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Display information for equation id:math.2152.12 on revision:2152

* Page found: Grenzbedingungen für Felder (eq math.2152.12)

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Grenzbedingungen für Felder Eq: math.2152.12

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TeX (original user input):

\begin{align}
& \int_{V}^{{}}{{}}{{d}^{3}}r\nabla \times \bar{E}=\oint\limits_{\partial V}{{}}d\bar{f}\times \bar{E}=-\int_{V}^{{}}{{}}{{d}^{3}}r\frac{\partial }{\partial t}\bar{B} \\
& \int_{V}^{{}}{{}}{{d}^{3}}r\nabla \times H\left( \bar{r},t \right)=\oint\limits_{\partial V}{{}}d\bar{f}\times H\left( \bar{r},t \right)=\int_{V}^{{}}{{}}{{d}^{3}}r\left( \bar{j}+\frac{\partial }{\partial t}\bar{D} \right) \\
& \begin{matrix}
\lim   \\
h->0  \\
\end{matrix}\oint\limits_{\partial V}{{}}d\bar{f}\times \bar{E}=\oint\limits_{\partial V}{{}}df\bar{n}\times \left( {{{\bar{E}}}^{(1)}}-{{{\bar{E}}}^{(2)}} \right) \\
& \begin{matrix}
\lim   \\
h->0  \\
\end{matrix}\oint\limits_{\partial V}{{}}d\bar{f}\times H\left( \bar{r},t \right)=\oint\limits_{\partial V}{{}}df\bar{n}\times \left( H{{\left( \bar{r},t \right)}^{(1)}}-H{{\left( \bar{r},t \right)}^{(2)}} \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&\int _{V}^{}{}{{d}^{3}}r\nabla \times {\bar {E}}=\oint \limits _{\partial V}{}d{\bar {f}}\times {\bar {E}}=-\int _{V}^{}{}{{d}^{3}}r{\frac {\partial }{\partial t}}{\bar {B}}\\&\int _{V}^{}{}{{d}^{3}}r\nabla \times H\left({\bar {r}},t\right)=\oint \limits _{\partial V}{}d{\bar {f}}\times H\left({\bar {r}},t\right)=\int _{V}^{}{}{{d}^{3}}r\left({\bar {j}}+{\frac {\partial }{\partial t}}{\bar {D}}\right)\\&{\begin{matrix}\lim \\h->0\\\end{matrix}}\oint \limits _{\partial V}{}d{\bar {f}}\times {\bar {E}}=\oint \limits _{\partial V}{}df{\bar {n}}\times \left({{\bar {E}}^{(1)}}-{{\bar {E}}^{(2)}}\right)\\&{\begin{matrix}\lim \\h->0\\\end{matrix}}\oint \limits _{\partial V}{}d{\bar {f}}\times H\left({\bar {r}},t\right)=\oint \limits _{\partial V}{}df{\bar {n}}\times \left(H{{\left({\bar {r}},t\right)}^{(1)}}-H{{\left({\bar {r}},t\right)}^{(2)}}\right)\\\end{aligned}}

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\begin{matrix} \int_{V}^{} d^{3} r \nabla \times \bar{E} = \oint_{\partial V} d \bar{f} \times \bar{E} = - \int_{V}^{} d^{3} r \frac{\partial}{\partial t} \bar{B} \\ \int_{V}^{} d^{3} r \nabla \times H (\bar{r}, t) = \oint_{\partial V} d \bar{f} \times H (\bar{r}, t) = \int_{V}^{} d^{3} r (\bar{j} + \frac{\partial}{\partial t} \bar{D}) \\ \begin{matrix} lim \\ h - > 0 \end{matrix} \oint_{\partial V} d \bar{f} \times \bar{E} = \oint_{\partial V} d f \bar{n} \times ({\bar{E}}^{(1)} - {\bar{E}}^{(2)}) \\ \begin{matrix} lim \\ h - > 0 \end{matrix} \oint_{\partial V} d \bar{f} \times H (\bar{r}, t) = \oint_{\partial V} d f \bar{n} \times (H {(\bar{r}, t)}^{(1)} - H {(\bar{r}, t)}^{(2)}) \end{matrix}

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Identifiers

$V$

$r$

$\bar{E}$

$V$

$d$

$\bar{f}$

$\bar{E}$

$V$

$r$

$t$

$\bar{B}$

$V$

$r$

$H$

$\bar{r}$

$t$

$V$

$d$

$\bar{f}$

$H$

$\bar{r}$

$t$

$V$

$r$

$\bar{j}$

$t$

$\bar{D}$

$h$

$V$

$d$

$\bar{f}$

$\bar{E}$

$V$

$d$

$f$

$\bar{n}$

$\bar{E}$

$\bar{E}$

$h$

$V$

$d$

$\bar{f}$

$H$

$\bar{r}$

$t$

$V$

$d$

$f$

$\bar{n}$

$H$

$\bar{r}$

$t$

$H$

$\bar{r}$

$t$

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