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Display information for equation id:math.1443.137 on revision:1443
* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1443.137)
(force rerendering)Occurrences on the following pages:
Hash: e1b787816025a6528f1283ccee7be72a
TeX (original user input):
\begin{align}
& \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}\int_{V}^{{}}{{}}{{d}^{3}}r\frac{\partial }{\partial t}\bar{B} \\
& \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)=\begin{matrix}
\lim \\
h->0 \\
\end{matrix}\int_{V}^{{}}{{}}{{d}^{3}}r\left( \bar{j}+\frac{\partial }{\partial t}\bar{D} \right) \\
\end{align}
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MathML (5.886 KB / 607 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>lim</mi></mtd></mtr><mtr><mtd><mi>h</mi><mo>−</mo><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><munder><mstyle displaystyle="true"><mo>∮</mo></mstyle><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>V</mi></mrow></mrow></munder><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>f</mi><mo>¯</mo></mover></mrow></mrow><mo>×</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><munder><mstyle displaystyle="true"><mo>∮</mo></mstyle><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>V</mi></mrow></mrow></munder><mi>d</mi><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>n</mi><mo>¯</mo></mover></mrow></mrow><mo>×</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></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>−</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow 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>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>lim</mi></mtd></mtr><mtr><mtd><mi>h</mi><mo>−</mo><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>lim</mi></mtd></mtr><mtr><mtd><mi>h</mi><mo>−</mo><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><munder><mstyle displaystyle="true"><mo>∮</mo></mstyle><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>V</mi></mrow></mrow></munder><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>f</mi><mo>¯</mo></mover></mrow></mrow><mo>×</mo><mi>H</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><munder><mstyle displaystyle="true"><mo>∮</mo></mstyle><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>V</mi></mrow></mrow></munder><mi>d</mi><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>n</mi><mo>¯</mo></mover></mrow></mrow><mo>×</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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><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>−</mo><mi>H</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><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>2</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>lim</mi></mtd></mtr><mtr><mtd><mi>h</mi><mo>−</mo><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>j</mi><mo>¯</mo></mover></mrow></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>D</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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