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Display information for equation id:math.2152.20 on revision:2152

* Page found: Grenzbedingungen für Felder (eq math.2152.20)

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Grenzbedingungen für Felder Eq: math.2152.20

Hash: a4aa7ffb47e8a07d4c9d36579d7e1c89

TeX (original user input):

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

TeX (checked):

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

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

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data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><munder><mo>&#x222E;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>V</mi></mrow></mrow></munder><mi>d</mi><mi>f</mi><mover><mi>n</mi><mo>¯</mo></mover><mo stretchy="false">×</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>H</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo stretchy="false">−</mo><mi>H</mi><msup><mrow data-mjx-texclass="INNER"><mo 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Identifiers

$h$

$V$

$r$

$t$

$\bar{B}$

$h$

$V$

$r$

$t$

$\bar{D}$

$h$

$V$

$r$

$\bar{j}$

$t$

$\bar{D}$

$F$

$f$

$\bar{g}$

$x$

$y$

$t$

$V$

$d$

$f$

$\bar{n}$

$\bar{E}$

$\bar{E}$

$V$

$d$

$f$

$\bar{n}$

$H$

$\bar{r}$

$t$

$H$

$\bar{r}$

$t$

$F$

$f$

$\bar{g}$

$x$

$y$

$t$

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