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Display information for equation id:math.1198.284 on revision:1198
* Page found: Elektrodynamik Schöll (eq math.1198.284)
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Hash: 0331bcc839d5ca4d4d8b332605430359
TeX (original user input):
\begin{align}
& \Rightarrow \delta W={{\varepsilon }_{0}}\sum\limits_{\alpha }^{{}}{{{\Phi }_{\alpha }}}\oint\limits_{S\alpha }{{}}d\bar{f}\delta \bar{E}(\bar{r})=\sum\limits_{\alpha }^{{}}{{{\Phi }_{\alpha }}}\delta \sum\limits_{\beta =1}^{n}{{}}{{C}_{\alpha \beta }}{{\Phi }_{\beta }}=\sum\limits_{\alpha ,\beta =1}^{n}{{}}{{\Phi }_{\alpha }}{{C}_{\alpha \beta }}\delta {{\Phi }_{\beta }} \\
& \sum\limits_{\alpha ,\beta =1}^{n}{{}}{{\Phi }_{\alpha }}{{C}_{\alpha \beta }}\delta {{\Phi }_{\beta }}=\frac{1}{2}\left\{ \sum\limits_{\alpha ,\beta =1}^{n}{{}}{{\Phi }_{\beta }}{{C}_{\beta \alpha }}\delta {{\Phi }_{\alpha }}+\sum\limits_{\alpha ,\beta =1}^{n}{{}}{{\Phi }_{\alpha }}{{C}_{\alpha \beta }}\delta {{\Phi }_{\beta }} \right\} \\
& {{C}_{\beta \alpha }}={{C}_{\alpha \beta }} \\
& \Rightarrow \delta W=\frac{1}{2}\sum\limits_{\alpha ,\beta =1}^{n}{{}}{{C}_{\alpha \beta }}\left\{ {{\Phi }_{\beta }}\delta {{\Phi }_{\alpha }}+{{\Phi }_{\alpha }}\delta {{\Phi }_{\beta }} \right\}=\delta \left\{ \frac{1}{2}\sum\limits_{\alpha ,\beta =1}^{n}{{}}{{C}_{\alpha \beta }}{{\Phi }_{\alpha }}{{\Phi }_{\beta }} \right\} \\
\end{align}
TeX (checked):
{\begin{aligned}&\Rightarrow \delta W={{\varepsilon }_{0}}\sum \limits _{\alpha }^{}{{\Phi }_{\alpha }}\oint \limits _{S\alpha }{}d{\bar {f}}\delta {\bar {E}}({\bar {r}})=\sum \limits _{\alpha }^{}{{\Phi }_{\alpha }}\delta \sum \limits _{\beta =1}^{n}{}{{C}_{\alpha \beta }}{{\Phi }_{\beta }}=\sum \limits _{\alpha ,\beta =1}^{n}{}{{\Phi }_{\alpha }}{{C}_{\alpha \beta }}\delta {{\Phi }_{\beta }}\\&\sum \limits _{\alpha ,\beta =1}^{n}{}{{\Phi }_{\alpha }}{{C}_{\alpha \beta }}\delta {{\Phi }_{\beta }}={\frac {1}{2}}\left\{\sum \limits _{\alpha ,\beta =1}^{n}{}{{\Phi }_{\beta }}{{C}_{\beta \alpha }}\delta {{\Phi }_{\alpha }}+\sum \limits _{\alpha ,\beta =1}^{n}{}{{\Phi }_{\alpha }}{{C}_{\alpha \beta }}\delta {{\Phi }_{\beta }}\right\}\\&{{C}_{\beta \alpha }}={{C}_{\alpha \beta }}\\&\Rightarrow \delta W={\frac {1}{2}}\sum \limits _{\alpha ,\beta =1}^{n}{}{{C}_{\alpha \beta }}\left\{{{\Phi }_{\beta }}\delta {{\Phi }_{\alpha }}+{{\Phi }_{\alpha }}\delta {{\Phi }_{\beta }}\right\}=\delta \left\{{\frac {1}{2}}\sum \limits _{\alpha ,\beta =1}^{n}{}{{C}_{\alpha \beta }}{{\Phi }_{\alpha }}{{\Phi }_{\beta }}\right\}\\\end{aligned}}
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