四維電流密度

Multi tool use
Multi tool use





四維電流密度J{displaystyle J}J是在相對論中，對應電磁學的電流密度以及電荷密度的四維矢量。


定義為：


Ja=(cρ,j)=(cρ,jx,jy,jz){displaystyle J^{a}=(crho ,mathbf {j} )=(crho ,j_{x},j_{y},j_{z})}J^{a}=(crho ,{mathbf {j}})=(crho ,j_{x},j_{y},j_{z})

j{displaystyle j}j是一般的電流密度，ρ{displaystyle rho }rho 是電荷密度，c{displaystyle c}c是光速。


  • 電流連續方程可寫成

D⋅J=∂aJa=∂ρ∂t+∇⋅j=0{displaystyle Dcdot J=partial _{a}J^{a}={frac {partial rho }{partial t}}+nabla cdot mathbf {j} =0}Dcdot J=partial _{a}J^{a}={frac {partial rho }{partial t}}+nabla cdot {mathbf {j}}=0

其中D是四維梯度(1/c ∂/∂t, ∇)。


上述方程亦可寫作：



Ja,a=0{displaystyle J^{a}{}_{,a}=0,}J^{a}{}_{{,a}}=0,


Ja;a=0{displaystyle J^{a}{}_{;a}=0,}J^{a}{}_{{;a}}=0,（廣義相對論）


  • 四維電流密度亦應用在馬克士威方程組的相對論形式上：

∂Fαβ∂xα=μ0Jβ{displaystyle {frac {partial F^{alpha beta }}{partial x^{alpha }}}=mu _{0}J^{beta }}{frac {partial F^{{alpha beta }}}{partial x^{alpha }}}=mu _{0}J^{beta }



參見


  • 電磁張量


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  • 查

  • 论

  • 编


电磁学

靜電學


  • 電荷

  • 電場

  • 導體

  • 絕緣體

  • 摩擦起電效應

  • 静电放电

  • 静电感应

  • 库仑定律

  • 高斯定律

  • 电通量

  • 电势能

  • 电偶极矩

  • 電極化

  • 電位移
Solenoid
靜磁學


  • 安培定律

  • 磁場

  • 磁化强度

  • 磁通量

  • 毕奥-萨伐尔定律

  • 磁矩

  • 高斯磁定律

  • 磁矢勢
电动力学


  • 洛伦兹力

  • 電磁感應

  • 法拉第电磁感应定律

  • 楞次定律

  • 位移電流

  • 馬克士威方程組

  • 电磁场

  • 电磁波

  • 馬克士威應力張量

  • 坡印廷向量

  • 黎納-維謝勢

  • 傑斐緬柯方程式

  • 渦電流

  • 倫敦方程

  • 推遲勢

  • 自由空間
电路


  • 电流

  • 電勢

  • 電壓

  • 电阻

  • 欧姆定律

  • 串聯電路

  • 並聯電路

  • 直流電

  • 交流電

  • 带电流

  • 中性流

  • 電動勢

  • 電容

  • 电感

  • 阻抗

  • 电导

  • 波导

  • 憶阻器

  • 基爾霍夫電路定律
協變表述


  • 電磁張量

  • 四維電流密度

  • 電磁應力-能量張量

  • 四維勢
发展史


  • 庫侖

  • 安培

  • 高斯

  • 奧斯特

  • 亨利

  • 法拉第

  • 馬克士威

  • 黑維塞

  • 韋伯

  • 特斯拉

  • 勞侖茲

  • 赫茲

  • 伏打



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