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Display information for equation id:math.1443.198 on revision:1443
* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1443.198)
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Hash: a19ee01f82565580520500a24ebf2fce
TeX (original user input):
\begin{align}
& \rho =0 \\
& \nabla \times \bar{E}+\dot{\bar{B}}=0 \\
& \nabla \times \bar{B}-{{\mu }_{0}}\mu \varepsilon {{\varepsilon }_{0}}\dot{\bar{E}}={{\mu }_{0}}\mu \bar{j}={{\mu }_{0}}\mu \sigma \bar{E} \\
& \nabla \cdot \bar{E}=0 \\
& \nabla \cdot \bar{B}=0 \\
& \Rightarrow \nabla \times \left( \nabla \times \bar{E} \right)=\nabla \left( \nabla \cdot \bar{E} \right)-\Delta \bar{E}=-\Delta \bar{E}=-\nabla \times \dot{\bar{B}}=-{{\mu }_{0}}\mu \sigma \dot{\bar{E}}-{{\mu }_{0}}\mu \varepsilon {{\varepsilon }_{0}}\ddot{\bar{E}} \\
& \\
& \Delta \bar{E}={{\mu }_{0}}\mu \sigma \dot{\bar{E}}+{{\mu }_{0}}\mu \varepsilon {{\varepsilon }_{0}}\ddot{\bar{E}} \\
\end{align}
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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><mi>μ</mi><mi>ε</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><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><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>j</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>μ</mi><mi>σ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><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><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>E</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi mathvariant="normal">∇</mi><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>E</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><mo>−</mo><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><mo>−</mo><mi mathvariant="normal">∇</mi><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>B</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mo>=</mo><mo>−</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>μ</mi><mi>σ</mi><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><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>μ</mi><mi>ε</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><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></mtd></mtr><mtr><mtd></mtd><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>μ</mi><mi>σ</mi><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><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>μ</mi><mi>ε</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><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></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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