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Display information for equation id:math.1199.983 on revision:1199
* Page found: Elektrodynamik Schöll (eq math.1199.983)
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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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data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>e</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow></msub><mo>≡</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>n</mi><mo>¯</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><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><mi>ρ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow 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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>D</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><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mi>F</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>D</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>D</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><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mi>F</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mi>d</mi><mi>f</mi><mi>σ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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