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Display information for equation id:math.1199.278 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.278)

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TeX (original user input):

\begin{align}
& \Rightarrow \delta W=\frac{{{\varepsilon }_{0}}}{2}\int_{V}^{{}}{{{d}^{3}}r(2\bar{E}(\bar{r})\delta \bar{E}(\bar{r}))=-}{{\varepsilon }_{0}}\int_{V}^{{}}{{{d}^{3}}r(\nabla \Phi (\bar{r})\delta \bar{E}(\bar{r}))} \\
& (\nabla \Phi (\bar{r})\delta \bar{E}(\bar{r}))=\nabla \left( \Phi (\bar{r})\delta \bar{E}(\bar{r}) \right)-\Phi (\bar{r})\nabla \delta \bar{E}(\bar{r}) \\
& \nabla \cdot \delta \bar{E}(\bar{r})=\delta \nabla \cdot \bar{E}(\bar{r})=0,da\ \rho =0 \\
\end{align}

TeX (checked):

{\begin{aligned}&\Rightarrow \delta W={\frac {{\varepsilon }_{0}}{2}}\int _{V}^{}{{{d}^{3}}r(2{\bar {E}}({\bar {r}})\delta {\bar {E}}({\bar {r}}))=-}{{\varepsilon }_{0}}\int _{V}^{}{{{d}^{3}}r(\nabla \Phi ({\bar {r}})\delta {\bar {E}}({\bar {r}}))}\\&(\nabla \Phi ({\bar {r}})\delta {\bar {E}}({\bar {r}}))=\nabla \left(\Phi ({\bar {r}})\delta {\bar {E}}({\bar {r}})\right)-\Phi ({\bar {r}})\nabla \delta {\bar {E}}({\bar {r}})\\&\nabla \cdot \delta {\bar {E}}({\bar {r}})=\delta \nabla \cdot {\bar {E}}({\bar {r}})=0,da\ \rho =0\\\end{aligned}}

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\begin{aligned} \Rightarrow δ W = \frac{ε_{0}}{2} \int_{V}^{} d^{3} r (2 \bar{E} (\bar{r}) δ \bar{E} (\bar{r})) = - ε_{0} \int_{V}^{} d^{3} r (\nabla Φ (\bar{r}) δ \bar{E} (\bar{r})) \\ (\nabla Φ (\bar{r}) δ \bar{E} (\bar{r})) = \nabla (Φ (\bar{r}) δ \bar{E} (\bar{r})) - Φ (\bar{r}) \nabla δ \bar{E} (\bar{r}) \\ \nabla \cdot δ \bar{E} (\bar{r}) = δ \nabla \cdot \bar{E} (\bar{r}) = 0, d a ρ = 0 \end{aligned}

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Identifiers

$δ$

$W$

$ε_{0}$

$V$

$r$

$\bar{E}$

$\bar{r}$

$δ$

$\bar{E}$

$\bar{r}$

$ε_{0}$

$V$

$r$

$Φ$

$\bar{r}$

$δ$

$\bar{E}$

$\bar{r}$

$Φ$

$\bar{r}$

$δ$

$\bar{E}$

$\bar{r}$

$Φ$

$\bar{r}$

$δ$

$\bar{E}$

$\bar{r}$

$Φ$

$\bar{r}$

$δ$

$\bar{E}$

$\bar{r}$

$δ$

$\bar{E}$

$\bar{r}$

$δ$

$\bar{E}$

$\bar{r}$

$d$

$a$

$ρ$

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