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Display information for equation id:math.2141.32 on revision:2141

* Page found: Polarisation (eq math.2141.32)

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Polarisation Eq: math.2141.32

Hash: 905439da9a5a397cf2cf10cb9639ee3c

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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\begin{aligned} \nabla_{r} {\frac{1}{| \bar{r} - \bar{r} \overset{´}{} |} \bar{P} (\bar{r} \overset{´}{}, t - \frac{| \bar{r} - \bar{r} \overset{´}{} |}{c})} = - \nabla_{r \overset{´}{}} {\frac{1}{| \bar{r} - \bar{r} \overset{´}{} |} \bar{P} (\bar{r} \overset{´}{}, t - \frac{| \bar{r} - \bar{r} \overset{´}{} |}{c})} + \frac{1}{| \bar{r} - \bar{r} \overset{´}{} |} \nabla_{r \overset{´}{}} \bar{P} (\bar{r} \overset{´}{}, t - \frac{| \bar{r} - \bar{r} \overset{´}{} |}{c}) \\ t \overset{´}{} = t - \frac{| \bar{r} - \bar{r} \overset{´}{} |}{c} \\ \nabla_{r} {\frac{1}{| \bar{r} - \bar{r} \overset{´}{} |} \bar{P} (\bar{r} \overset{´}{}, t - \frac{| \bar{r} - \bar{r} \overset{´}{} |}{c})} = - \nabla_{r \overset{´}{}} {\frac{1}{| \bar{r} - \bar{r} \overset{´}{} |} \bar{P} (\bar{r} \overset{´}{}, t - \frac{| \bar{r} - \bar{r} \overset{´}{} |}{c})} + \frac{1}{| \bar{r} - \bar{r} \overset{´}{} |} \nabla_{r \overset{´}{}} \bar{P} (\bar{r} \overset{´}{}, t \overset{´}{}) \end{aligned}

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Identifiers

$r$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{P}$

$\bar{r}$

$\overset{´}{}$

$t$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$c$

$r$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{P}$

$\bar{r}$

$\overset{´}{}$

$t$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$c$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$r$

$\overset{´}{}$

$\bar{P}$

$\bar{r}$

$\overset{´}{}$

$t$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$c$

$t$

$\overset{´}{}$

$t$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$c$

$r$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{P}$

$\bar{r}$

$\overset{´}{}$

$t$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$c$

$r$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{P}$

$\bar{r}$

$\overset{´}{}$

$t$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$c$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$r$

$\overset{´}{}$

$\bar{P}$

$\bar{r}$

$\overset{´}{}$

$t$

$\overset{´}{}$

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