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Display information for equation id:math.1443.189 on revision:1443

* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1443.189)

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Mikroskopisches Modell der Polarisierbarkeit Eq: math.2156.29

Hash: 0dcc6d45700cc580ab364a7e98642898

TeX (original user input):

\begin{align}
& \bar{P}=\frac{{\bar{p}}}{\frac{4}{3}{{a}^{3}}\pi } \\
& \Rightarrow {{\Phi }_{0}}\left( {\bar{r}} \right)\approx {{{\bar{r}}}_{0}}{{{\bar{E}}}_{0}}=\frac{Q}{4\pi {{\varepsilon }_{0}}}\left\{ \begin{matrix}
\frac{{{{\bar{r}}}_{0}}\bar{r}}{{{a}^{3}}}r\le a  \\
\frac{{{{\bar{r}}}_{0}}\bar{r}}{{{r}^{3}}}r\ge a  \\
\end{matrix} \right.=\frac{1}{{{\varepsilon }_{0}}}\left\{ \begin{matrix}
\frac{\bar{P}\bar{r}}{3}r\le a  \\
\bar{P}\bar{r}\frac{{{a}^{3}}}{{{r}^{3}}}r\ge a  \\
\end{matrix} \right. \\
\end{align}

TeX (checked):

{\begin{aligned}&{\bar {P}}={\frac {\bar {p}}{{\frac {4}{3}}{{a}^{3}}\pi }}\\&\Rightarrow {{\Phi }_{0}}\left({\bar {r}}\right)\approx {{\bar {r}}_{0}}{{\bar {E}}_{0}}={\frac {Q}{4\pi {{\varepsilon }_{0}}}}\left\{{\begin{matrix}{\frac {{{\bar {r}}_{0}}{\bar {r}}}{{a}^{3}}}r\leq a\\{\frac {{{\bar {r}}_{0}}{\bar {r}}}{{r}^{3}}}r\geq a\\\end{matrix}}\right.={\frac {1}{{\varepsilon }_{0}}}\left\{{\begin{matrix}{\frac {{\bar {P}}{\bar {r}}}{3}}r\leq a\\{\bar {P}}{\bar {r}}{\frac {{a}^{3}}{{r}^{3}}}r\geq a\\\end{matrix}}\right.\\\end{aligned}}

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\begin{matrix} \bar{P} = \frac{\bar{p}}{\frac{4}{3} a^{3} π} \\ \Rightarrow Φ_{0} (\bar{r}) \approx {\bar{r}}_{0} {\bar{E}}_{0} = \frac{Q}{4 π ε_{0}} {\begin{matrix} \frac{{\bar{r}}_{0} \bar{r}}{a^{3}} r \leq a \\ \frac{{\bar{r}}_{0} \bar{r}}{r^{3}} r \geq a \end{matrix} = \frac{1}{ε_{0}} {\begin{matrix} \frac{\bar{P} \bar{r}}{3} r \leq a \\ \bar{P} \bar{r} \frac{a^{3}}{r^{3}} r \geq a \end{matrix} \end{matrix}

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Identifiers

$\bar{P}$

$\bar{p}$

$a$

$π$

$Φ_{0}$

$\bar{r}$

${\bar{r}}_{0}$

${\bar{E}}_{0}$

$Q$

$π$

$ε_{0}$

${\bar{r}}_{0}$

$\bar{r}$

$a$

$r$

$a$

${\bar{r}}_{0}$

$\bar{r}$

$r$

$r$

$a$

$ε_{0}$

$\bar{P}$

$\bar{r}$

$r$

$a$

$\bar{P}$

$\bar{r}$

$a$

$r$

$r$

$a$

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