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Display information for equation id:math.2123.12 on revision:2123
* Page found: Eichinvarianz (eq math.2123.12)
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Hash: 20c923fc8f8b0d9a64852c1b988cf8fb
TeX (original user input):
\begin{align}
& \nabla \cdot \bar{B}=0 \\
& \Rightarrow \exists \bar{A}\left( \bar{r},t \right)\Rightarrow \nabla \times \bar{A}\left( \bar{r},t \right)=\bar{B} \\
& \nabla \times \bar{E}=-\frac{\partial }{\partial t}\bar{B}=-\nabla \times \frac{\partial }{\partial t}\bar{A}\left( \bar{r},t \right)\Rightarrow \nabla \times \left( \bar{E}+\frac{\partial }{\partial t}\bar{A}\left( \bar{r},t \right) \right)=0 \\
& \Rightarrow \exists \Phi \left( \bar{r},t \right)\Rightarrow \bar{E}+\frac{\partial }{\partial t}\bar{A}\left( \bar{r},t \right)=-\nabla \Phi \left( \bar{r},t \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&\nabla \cdot {\bar {B}}=0\\&\Rightarrow \exists {\bar {A}}\left({\bar {r}},t\right)\Rightarrow \nabla \times {\bar {A}}\left({\bar {r}},t\right)={\bar {B}}\\&\nabla \times {\bar {E}}=-{\frac {\partial }{\partial t}}{\bar {B}}=-\nabla \times {\frac {\partial }{\partial t}}{\bar {A}}\left({\bar {r}},t\right)\Rightarrow \nabla \times \left({\bar {E}}+{\frac {\partial }{\partial t}}{\bar {A}}\left({\bar {r}},t\right)\right)=0\\&\Rightarrow \exists \Phi \left({\bar {r}},t\right)\Rightarrow {\bar {E}}+{\frac {\partial }{\partial t}}{\bar {A}}\left({\bar {r}},t\right)=-\nabla \Phi \left({\bar {r}},t\right)\\\end{aligned}}
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<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 mathvariant="normal">∇</mi><mo stretchy="false">⋅</mo><mover><mi>B</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mover><mi>A</mi><mo>¯</mo></mover><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><mo stretchy="false">⇒</mo><mi mathvariant="normal">∇</mi><mo stretchy="false">×</mo><mover><mi>A</mi><mo>¯</mo></mover><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><mo stretchy="false">=</mo><mover><mi>B</mi><mo>¯</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi mathvariant="normal">∇</mi><mo stretchy="false">×</mo><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mo stretchy="false">−</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><mover><mi>B</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi mathvariant="normal">∇</mi><mo stretchy="false">×</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><mover><mi>A</mi><mo>¯</mo></mover><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><mo stretchy="false">⇒</mo><mi mathvariant="normal">∇</mi><mo stretchy="false">×</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">+</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><mover><mi>A</mi><mo>¯</mo></mover><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><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"><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>Φ</mi><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><mo stretchy="false">⇒</mo><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">+</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><mover><mi>A</mi><mo>¯</mo></mover><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><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi mathvariant="normal">∇</mi><mi>Φ</mi><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></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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