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Display information for equation id:math.2182.2 on revision:2182

* Page found: Inhomogene Maxwellgleichungen im Vakuum (eq math.2182.2)

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\begin{align}
& {{\partial }_{2}}{{B}^{3}}-{{\partial }_{3}}{{B}^{2}}={{\mu }_{0}}{{j}^{1}}+{{\varepsilon }_{0}}{{\mu }_{0}}\frac{\partial }{\partial t}{{E}^{1}} \\
& {{\mu }_{0}}c=\frac{1}{{{\varepsilon }_{0}}c} \\
& \Leftrightarrow {{\partial }_{2}}{{F}^{21}}-.{{\partial }_{3}}{{F}^{13}}=\frac{1}{{{\varepsilon }_{0}}c}{{j}^{1}}+.{{\partial }_{0}}{{F}^{10}} \\
& {{\partial }_{2}}{{F}^{21}}+{{\partial }_{3}}{{F}^{31}}+{{\partial }_{0}}{{F}^{01}}=\frac{1}{{{\varepsilon }_{0}}c}{{j}^{1}} \\
& \Leftrightarrow {{\partial }_{\nu }}{{F}^{\nu 1}}=\frac{1}{{{\varepsilon }_{0}}c}{{j}^{1}} \\
& wegen{{\partial }_{1}}{{F}^{11}}=0 \\
\end{align}

TeX (checked): 

{\begin{aligned}&{{\partial }_{2}}{{B}^{3}}-{{\partial }_{3}}{{B}^{2}}={{\mu }_{0}}{{j}^{1}}+{{\varepsilon }_{0}}{{\mu }_{0}}{\frac {\partial }{\partial t}}{{E}^{1}}\\&{{\mu }_{0}}c={\frac {1}{{{\varepsilon }_{0}}c}}\\&\Leftrightarrow {{\partial }_{2}}{{F}^{21}}-.{{\partial }_{3}}{{F}^{13}}={\frac {1}{{{\varepsilon }_{0}}c}}{{j}^{1}}+.{{\partial }_{0}}{{F}^{10}}\\&{{\partial }_{2}}{{F}^{21}}+{{\partial }_{3}}{{F}^{31}}+{{\partial }_{0}}{{F}^{01}}={\frac {1}{{{\varepsilon }_{0}}c}}{{j}^{1}}\\&\Leftrightarrow {{\partial }_{\nu }}{{F}^{\nu 1}}={\frac {1}{{{\varepsilon }_{0}}c}}{{j}^{1}}\\&wegen{{\partial }_{1}}{{F}^{11}}=0\\\end{aligned}}

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∂ 2 ⁡ B 3 - ∂ 3 ⁡ B 2 = μ 0 ⁢ j 1 + ε 0 ⁢ μ 0 ⁢ ∂ ∂ ⁡ t ⁢ E 1 μ 0 ⁢ c = 1 ε 0 ⁢ c ⇔ ∂ 2 F 21 - . ∂ 3 F 13 = 1 ε 0 ⁢ c j 1 + . ∂ 0 F 10 ∂ 2 ⁡ F 21 + ∂ 3 ⁡ F 31 + ∂ 0 ⁡ F 01 = 1 ε 0 ⁢ c ⁢ j 1 ⇔ ∂ ν ⁡ F ν ⁢ 1 = 1 ε 0 ⁢ c ⁢ j 1 w ⁢ e ⁢ g ⁢ e ⁢ n ⁢ ∂ 1 ⁡ F 11 = 0 missing-subexpression subscript 2 superscript 𝐵 3 subscript 3 superscript 𝐵 2 subscript 𝜇 0 superscript 𝑗 1 subscript 𝜀 0 subscript 𝜇 0 𝑡 superscript 𝐸 1 missing-subexpression subscript 𝜇 0 𝑐 1 subscript 𝜀 0 𝑐 missing-subexpression fragments ⇔ subscript 2 superscript 𝐹 21 . subscript 3 superscript 𝐹 13 1 subscript 𝜀 0 𝑐 superscript 𝑗 1 . subscript 0 superscript 𝐹 10 missing-subexpression subscript 2 superscript 𝐹 21 subscript 3 superscript 𝐹 31 subscript 0 superscript 𝐹 01 1 subscript 𝜀 0 𝑐 superscript 𝑗 1 missing-subexpression ⇔ absent subscript 𝜈 superscript 𝐹 𝜈 1 1 subscript 𝜀 0 𝑐 superscript 𝑗 1 missing-subexpression 𝑤 𝑒 𝑔 𝑒 𝑛 subscript 1 superscript 𝐹 11 0 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle{{\partial}_{2}}{{B}% ^{3}}-{{\partial}_{3}}{{B}^{2}}={{\mu}_{0}}{{j}^{1}}+{{\varepsilon}_{0}}{{\mu}% _{0}}\frac{\partial}{\partial t}{{E}^{1}}\\ &\displaystyle{{\mu}_{0}}c=\frac{1}{{{\varepsilon}_{0}}c}\\ &\displaystyle\Leftrightarrow{{\partial}_{2}}{{F}^{21}}-.{{\partial}_{3}}{{F}^% {13}}=\frac{1}{{{\varepsilon}_{0}}c}{{j}^{1}}+.{{\partial}_{0}}{{F}^{10}}\\ &\displaystyle{{\partial}_{2}}{{F}^{21}}+{{\partial}_{3}}{{F}^{31}}+{{\partial% }_{0}}{{F}^{01}}=\frac{1}{{{\varepsilon}_{0}}c}{{j}^{1}}\\ &\displaystyle\Leftrightarrow{{\partial}_{\nu}}{{F}^{\nu 1}}=\frac{1}{{{% \varepsilon}_{0}}c}{{j}^{1}}\\ &\displaystyle wegen{{\partial}_{1}}{{F}^{11}}=0\\ \end{aligned}}}

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∂2B3−∂3B2=μ0j1+ε0μ0∂∂tE1μ0c=1ε0c⇔∂2F21−.∂3F13=1ε0cj1+.∂0F10∂2F21+∂3F31+∂0F01=1ε0cj1⇔∂νFν1=1ε0cj1wegen∂1F11=0

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Calculated based on the variables occurring on the entire Inhomogene Maxwellgleichungen im Vakuum page

Identifiers

  • B
  • B
  • μ0
  • j
  • ε0
  • μ0
  • t
  • E
  • μ0
  • c
  • ε0
  • c
  • F
  • F
  • ε0
  • c
  • j
  • F
  • F
  • F
  • F
  • ε0
  • c
  • j
  • ν
  • F
  • ν
  • ε0
  • c
  • j
  • w
  • e
  • g
  • e
  • n
  • F

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