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Display information for equation id:math.1198.236 on revision:1198
* Page found: Elektrodynamik Schöll (eq math.1198.236)
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TeX (original user input):
\begin{align}
& \Phi (\bar{r}\acute{\ }){{\left. {} \right|}_{\bar{r}\acute{\ }\in S\beta }}=\int_{V}^{{}}{{{d}^{3}}r}G\left( \bar{r}-\bar{r}\acute{\ } \right){{\left. {} \right|}_{\bar{r}\acute{\ }\in S\beta }}\rho \left( {\bar{r}} \right)+{{\varepsilon }_{0}}\sum\limits_{\alpha =1}^{n}{{{\Phi }_{\alpha }}\oint\limits_{S\alpha }{{}}d\bar{f}\cdot {{\nabla }_{r}}}G\left( \bar{r}-\bar{r}\acute{\ } \right){{\left. {} \right|}_{\bar{r}\acute{\ }\in S\beta }} \\
& G\left( \bar{r}-\bar{r}\acute{\ } \right){{\left. {} \right|}_{\bar{r}\acute{\ }\in S\beta }}\rho \left( {\bar{r}} \right)=0 \\
& \Rightarrow \Phi (\bar{r}\acute{\ }){{\left. {} \right|}_{\bar{r}\acute{\ }\in S\beta }}={{\varepsilon }_{0}}\sum\limits_{\alpha =1}^{n}{{{\Phi }_{\alpha }}\oint\limits_{S\alpha }{{}}d\bar{f}\cdot {{\nabla }_{r}}}G\left( \bar{r}-\bar{r}\acute{\ } \right){{\left. {} \right|}_{\bar{r}\acute{\ }\in S\beta }}=-{{\varepsilon }_{0}}\int_{\partial V}^{{}}{{}}d\bar{f}\cdot \Phi (\bar{r}){{\nabla }_{r}}G\left( \bar{r}-\bar{r}\acute{\ } \right){{\left. {} \right|}_{\bar{r}\acute{\ }\in S\beta }} \\
\end{align}
TeX (checked):
{\begin{aligned}&\Phi ({\bar {r}}{\acute {\ }}){{\left.{}\right|}_{{\bar {r}}{\acute {\ }}\in S\beta }}=\int _{V}^{}{{{d}^{3}}r}G\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right){{\left.{}\right|}_{{\bar {r}}{\acute {\ }}\in S\beta }}\rho \left({\bar {r}}\right)+{{\varepsilon }_{0}}\sum \limits _{\alpha =1}^{n}{{{\Phi }_{\alpha }}\oint \limits _{S\alpha }{}d{\bar {f}}\cdot {{\nabla }_{r}}}G\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right){{\left.{}\right|}_{{\bar {r}}{\acute {\ }}\in S\beta }}\\&G\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right){{\left.{}\right|}_{{\bar {r}}{\acute {\ }}\in S\beta }}\rho \left({\bar {r}}\right)=0\\&\Rightarrow \Phi ({\bar {r}}{\acute {\ }}){{\left.{}\right|}_{{\bar {r}}{\acute {\ }}\in S\beta }}={{\varepsilon }_{0}}\sum \limits _{\alpha =1}^{n}{{{\Phi }_{\alpha }}\oint \limits _{S\alpha }{}d{\bar {f}}\cdot {{\nabla }_{r}}}G\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right){{\left.{}\right|}_{{\bar {r}}{\acute {\ }}\in S\beta }}=-{{\varepsilon }_{0}}\int _{\partial V}^{}{}d{\bar {f}}\cdot \Phi ({\bar {r}}){{\nabla }_{r}}G\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right){{\left.{}\right|}_{{\bar {r}}{\acute {\ }}\in S\beta }}\\\end{aligned}}
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