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Display information for equation id:math.1444.32 on revision:1444
* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1444.32)
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TeX (original user input):
\begin{align}
& {{\nabla }_{r}}\left\{ \frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}\bar{P}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \right) \right\}=-{{\nabla }_{r\acute{\ }}}\left\{ \frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}\bar{P}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \right) \right\}+\frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}{{\nabla }_{r\acute{\ }}}\bar{P}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \right) \\
& t\acute{\ }=t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \\
& {{\nabla }_{r}}\left\{ \frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}\bar{P}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \right) \right\}=-{{\nabla }_{r\acute{\ }}}\left\{ \frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}\bar{P}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \right) \right\}+\frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}{{\nabla }_{r\acute{\ }}}\bar{P}\left( \bar{r}\acute{\ },t\acute{\ } \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\nabla }_{r}}\left\{{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{\bar {P}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\right\}=-{{\nabla }_{r{\acute {\ }}}}\left\{{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{\bar {P}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\right\}+{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{{\nabla }_{r{\acute {\ }}}}{\bar {P}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\\&t{\acute {\ }}=t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\\&{{\nabla }_{r}}\left\{{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{\bar {P}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\right\}=-{{\nabla }_{r{\acute {\ }}}}\left\{{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{\bar {P}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\right\}+{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{{\nabla }_{r{\acute {\ }}}}{\bar {P}}\left({\bar {r}}{\acute {\ }},t{\acute {\ }}\right)\\\end{aligned}}
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