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Display information for equation id:math.1199.499 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.499)

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Hash: c7322b35c7728c56edb577290272ce2b

TeX (original user input): 

\begin{align}
& \bar{E}\times \left( \nabla \times \bar{E} \right)=\nabla \cdot \left\{ \left( 1 \right)\frac{1}{2}\left( \bar{E}\cdot \bar{E} \right)-\bar{E}\otimes \bar{E} \right\}+\bar{E}\left( \nabla \cdot \bar{E} \right)=\nabla \cdot \left\{ \left( 1 \right)\frac{1}{2}\left( \bar{E}\cdot \bar{E} \right)-\bar{E}\otimes \bar{E} \right\}+\bar{E}\frac{\rho }{{{\varepsilon }_{0}}} \\
& \Rightarrow \frac{\partial }{\partial t}\left( \bar{D}\times \bar{B} \right)+\nabla \cdot \left\{ \left( 1 \right)\frac{1}{2}\left( {{\varepsilon }_{0}}{{E}^{2}}+\frac{1}{{{\mu }_{0}}}{{B}^{2}} \right)-{{\varepsilon }_{0}}\bar{E}\otimes \bar{E}-\frac{1}{{{\mu }_{0}}}\bar{B}\otimes \bar{B} \right\}=-\left( \bar{E}\rho +\bar{j}\times \bar{B} \right) \\
\end{align}

TeX (checked): 

{\begin{aligned}&{\bar {E}}\times \left(\nabla \times {\bar {E}}\right)=\nabla \cdot \left\{\left(1\right){\frac {1}{2}}\left({\bar {E}}\cdot {\bar {E}}\right)-{\bar {E}}\otimes {\bar {E}}\right\}+{\bar {E}}\left(\nabla \cdot {\bar {E}}\right)=\nabla \cdot \left\{\left(1\right){\frac {1}{2}}\left({\bar {E}}\cdot {\bar {E}}\right)-{\bar {E}}\otimes {\bar {E}}\right\}+{\bar {E}}{\frac {\rho }{{\varepsilon }_{0}}}\\&\Rightarrow {\frac {\partial }{\partial t}}\left({\bar {D}}\times {\bar {B}}\right)+\nabla \cdot \left\{\left(1\right){\frac {1}{2}}\left({{\varepsilon }_{0}}{{E}^{2}}+{\frac {1}{{\mu }_{0}}}{{B}^{2}}\right)-{{\varepsilon }_{0}}{\bar {E}}\otimes {\bar {E}}-{\frac {1}{{\mu }_{0}}}{\bar {B}}\otimes {\bar {B}}\right\}=-\left({\bar {E}}\rho +{\bar {j}}\times {\bar {B}}\right)\\\end{aligned}}

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E¯×(∇×E¯)=∇⋅{(1)12(E¯⋅E¯)−E¯⊗E¯}+E¯(∇⋅E¯)=∇⋅{(1)12(E¯⋅E¯)−E¯⊗E¯}+E¯ρε0⇒∂∂t(D¯×B¯)+∇⋅{(1)12(ε0E2+1μ0B2)−ε0E¯⊗E¯−1μ0B¯⊗B¯}=−(E¯ρ+j¯×B¯)
<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"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x00D7;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">&#x2207;</mi><mo>&#x00D7;</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">&#x2207;</mi><mo>&#x22C5;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo 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data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">&#x2207;</mi><mo>&#x22C5;</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">&#x2207;</mi><mo>&#x22C5;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x22C5;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo 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data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>D</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x00D7;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mi mathvariant="normal">&#x2207;</mi><mo>&#x22C5;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>&#x03B5;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>&#x03BC;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mfrac></mrow><msup><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2212;</mo><msub><mi>&#x03B5;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2297;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>&#x03BC;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2297;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo>=</mo><mo>&#x2212;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mi>&#x03C1;</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>j</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x00D7;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Elektrodynamik Schöll page

Identifiers

  • E¯
  • E¯
  • E¯
  • E¯
  • E¯
  • E¯
  • E¯
  • E¯
  • E¯
  • E¯
  • E¯
  • E¯
  • E¯
  • ρ
  • ε0
  • t
  • D¯
  • B¯
  • ε0
  • E
  • μ0
  • B
  • ε0
  • E¯
  • E¯
  • μ0
  • B¯
  • B¯
  • E¯
  • ρ
  • j¯
  • B¯

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