bi fonksiyona ${\displaystyle \varphi }$ tê temsîlkirin, dikare were pênasekirin ku ${\displaystyle \mathbf {E} =-\nabla \varphi }$. Ev formulekirin mîna têgeha potansiyela gravîtasyonê ye. Cudahiya skalar a potansiyela elektrîkê di navbera her du xalên fezayî de wekî cudahiya potansiyelê tê binavkirin, ku bi gelemperî wekî Voltaj tê zanîn.

Lê belê, di çarçoveyek giştîtir de, qada elektrîkê nikare serbixwe ji qada magnetîkî were taybetmendîkirin. Digel vê yekê, bi karanîna potansiyela vektorî ya magnetîkî, A, ku bi vî awayî tê pênasekirin ku ⁠${\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }$⁠, potansiyela elektrîkê ${\displaystyle \varphi }$ dîsa jî dikare were damezrandin, ku têkiliya jêrîn têr dike: $${\displaystyle \mathbf {E} =-\nabla \varphi -{\frac {\partial \mathbf {A} }{\partial t}},}$$ li vir ${\displaystyle \nabla \varphi }$ gradiyenta potansiyela elektrîkê nîşan dide, û ${\displaystyle {\frac {\partial \mathbf {A} }{\partial t}}}$ derîvatîfa qismî ya A li gorî demê temsîl dike.

Zagona biderxistinê ya Faraday dikare bi hesabkirina curl a hevkêşeya jorîn were derxistin, ku encam dide $${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial (\nabla \times \mathbf {A} )}{\partial t}}=-{\frac {\partial \mathbf {B} }{\partial t}},}$$. Ev encam paşverû îfadeya berê hatî damezrandin ji bo E piştrast dike.

Temsîlkirina Barê Berdewam li hember Dîskret

Her çend ku hevkêşeyên Bingehîn ên elektromanyetîzmê bi awayekî herî baş bi karanîna ravekirineke berdewam têne formulekirin jî, barên elektrîkê carinan bi awayekî bibandortir wekî yekîneyên cuda têne nîşandan. Mînak, hin modelên teorîk elektronan wekî çavkaniyên xalî dihesibînin, ku ev yek tê wateya Tîrbûneke barê Bêdawî Di nav herêmeke fezayî ya pir biçûk de.

Bareke xalî, ku wekî ${\displaystyle q}$ tê nîşankirin û li pozîsyona r28 {\displaystyle \mathbf {r} _{0}} ye, dikare bi awayekî matematîkî wekî Tîrbûneke barê ⁠ρ<!-- ρ --> ( r ) = q δ<!-- δ --> ( r −<!-- − --> r80 ) {\displaystyle \rho (\mathbf {r} )=q\delta (\mathbf {r} -\mathbf {r} _{0})} ⁠ were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were were 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Electrostatic Fields

Electrostatic fields are defined as electric fields that exhibit no temporal variation. These fields arise in scenarios where charged matter systems remain static or when electric currents maintain a constant state. Under such conditions, Coulomb's law provides a complete description of the field.

Parallels Between Electrostatic and Gravitational Fields

Qanûna Coulomb, ku danûstendina di navbera barên elektrîkî de diyar dike, dişibiya qanûna gravîtasyonê ya gerdûnî ya Newton. Îfadeyên matematîkî yên van hêzên Bingehîn wiha têne pêşkêş kirin: ) = q E {\displaystyle \mathbf {F} =q\left({\frac {Q}{4\pi \varepsilon _{0}}}{\frac {\mathbf {\hat {r}} }{|\mathbf {r} |^{2}}}\right)=q\mathbf {E} } û F = m ( −<!-- − --> G M r ^<!-- ^ --> | r | 148 ) = m g {\displaystyle \mathbf {F} =m\left(-GM{\frac {\mathbf {\hat {r}} }{|\mathbf {r} |^{2}}}\right)=m\mathbf {g} } li ku derê ${\textstyle \mathbf {\hat {r}} =\mathbf {\frac {r}{|r|}} }$ vektora yekîneyê nîşan dide.

Ev Çavdêrî, xwezaya analog a qada elektrîkê E û qada gravîtasyonê g, û her weha potansiyelên wan ên têkildar, ronî dike. Wekî encam, Girse carinan wekî "bara gravîtasyonê" tê binavkirin.

Her du hêzên elektrostatîk û gravîtasyonê jî bi Bûyîn a navendî, parastî, û li gorî qanûnek berevajî-çarçikî tevdigerin, têne taybetmendî kirin.

Qadên Yekreng

Qadeke elektrîkê ya yekreng bi vektora qada elektrîkê ya Berdewam li her xala fezayî tê taybetmendîkirin. Qadeke wisa dikare Nêzîkî were kirin bi danîna du lewheyên ragihîner ên paralel û sepandina cûdahiyek potansiyelê di navbera wan de. Ev veavakirina Nêzîkîbûnekê peyda dike ji ber bandorên Sînor, ku qada elektrîkê ya Nêzîkî qiraxên lewheyan tevliheviyê nîşan dide Ji ber ku geometriya planar ne Bêdawî ye. Di bin îdealîzasyona balafirên Bêdawî de, Mezinahîya qada elektrîkê, ku wekî E tê nîşankirin, wiha tê îfadekirin: $${\displaystyle E=-{\frac {\Delta V}{d}},}$$ Li vir, ΔV cûdahiya potansiyelê di navbera lewheyan de nîşan dide, û d dûrahiya veqetandinê ya di navbera wan de destnîşan dike. Nîşana neyînî destnîşan dike ku barên pozîtîf Hêz'eke dûrxistinê diceribînin, ango barek pozîtîf dê ji lewheya bi bara pozîtîf were dûrxistin, di aliyekî berevajî zêdebûna Voltaj'ê de. Ji bo sepanên Pûlik'a mîkro û nano, wek yên ku nîvragihîneran dihewînin, Mezinahîyên qada elektrîkê bi gelemperî digihîjin Nêzîkî 5051 V⋅m−1. Ev Mezinahî bi gelemperî tê bidestxistin bi sepandina Voltaj'ek Nêzîkî 1 volt li ser ragihînerên ku bi 1 μm ji hev veqetandî ne.

Qadên Elektromanyetîk

Qadên Elektromanyetîk hem qadên elektrîkê hem jî yên magnetîkî di nav xwe de dihewînin, ku dikarin Guhertoyî'ya demkî nîşan bidin, nemaze dema ku barên elektrîkê di tevgerê de ne. Tevgera baran qadeke magnetîkî çêdike, wek ku ji hêla qanûna çerxê ya Ampère ve hatî vegotin (ku bi terma Herrik'a jicîhûwarkirinê ya Maxwell ve hatî zêdekirin). Ev qanûn, ligel hevkêşeyên din ên Bingehîn ên Maxwell, qada magnetîkî, ${\displaystyle \mathbf {B} }$, bi kurmîla wê ve diyar dike: ∇<!-- ∇ --> ×<!-- × --> B = μ<!-- μ -->41 ( J + ε 60 ∂ E ∂ t ) , {\displaystyle \nabla \times \mathbf {B} =\mu _{0}\left(\mathbf {J} +\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right),} Di vê hevkêşeyê de, ${\displaystyle \mathbf {J} }$ Tîrbûn'a Herrik'ê destnîşan dike, μ<!-- μ -->127128{\displaystyle \mu _{0}} permeability'ya Valahiya Fezayê nîşan dide, û ε<!-- ε -->150 {\displaystyle \varepsilon _{0}} permittivity'ya Valahiya Fezayê ye.

Kurla qada manyetîk hem ji aliyê tîrbûna herrika elektrîkê ve, hem jî ji aliyê derîvatîva qismî ya demkî ya qada elektrîkê ve bandor dibe. Herwiha, hevkêşeya Maxwell–Faraday wiha tê îfadekirin: $${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}.}$$ Van formûlasyonan du ji çar hevkêşeyên bingehîn ên Maxwell pêk tînin, ku girêdanek tevlihev di navbera qadên elektrîkî û manyetîkî de nîşan didin, yên ku bi hev re qada elektromanyetîk pêk tînin. Van hevkêşeyan pergalek ji çar hevkêşeyên diferensiyel ên qismî yên pir-dimensî yên girêdayî pêk tînin, ku, piştî çareseriyê ji bo pergalek diyarkirî, dînamîkên yekbûyî yên qadên elektromanyetîk ronî dikin. Bi gelemperî, hêza ku li ser barek ceribandinê di nav qadeke elektromanyetîk de tê kirin, ji hêla qanûna hêzê ya Lorentz ve tê pênasekirin: $${\displaystyle \mathbf {F} =q\mathbf {E} +q\mathbf {v} \times \mathbf {B} .}$$

Enerjî Di Nav Qada Elektromanyetîk De

Qada elektromanyetîk enerjiyek giştî li gorî qebareya yekîneyê dihewîne, ku wiha tê îfadekirin: u EM = ε<!-- ε --> 21 | E | 38 + 46§4950§ μ <!-- μ --> | B | §7071§ {\displaystyle u_{\text{EM}}={\frac {\varepsilon }{2}}|\mathbf {E} |^{2}+{\frac {1}{2\mu }}|\mathbf {B} |^{2}} Di vê hevkêşeyê de, ε destûrdayîna navgînê ya ku qadê dihewîne nîşan dide, ${\displaystyle \mu }$ permeabiliyeta wê ya manyetîk temsîl dike, û E û B bi rêzê ve bi vektorên qada elektrîkî û manyetîkî re têkildar in.

Ji ber girêdana bingehîn di navbera qadên E û B de, veqetandina vê îfadeyê li beşên cuda yên "elektrîkî" û "manyetîkî" ji aliyê têgînî ve dê nerast be. Bi taybetî, qadeke elektrostatîk a ku di çarçoveyek referansê de tê dîtin, bi gelemperî dê bi pêkhateyeke manyetîk xuya bibe dema ku ji çarçoveyek ku bi awayekî nisbî tevdigere tê dîtin. Wekî encam, rizîna qada elektromanyetîk li pêkhateyên wê yên elektrîkî û manyetîkî bi çarçoveya referansê ya hilbijartî ve girêdayî ye, prensîbek ku ji bo enerjîya têkildar jî derbasdar e.

Enerjiya giştî U_EM ku di nav qadeke elektromanyetîk de di qebareke diyarkirî V de tê hilanîn, bi awayekî matematîkî wiha tê îfadekirin: U EM =28 §3031§ ∫ V ( ε | E | + §7273§ μ | B | ) d V . {\displaystyle U_{\text{EM}}={\frac {1}{2}}\int _{V}\left(\varepsilon |\mathbf {E} |^{2}+{\frac {1}{\mu }}|\mathbf {B} |^{2}\right)dV\,.}

Qada Jicîhûwarkirina Elektrîkî

Hevkêşeya Diyarker a Qadên Vektorî

Dema ku made niha be, feyde ye ku têgeha qada elektrîkê di sê qadên vektorî yên cuda de were berfireh kirin, ku wiha têne îfadekirin: D = ε<!-- ε -->17 E + P {\displaystyle \mathbf {D} =\varepsilon _{0}\mathbf {E} +\mathbf {P} } Li vir, P polarîzasyona elektrîkî temsîl dike, ku tîrbûna qebareyî ya momentên dîpolên elektrîkî ye, û D qada jicîhûwarkirina elektrîkî nîşan dide. Ji ber ku E û P bi serê xwe hatine pênasekirin, ev hevkêşe ji bo pênasekirina D xizmet dike. Her çend şîrovekirina fîzîkî ya D ji ya E (ku bi bandor qada li ser madeyê tê sepandin temsîl dike) an jî P (qada înduktekirî ya ku ji dîpolên di nav madeyê de derdikeve) kêmtir rasterast be jî, ew dîsa jî hêsankariyek matematîkî ya pratîkî pêşkêş dike, ji ber ku ew dihêle ku hevkêşeyên Maxwell di warê barkêşên azad û herikan de werin hêsankirin.

Têkiliya Bingehîn

Qadên E û D bi rêya destûrdariya madeyê, ku wekî ε tê nîşankirin, bi hev ve girêdayî ne.

Di madeyên xêzî, homojen û îzotropîk de, qadên E û D rêjeyî ne û li seranserê herêmê berdevam dimînin, ku ev yek nebûna girêdana bi cîhê re nîşan dide, wekî ku tê xuyakirin: $${\displaystyle \mathbf {D} (\mathbf {r} )=\varepsilon \mathbf {E} (\mathbf {r} ).}$$

Berovajî, ji bo madeyên nehomojen, girêdanek cîhî li seranserê madeyê tê dîtin, wekî ku bi vê yekê tê vegotin: $${\displaystyle \mathbf {D} (\mathbf {r} )=\varepsilon (\mathbf {r} )\mathbf {E} (\mathbf {r} )}$$

Di materyalên anîzotropîk de, qada elektrîkê E û qada veguheztina elektrîkê D ne hev-xêz in. Wekî encam, E û D bi rêya tensorê destûrdayînê, ku qadek tensorê ya rêkûpêkî ya duyemîn pêk tîne, bi hev ve girêdayî ne. Ev têkilî bi forma pêkhateyî wiha tê îfadekirin: $${\displaystyle D_{i}=\varepsilon _{ij}E_{j}}$$

Di medyayên ne-xêzî de, qada elektrîkê E û qada veguheztina elektrîkê D têkiliyek rêjeyî nîşan nadin. Materyal dikarin pileyan cuda yên xêzîbûn, homojenîbûn û îzotropîbûnê nîşan bidin.

Bandorên Relatîvîstîk li ser Qada Elektrîkê

Barê Xalî di Tevgera Yekreng de

Qada elektrîkê ya ku ji hêla barek xalî ya bi tevgera yekreng ve tê çêkirin, dikare bi bikaranîna neguherîna hevkêşeyên Maxwell di bin veguherîna Lorentz de were bidestxistin. Piştrastên ezmûnî vê yekê piştrast dikin ku barê parçikekê di çarçoveyên referansê yên cihê de neguher dimîne. Rêbazeke din a derxistinê ev e ku veguherîna Lorentz li ser çar-Hêzê ya ku ji hêla barên ceribandinê ve di nav çarçoveya bêhnvedanê ya Çavkanîyê de tê hîskirin, were sepandin, wekî ku ji hêla qanûna Coulomb ve hatî vegotin. Dûv re, qadên elektrîkî û magnetîkî li gorî formulasyona Hêza Lorentz têne pênasekirin. JGirîng e ku meriv vê Nota bike ku hevkêşeya jêrîn tenê ji bo rewşên ku parçik Lezdan nekiriye derbasdar e, ku ev yek rê dide sepandina qanûna Coulomb an jî bikaranîna argumanên Sîmetrîyê ji bo hêsankirina hevkêşeyên Maxwell. Wekî encam, qada elektrîkê ji bo barek xalî ya bi tevgera yekreng a wiha wiha tê îfadekirin: 45 − β §5556§ ( 63 − β §7374§ sin §8182§ ⁡ θ ) §9596§ / §101102§ r , {\displaystyle \mathbf {E} ={\frac {q}{4\pi \varepsilon _{0}r^{3}}}{\frac {1-\beta ^{2}}{(1-\beta ^{2}\sin ^{2}\theta )^{3/2}}}\mathbf {r} ,} li vir ${\displaystyle q}$ barê Çavkanîya xalî nîşan dide, ${\displaystyle \mathbf {r} }$ vektora pozîsyonê ya ku ji Çavkanîya xalî ber bi xala Çavdêrîyê ve di Feza de dirêj dibe destnîşan dike, ${\displaystyle \beta }$ rêjeya Leza Çavdêrîkirî ya parçika barkirî li gorî Leza Sivik destnîşan dike, û ${\displaystyle \theta }$ goşeya ku di navbera ${\displaystyle \mathbf {r} }$ û vektora Leza Çavdêrîkirî ya parçika barkirî de çêdibe ye.

Di lezên ne-îzafî de, ev hevkêşe ji bo barekî xalî hêsan dibe qanûna Coulomb. Sîmetrîya gogî tune ye ji ber ku arasteya diyarkirî ya Lezê ji bo hesabkirina qadê bi eslê xwe vê sîmetrîyê dişikîne. Wekî encam, xetên qadê yên barên tevgerîn Gelek caran wekî xetên radyal ên bi dûrîyên ne-wekhev têne nîşandan, Her çend ew ê Di nav de çarçoveyek referansê ya hevreger de bi dûrîyên wekhev xuya bikin.

Belavbûna Tevlihevîyan Di Qadên Elektrikî de.

Teorîya Îzafîyetê ya Taybet prensîba lokalîteyê ferz dike, ku destnîşan dike ku sedem û encam divê bûyerên dem-wekhev veqetandî bin, piştrast dike ku bandora sedemî ji leza ronahiyê derbas nabe. Hevkêşeyên Maxwell bi vî prensîbî li hev dikin, ji ber ku bişêvkên wan ên qadê yên giştî bi karanîna dema derengmayî têne îfadekirin, nîşan dide ku tevlihevîyên elektromagnetîk bi leza ronahiyê belav dibin. Berovajî, dema pêşketî, her çend ew jî Bişêvkekê ji bo hevkêşeyên Maxwell pêşkêş dike, ji ber encamên xwe yên ne-fîzîkî tê paşguhkirin.

Senaryoya parçikek barkirî ya di tevgerê de bifikirin, bi taybetî dema ku ew ji nişka ve tevgerê rawestîne. Qadên elektrikî li xalên Dûr tavilê venagerin veavakirina taybetmendiya barekî Rawestayî. Dema ku disekine, qada li derdora nêzîk dest bi veguherînê dike rewşa xwe ya Rawestayî ya bendewar, bi vê bandorê ku ber bi derve bi leza ronahiyê belav dibe. Di heman demê de, xetên qada elektrikî yên Dûr berdewam dikin ku bi radyalî ber bi pozîsyona ku bar dê dagir bikira ger ew berdewam bikira di tevgerê de nîşan bidin. Ev "barê virtual" yê xuya Di nav de qada belavbûnê ya tevliheviya qada elektromagnetîk dimîne Ji ber ku parçikên barkirî bi lezên kêmtir ji leza ronahiyê ve sînordar in. Ev sînor rê li ber çêkirina Rûxarekî Gaussian Di nav de vê herêmê digire ku dê qanûna Gauss binpê bikira. Lêkolînek teknîkî ya din ku vê Bûyerê piştgirî dike ev e ku parçikên barkirî yên ku bi leza ronahiyê an jor wê digerin dema derengmayî ya Bêhempa tune ye. Ji ber berdewamiya xetên qada elektrikî, Wekî encam, Lêdanek Dil Radyasyonê ya elektromagnetîk tê çêkirin, ku li Sînorê vê tevlihevîyê tê girêdan û ber bi derve bi leza ronahiyê belav dibe. Bi gelemperî, her barekî xalî yê Lezdanê pêlên elektromagnetîk derdixe; Lê belê, Lezdanek ne-radyasyonî dikare Di nav de pergalên ku ji gelek baran pêk tên de çêbibe.

Barê xalî yê ku bi awayekî bêserûber digere.

Ji bo ku bi duristî belavbûna qadên potansiyel, wekî qadên pîvana Lorenz, bi leza ronahiyê ji bo barên xalî yên ku bi awayekî bêserûber digerin were vegotin, divê potansiyela Liénard–Wiechert were bikaranîn. Ji ber ku ev potansiyel bi eslê xwe hevkêşeyên Maxwell bicîh tînin, qadên encamdar ên ku ji bo barekî xalî hatine derxistin Bi heman rengî li gorî hevkêşeyên Maxwell tevdigerin. Qada elektrikî bi fermî bi hevkêşeya jêrîn tê temsîl kirin:

Yekanebûna bişêvkê ji bo ${\textstyle {t_{r}}}$, ku ${\displaystyle t}$, ${\displaystyle \mathbf {r} }$, û ${\displaystyle r_{s}(t)}$ hatî dayîn, ji bo parçikên barkirî yên ku di bin leza sivik de dimeşin derbasdar e. Radyasyona elektromanyetîk a ku ji aliyê barên lezker ve tê derxistin, ji pêkhateya girêdayî lezdanê ya di nav qada elektrîkê de derdikeve, ku paşê rastkirina relatîvîstîk ji bo formula Larmor peyda dike.

Komek din a bişêvkên ji bo hevkêşeyên Maxwell heye, ku heman formê parve dikin lê demeke pêşkeftî, ${\textstyle {t_{a}}}$, li şûna dema paşdemayî, bi kar tînin, wekî ku ji hêla bişêvka jêrîn ve hatî pênasekirin:

$${\displaystyle t_{a}=t+{\frac {\left|\mathbf {r} -\mathbf {r} _{s}(t_{a})\right|}{c}}}$$

Şîrovekirina fîzîkî ya vê bişêvkê destnîşan dike ku qada elektrîkê li xalek taybetî ji hêla rewşa pêşeroj a parçikê ve tê destnîşankirin, ku dibe sedema dabeşkirina wê wekî bişêvkek nefîzîkî û paşê jî paşguhkirina wê. Tevî vê yekê, hin teorî, wekî teoriya absorberê ya Feynman-Wheeler, bişêvkên dema pêşkeftî yên hevkêşeyên Maxwell lêkolîn kirine.

Her çend hevkêşeya jorîn bi tevgera barên xalî yên bi yekrengî dimeşin û sînorê wê yê nerelatîvîstîk re hevaheng be jî, ew rastkirinên ji bo bandorên kuantum-mekanîkî nagire nav xwe.

Formûlasyonên Standard

Qada elektrîkê ya ku tavilê li kêleka rûxareke gihîner a di hevsengiya elektrostatîk de ye, ku tîrbûna barekî ${\displaystyle \sigma }$ li wê cihê taybetî heye, bi σ<!-- σ --> ε<!-- ε -->33 x ^ {\textstyle {\frac {\sigma }{\varepsilon _{0}}}{\hat {\mathbf {x} }}} tê dayîn. Ev ji ber ku bar bi taybetî li ser rûxarê kom dibin, ku, di pûlikeke bêdawî biçûk de, nêzî balafireke du-alî ya bêdawî dibe. Ji bo gihînerên qûçkî yên bêyî qadên derve, belavbûna bar li ser rûxarê yekreng e, ku di encamê de qadeke elektrîkê ya wekhev bi ya ku ji hêla belavbûna barekî rûxarê qûçkî ya yekreng ve tê hilberandin çêdibe.

Elektromanyetîzma Klasîk

• Elektromanyetîzma Klasîk
• Elektromanyetîzma Relatîvîstîk
• Elektrîk
• Dîroka Teorîya Elektromanyetîk
• Qada Elektromanyetîk
• Manyetîzma
• Lûleya Teltron
• Teledeltos, kaxizekî taybetmendî yê gihîner, dikare wekî kompîterek analog a bingehîn ji bo modelkirina qadên cihêreng fonksîyon bike.

Purcell, Edward; Morin, David (2013). Elektrîk û Manyetîzma (çapa 3yemîn). Çapxaneya Zanîngeha Cambridge, New York. ISBN 978-1-107-01402-2.

• Purcell, Edward; Morin, David (2013). Elektrîk û Manyetîzma (çapa 3yemîn). Çapxaneya Zanîngeha Cambridge, New York. ISBN 978-1-107-01402-2.Browne, Michael (2011). Fîzîk ji bo Endezyarî û Zanistê (çapa 2yemîn). McGraw-Hill, Schaum, New York. ISBN 978-0-07-161399-6.
• Qad – beşek ji pirtûkek dersê ya serhêl.