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Display information for equation id:math.1199.766 on revision:1199
* Page found: Elektrodynamik Schöll (eq math.1199.766)
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Hash: ecb942b54903ac2387fecb8bd271b513
TeX (original user input):
\begin{align}
& \frac{\partial }{\partial t}\Phi \left( \bar{r},t \right)=-{{c}^{2}}\nabla \cdot \bar{A}\left( \bar{r},t \right)=-\frac{{{\mu }_{0}}{{c}^{2}}}{4\pi }\nabla \cdot \left( \nabla \times \frac{1}{r}\bar{m} \right)\equiv 0 \\
& \Rightarrow \Phi \left( \bar{r},t \right)=\Phi \left( {\bar{r}} \right)=!=0 \\
\end{align}
TeX (checked):
{\begin{aligned}&{\frac {\partial }{\partial t}}\Phi \left({\bar {r}},t\right)=-{{c}^{2}}\nabla \cdot {\bar {A}}\left({\bar {r}},t\right)=-{\frac {{{\mu }_{0}}{{c}^{2}}}{4\pi }}\nabla \cdot \left(\nabla \times {\frac {1}{r}}{\bar {m}}\right)\equiv 0\\&\Rightarrow \Phi \left({\bar {r}},t\right)=\Phi \left({\bar {r}}\right)=!=0\\\end{aligned}}
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<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"><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><mi mathvariant="normal">Φ</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><mo>−</mo><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><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><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi></mrow></mrow></mfrac></mrow><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">∇</mi><mo>×</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>m</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>≡</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi mathvariant="normal">Φ</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><mi mathvariant="normal">Φ</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 data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>!</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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