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Display information for equation id:math.2075.19 on revision:2075
* Page found: Poisson- Gleichung und Greensche Funktion (eq math.2075.19)
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Hash: 0f5579b2ddcea579f2e04fc060a6f8e6
TeX (original user input):
\begin{align}
& \int_{V}^{{}}{{{d}^{3}}}r\Delta \Phi (\bar{r})=\frac{1}{4\pi {{\varepsilon }_{0}}}\int_{{{R}^{3}}}^{{}}{{{d}^{3}}r\acute{\ }}\rho \left( \bar{r}\acute{\ } \right)\oint\limits_{\partial V}{d\bar{f}\cdot {{\nabla }_{r}}}\frac{1}{|\bar{r}-\bar{r}\acute{\ }|} \\
& {{\nabla }_{r}}\frac{1}{|\bar{r}-\bar{r}\acute{\ }|}=-\frac{\left( \bar{r}-\bar{r}\acute{\ } \right)}{|\bar{r}-\bar{r}\acute{\ }{{|}^{3}}} \\
\end{align}
TeX (checked):
{\begin{aligned}&\int _{V}^{}{{d}^{3}}r\Delta \Phi ({\bar {r}})={\frac {1}{4\pi {{\varepsilon }_{0}}}}\int _{{R}^{3}}^{}{{{d}^{3}}r{\acute {\ }}}\rho \left({\bar {r}}{\acute {\ }}\right)\oint \limits _{\partial V}{d{\bar {f}}\cdot {{\nabla }_{r}}}{\frac {1}{|{\bar {r}}-{\bar {r}}{\acute {\ }}|}}\\&{{\nabla }_{r}}{\frac {1}{|{\bar {r}}-{\bar {r}}{\acute {\ }}|}}=-{\frac {\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right)}{|{\bar {r}}-{\bar {r}}{\acute {\ }}{{|}^{3}}}}\\\end{aligned}}
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