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Display information for equation id:math.2084.12 on revision:2084
* Page found: Die elektrostatische Feldenergie (eq math.2084.12)
(force rerendering)Occurrences on the following pages:
Hash: 057d613e90d8ba66fe00f18c9388b1b3
TeX (original user input):
\begin{align}
& W=\frac{{{\varepsilon }_{0}}}{2}\left[ \int_{{{S}_{\infty }}}^{{}}{\left( \Phi (\bar{r})\bar{E} \right)d\bar{f}}+\int_{{{R}^{3}}}^{{}}{{{{\bar{E}}}^{2}}(\bar{r}){{d}^{3}}r} \right] \\
& \begin{matrix}
\lim \\
r\to \infty \\
\end{matrix}\left( \Phi (\bar{r})\bar{E} \right)=0 \\
& \\
\end{align}
TeX (checked):
{\begin{aligned}&W={\frac {{\varepsilon }_{0}}{2}}\left[\int _{{S}_{\infty }}^{}{\left(\Phi ({\bar {r}}){\bar {E}}\right)d{\bar {f}}}+\int _{{R}^{3}}^{}{{{\bar {E}}^{2}}({\bar {r}}){{d}^{3}}r}\right]\\&{\begin{matrix}\lim \\r\to \infty \\\end{matrix}}\left(\Phi ({\bar {r}}){\bar {E}}\right)=0\\&\\\end{aligned}}
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MathML (2.526 KB / 536 B) :
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>W</mi><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>Φ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mover><mi>E</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>d</mi><mover><mi>f</mi><mo>¯</mo></mover></mrow><mo stretchy="false">+</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mrow data-mjx-texclass="ORD"><msup><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><mo>lim</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo stretchy="false" accent="false">→</mo><mi mathvariant="normal">∞</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>Φ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mover><mi>E</mi><mo>¯</mo></mover><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"></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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