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Display information for equation id:math.2152.4 on revision:2152

* Page found: Grenzbedingungen für Felder (eq math.2152.4)

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Grenzbedingungen für Felder Eq: math.2152.4

Hash: 690149f1bccd08a5997b4c5938a9edce

TeX (original user input):

\begin{align}
& \rho \left( \bar{r},t \right)=\sigma \left( x,y,t \right)\delta \left( z \right) \\
& {{{\bar{e}}}_{z}}\equiv \bar{n} \\
& \Rightarrow \begin{matrix}
\lim   \\
h->0  \\
\end{matrix}\int_{V}^{{}}{{}}{{d}^{3}}r\rho \left( \bar{r},t \right)=Q=\int_{F}^{{}}{{}}df\sigma \left( x,y,t \right) \\
& \begin{matrix}
\lim   \\
h->0  \\
\end{matrix}\oint\limits_{\partial V}{{}}d\bar{f}\cdot \bar{D}\left( \bar{r},t \right)=\int_{F}^{{}}{{}}d\bar{f}\left( {{{\bar{D}}}^{(1)}}-{{{\bar{D}}}^{(2)}} \right)=\int_{F}^{{}}{{}}df\bar{n}\left( {{{\bar{D}}}^{(1)}}-{{{\bar{D}}}^{(2)}} \right)=\int_{F}^{{}}{{}}df\sigma \left( x,y,t \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&\rho \left({\bar {r}},t\right)=\sigma \left(x,y,t\right)\delta \left(z\right)\\&{{\bar {e}}_{z}}\equiv {\bar {n}}\\&\Rightarrow {\begin{matrix}\lim \\h->0\\\end{matrix}}\int _{V}^{}{}{{d}^{3}}r\rho \left({\bar {r}},t\right)=Q=\int _{F}^{}{}df\sigma \left(x,y,t\right)\\&{\begin{matrix}\lim \\h->0\\\end{matrix}}\oint \limits _{\partial V}{}d{\bar {f}}\cdot {\bar {D}}\left({\bar {r}},t\right)=\int _{F}^{}{}d{\bar {f}}\left({{\bar {D}}^{(1)}}-{{\bar {D}}^{(2)}}\right)=\int _{F}^{}{}df{\bar {n}}\left({{\bar {D}}^{(1)}}-{{\bar {D}}^{(2)}}\right)=\int _{F}^{}{}df\sigma \left(x,y,t\right)\\\end{aligned}}

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\begin{matrix} ρ (\bar{r}, t) = σ (x, y, t) δ (z) \\ {\bar{e}}_{z} \equiv \bar{n} \\ \Rightarrow \begin{matrix} lim \\ h - > 0 \end{matrix} \int_{V}^{} d^{3} r ρ (\bar{r}, t) = Q = \int_{F}^{} d f σ (x, y, t) \\ \begin{matrix} lim \\ h - > 0 \end{matrix} \oint_{\partial V} d \bar{f} \cdot \bar{D} (\bar{r}, t) = \int_{F}^{} d \bar{f} ({\bar{D}}^{(1)} - {\bar{D}}^{(2)}) = \int_{F}^{} d f \bar{n} ({\bar{D}}^{(1)} - {\bar{D}}^{(2)}) = \int_{F}^{} d f σ (x, y, t) \end{matrix}

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Identifiers

$ρ$

$\bar{r}$

$t$

$σ$

$x$

$y$

$t$

$δ$

$z$

${\bar{e}}_{z}$

$\bar{n}$

$h$

$V$

$r$

$ρ$

$\bar{r}$

$t$

$Q$

$F$

$f$

$σ$

$x$

$y$

$t$

$h$

$V$

$d$

$\bar{f}$

$\bar{D}$

$\bar{r}$

$t$

$F$

$\bar{f}$

$\bar{D}$

$\bar{D}$

$F$

$f$

$\bar{n}$

$\bar{D}$

$\bar{D}$

$F$

$f$

$σ$

$x$

$y$

$t$

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