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Display information for equation id:math.2156.8 on revision:2156

* Page found: Mikroskopisches Modell der Polarisierbarkeit (eq math.2156.8)

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Mikroskopisches Modell der Polarisierbarkeit Eq: math.2156.8

Hash: e5093dc39b2bb10586745130007919fb

TeX (original user input):

\begin{align}
& {{\varepsilon }_{0}}\oint\limits_{\partial V(r\acute{\ })}{{}}d\bar{f}\cdot \bar{E}\left( \bar{r},t \right)=\int_{V(r\acute{\ })}^{{}}{{}}\frac{Q}{\frac{4}{3}\pi {{R}^{3}}}=\frac{r{{\acute{\ }}^{3}}}{{{R}^{3}}}Q \\
& \Rightarrow 4r{{\acute{\ }}^{2}}\pi {{\varepsilon }_{0}}\left| \bar{E}\left( \bar{r},t \right) \right|=\frac{r{{\acute{\ }}^{3}}}{{{R}^{3}}}Q \\
& \Rightarrow \left| \bar{E}\left( \bar{r},t \right) \right|=\frac{r\acute{\ }}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}Q \\
\end{align}

TeX (checked):

{\begin{aligned}&{{\varepsilon }_{0}}\oint \limits _{\partial V(r{\acute {\ }})}{}d{\bar {f}}\cdot {\bar {E}}\left({\bar {r}},t\right)=\int _{V(r{\acute {\ }})}^{}{}{\frac {Q}{{\frac {4}{3}}\pi {{R}^{3}}}}={\frac {r{{\acute {\ }}^{3}}}{{R}^{3}}}Q\\&\Rightarrow 4r{{\acute {\ }}^{2}}\pi {{\varepsilon }_{0}}\left|{\bar {E}}\left({\bar {r}},t\right)\right|={\frac {r{{\acute {\ }}^{3}}}{{R}^{3}}}Q\\&\Rightarrow \left|{\bar {E}}\left({\bar {r}},t\right)\right|={\frac {r{\acute {\ }}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}}Q\\\end{aligned}}

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\begin{aligned} ε_{0} \oint_{\partial V (r \overset{´}{})} d \bar{f} \cdot \bar{E} (\bar{r}, t) = \int_{V (r \overset{´}{})}^{} \frac{Q}{\frac{4}{3} π R^{3}} = \frac{r {\overset{´}{}}^{3}}{R^{3}} Q \\ \Rightarrow 4 r {\overset{´}{}}^{2} π ε_{0} | \bar{E} (\bar{r}, t) | = \frac{r {\overset{´}{}}^{3}}{R^{3}} Q \\ \Rightarrow | \bar{E} (\bar{r}, t) | = \frac{r \overset{´}{}}{4 π ε_{0} R^{3}} Q \end{aligned}

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Identifiers

$ε_{0}$

$V$

$r$

$\overset{´}{}$

$d$

$\bar{f}$

$\bar{E}$

$\bar{r}$

$t$

$V$

$r$

$\overset{´}{}$

$Q$

$π$

$R$

$r$

$\overset{´}{}$

$R$

$Q$

$r$

$\overset{´}{}$

$π$

$ε_{0}$

$\bar{E}$

$\bar{r}$

$t$

$r$

$\overset{´}{}$

$R$

$Q$

$\bar{E}$

$\bar{r}$

$t$

$r$

$\overset{´}{}$

$π$

$ε_{0}$

$R$

$Q$

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