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Display information for equation id:math.2107.3 on revision:2107
* Page found: TCP- Invarianz (eq math.2107.3)
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Hash: a576d27c721a07a3dbb6e6711102a3e5
TeX (original user input):
\begin{align}
& T:\left\{ {{\nabla }_{r}}\times \bar{E}=0 \right\}\to \left\{ {{\nabla }_{r}}\times \bar{E}=0 \right\} \\
& T:\left\{ {{\varepsilon }_{0}}{{\nabla }_{r}}\cdot \bar{E}=\rho \right\}\to \left\{ {{\varepsilon }_{0}}{{\nabla }_{r}}\cdot \bar{E}=\rho \right\} \\
& T:\left\{ {{\nabla }_{r}}\cdot \bar{B}=0 \right\}\to \left\{ -{{\nabla }_{r}}\cdot \bar{B}=0 \right\}\Leftrightarrow \left\{ {{\nabla }_{r}}\cdot \bar{B}=0 \right\} \\
& T:\left\{ \nabla \times \bar{B}={{\mu }_{0}}\bar{j} \right\}\to \left\{ -\nabla \times \bar{B}=-{{\mu }_{0}}\bar{j} \right\} \\
& \\
\end{align}
TeX (checked):
{\begin{aligned}&T:\left\{{{\nabla }_{r}}\times {\bar {E}}=0\right\}\to \left\{{{\nabla }_{r}}\times {\bar {E}}=0\right\}\\&T:\left\{{{\varepsilon }_{0}}{{\nabla }_{r}}\cdot {\bar {E}}=\rho \right\}\to \left\{{{\varepsilon }_{0}}{{\nabla }_{r}}\cdot {\bar {E}}=\rho \right\}\\&T:\left\{{{\nabla }_{r}}\cdot {\bar {B}}=0\right\}\to \left\{-{{\nabla }_{r}}\cdot {\bar {B}}=0\right\}\Leftrightarrow \left\{{{\nabla }_{r}}\cdot {\bar {B}}=0\right\}\\&T:\left\{\nabla \times {\bar {B}}={{\mu }_{0}}{\bar {j}}\right\}\to \left\{-\nabla \times {\bar {B}}=-{{\mu }_{0}}{\bar {j}}\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>T</mi><mo stretchy="false">:</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo stretchy="false">×</mo><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo stretchy="false" accent="false">→</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo stretchy="false">×</mo><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">}</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>T</mi><mo stretchy="false">:</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo stretchy="false">⋅</mo><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mi>ρ</mi><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo stretchy="false" accent="false">→</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo stretchy="false">⋅</mo><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mi>ρ</mi><mo data-mjx-texclass="CLOSE">}</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>T</mi><mo stretchy="false">:</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo stretchy="false">⋅</mo><mover><mi>B</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo stretchy="false" accent="false">→</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mo stretchy="false">−</mo><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo stretchy="false">⋅</mo><mover><mi>B</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo stretchy="false">⇔</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo stretchy="false">⋅</mo><mover><mi>B</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">}</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>T</mi><mo stretchy="false">:</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mi mathvariant="normal">∇</mi><mo stretchy="false">×</mo><mover><mi>B</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mover><mi>j</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo stretchy="false" accent="false">→</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mo stretchy="false">−</mo><mi mathvariant="normal">∇</mi><mo stretchy="false">×</mo><mover><mi>B</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mo stretchy="false">−</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mover><mi>j</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE">}</mo></mrow></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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