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* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1444.137)

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TeX (original user input): 

\begin{align}
& \begin{matrix}
\lim   \\
h->0  \\
\end{matrix}\oint\limits_{\partial V}{{}}d\bar{f}\times \bar{E}=\oint\limits_{\partial V}{{}}df\bar{n}\times \left( {{{\bar{E}}}^{(1)}}-{{{\bar{E}}}^{(2)}} \right)=-\begin{matrix}
\lim   \\
h->0  \\
\end{matrix}\int_{V}^{{}}{{}}{{d}^{3}}r\frac{\partial }{\partial t}\bar{B} \\
& \begin{matrix}
\lim   \\
h->0  \\
\end{matrix}\oint\limits_{\partial V}{{}}d\bar{f}\times H\left( \bar{r},t \right)=\oint\limits_{\partial V}{{}}df\bar{n}\times \left( H{{\left( \bar{r},t \right)}^{(1)}}-H{{\left( \bar{r},t \right)}^{(2)}} \right)=\begin{matrix}
\lim   \\
h->0  \\
\end{matrix}\int_{V}^{{}}{{}}{{d}^{3}}r\left( \bar{j}+\frac{\partial }{\partial t}\bar{D} \right) \\
\end{align}

TeX (checked): 

{\begin{aligned}&{\begin{matrix}\lim \\h->0\\\end{matrix}}\oint \limits _{\partial V}{}d{\bar {f}}\times {\bar {E}}=\oint \limits _{\partial V}{}df{\bar {n}}\times \left({{\bar {E}}^{(1)}}-{{\bar {E}}^{(2)}}\right)=-{\begin{matrix}\lim \\h->0\\\end{matrix}}\int _{V}^{}{}{{d}^{3}}r{\frac {\partial }{\partial t}}{\bar {B}}\\&{\begin{matrix}\lim \\h->0\\\end{matrix}}\oint \limits _{\partial V}{}d{\bar {f}}\times H\left({\bar {r}},t\right)=\oint \limits _{\partial V}{}df{\bar {n}}\times \left(H{{\left({\bar {r}},t\right)}^{(1)}}-H{{\left({\bar {r}},t\right)}^{(2)}}\right)={\begin{matrix}\lim \\h->0\\\end{matrix}}\int _{V}^{}{}{{d}^{3}}r\left({\bar {j}}+{\frac {\partial }{\partial t}}{\bar {D}}\right)\\\end{aligned}}

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MathML (56.085 KB / 5.726 KB) :

lim h - > 0 ⁢ ∮ ∂ ⁡ V 𝑑 f ¯ × E ¯ = ∮ ∂ ⁡ V 𝑑 f ⁢ n ¯ × ( E ¯ ( 1 ) - E ¯ ( 2 ) ) = - lim h - > 0 ⁢ ∫ V d 3 ⁢ r ⁢ ∂ ∂ ⁡ t ⁢ B ¯ lim h - > 0 ⁢ ∮ ∂ ⁡ V 𝑑 f ¯ × H ⁢ ( r ¯ , t ) = ∮ ∂ ⁡ V 𝑑 f ⁢ n ¯ × ( H ⁢ ( r ¯ , t ) ( 1 ) - H ⁢ ( r ¯ , t ) ( 2 ) ) = lim h - > 0 ⁢ ∫ V d 3 ⁢ r ⁢ ( j ¯ + ∂ ∂ ⁡ t ⁢ D ¯ ) missing-subexpression limit-from ℎ 0 subscript contour-integral 𝑉 differential-d ¯ 𝑓 ¯ 𝐸 subscript contour-integral 𝑉 differential-d 𝑓 ¯ 𝑛 superscript ¯ 𝐸 1 superscript ¯ 𝐸 2 limit-from ℎ 0 subscript 𝑉 superscript 𝑑 3 𝑟 𝑡 ¯ 𝐵 missing-subexpression limit-from ℎ 0 subscript contour-integral 𝑉 differential-d ¯ 𝑓 𝐻 ¯ 𝑟 𝑡 subscript contour-integral 𝑉 differential-d 𝑓 ¯ 𝑛 𝐻 superscript ¯ 𝑟 𝑡 1 𝐻 superscript ¯ 𝑟 𝑡 2 limit-from ℎ 0 subscript 𝑉 superscript 𝑑 3 𝑟 ¯ 𝑗 𝑡 ¯ 𝐷 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\begin{matrix}\lim\\ h->0\\ \end{matrix}\oint\limits_{\partial V}{{}}d\bar{f}\times\bar{E}=\oint\limits_{% \partial V}{{}}df\bar{n}\times\left({{{\bar{E}}}^{(1)}}-{{{\bar{E}}}^{(2)}}% \right)=-\begin{matrix}\lim\\ h->0\\ \end{matrix}\int_{V}{{}}{{d}^{3}}r\frac{\partial}{\partial t}\bar{B}\\ &\displaystyle\begin{matrix}\lim\\ h->0\\ \end{matrix}\oint\limits_{\partial V}{{}}d\bar{f}\times H\left(\bar{r},t\right% )=\oint\limits_{\partial V}{{}}df\bar{n}\times\left(H{{\left(\bar{r},t\right)}% ^{(1)}}-H{{\left(\bar{r},t\right)}^{(2)}}\right)=\begin{matrix}\lim\\ h->0\\ \end{matrix}\int_{V}{{}}{{d}^{3}}r\left(\bar{j}+\frac{\partial}{\partial t}% \bar{D}\right)\\ \end{aligned}}}

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limh−>0∮∂Vdf¯×E¯=∮∂Vdfn¯×(E¯(1)−E¯(2))=−limh−>0∫Vd3r∂∂tB¯limh−>0∮∂Vdf¯×H(r¯,t)=∮∂Vdfn¯×(H(r¯,t)(1)−H(r¯,t)(2))=limh−>0∫Vd3r(j¯+∂∂tD¯)

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Identifiers

  • h
  • V
  • d
  • f¯
  • E¯
  • V
  • d
  • f
  • n¯
  • E¯
  • E¯
  • h
  • V
  • r
  • t
  • B¯
  • h
  • V
  • d
  • f¯
  • H
  • r¯
  • t
  • V
  • d
  • f
  • n¯
  • H
  • r¯
  • t
  • H
  • r¯
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  • h
  • V
  • r
  • j¯
  • t
  • D¯

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