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Display information for equation id:math.1199.418 on revision:1199
* Page found: Elektrodynamik Schöll (eq math.1199.418)
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Hash: f73be062bf947077e8191c6bae3d4e6a
TeX (original user input):
\begin{align}
& 0=\frac{\partial }{\partial t}\left( {{\varepsilon }_{0}}{{\nabla }_{r}}\cdot \bar{E}-\rho \right)={{\varepsilon }_{0}}{{\nabla }_{r}}\cdot \dot{\bar{E}}-\dot{\rho }=\frac{{{\varepsilon }_{0}}}{{{a}_{2}}}\nabla \cdot \left( \nabla \times \bar{B}-{{\mu }_{0}}\bar{j} \right)-\dot{\rho } \\
& \frac{{{\varepsilon }_{0}}}{{{a}_{2}}}\nabla \cdot \nabla \times \bar{B}=0 \\
& \Rightarrow \frac{{{\varepsilon }_{0}}}{{{a}_{2}}}\nabla \cdot \left( {{\mu }_{0}}\bar{j} \right)-\dot{\rho }=0 \\
& \Rightarrow {{a}_{2}}={{\varepsilon }_{0}}{{\mu }_{0}} \\
\end{align}
TeX (checked):
{\begin{aligned}&0={\frac {\partial }{\partial t}}\left({{\varepsilon }_{0}}{{\nabla }_{r}}\cdot {\bar {E}}-\rho \right)={{\varepsilon }_{0}}{{\nabla }_{r}}\cdot {\dot {\bar {E}}}-{\dot {\rho }}={\frac {{\varepsilon }_{0}}{{a}_{2}}}\nabla \cdot \left(\nabla \times {\bar {B}}-{{\mu }_{0}}{\bar {j}}\right)-{\dot {\rho }}\\&{\frac {{\varepsilon }_{0}}{{a}_{2}}}\nabla \cdot \nabla \times {\bar {B}}=0\\&\Rightarrow {\frac {{\varepsilon }_{0}}{{a}_{2}}}\nabla \cdot \left({{\mu }_{0}}{\bar {j}}\right)-{\dot {\rho }}=0\\&\Rightarrow {{a}_{2}}={{\varepsilon }_{0}}{{\mu }_{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><mn>0</mn><mo>=</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><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>⋅</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>−</mo><mi>ρ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</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>⋅</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ρ</mi><mo>˙</mo></mover></mrow></mrow><mo>=</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"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></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"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mo>−</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>j</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ρ</mi><mo>˙</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><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"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><mi mathvariant="normal">∇</mi><mo>⋅</mo><mi mathvariant="normal">∇</mi><mo>×</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</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"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>j</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ρ</mi><mo>˙</mo></mover></mrow></mrow><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>=</mo><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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