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Display information for equation id:math.2117.0 on revision:2117

* Page found: Impulsbilanz (eq math.2117.0)

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Hash: 2694f6cf2aa2a9a07e86450cf62860c0

TeX (original user input):

\begin{align}
& \frac{\partial }{\partial t}\left( \bar{D}\times \bar{B} \right)=\dot{\bar{D}}\times \bar{B}+\bar{D}\times \dot{\bar{B}} \\
& \dot{\bar{D}}=\nabla \times \bar{H}-\bar{j} \\
& \dot{\bar{B}}=-\nabla \times \bar{E} \\
& \Rightarrow \frac{\partial }{\partial t}\left( \bar{D}\times \bar{B} \right)=-\frac{1}{{{\mu }_{0}}}\bar{B}\times \left( \nabla \times \bar{B} \right)-\bar{j}\times \bar{B}-{{\varepsilon }_{o}}\bar{E}\times \left( \nabla \times \bar{E} \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {\partial }{\partial t}}\left({\bar {D}}\times {\bar {B}}\right)={\dot {\bar {D}}}\times {\bar {B}}+{\bar {D}}\times {\dot {\bar {B}}}\\&{\dot {\bar {D}}}=\nabla \times {\bar {H}}-{\bar {j}}\\&{\dot {\bar {B}}}=-\nabla \times {\bar {E}}\\&\Rightarrow {\frac {\partial }{\partial t}}\left({\bar {D}}\times {\bar {B}}\right)=-{\frac {1}{{\mu }_{0}}}{\bar {B}}\times \left(\nabla \times {\bar {B}}\right)-{\bar {j}}\times {\bar {B}}-{{\varepsilon }_{o}}{\bar {E}}\times \left(\nabla \times {\bar {E}}\right)\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (33.26 KB / 3.787 KB) :

t ( D ¯ × B ¯ ) = D ¯ ˙ × B ¯ + D ¯ × B ¯ ˙ D ¯ ˙ = × H ¯ - j ¯ B ¯ ˙ = - × E ¯ t ( D ¯ × B ¯ ) = - 1 μ 0 B ¯ × ( × B ¯ ) - j ¯ × B ¯ - ε o E ¯ × ( × E ¯ ) missing-subexpression 𝑡 ¯ 𝐷 ¯ 𝐵 ˙ ¯ 𝐷 ¯ 𝐵 ¯ 𝐷 ˙ ¯ 𝐵 missing-subexpression ˙ ¯ 𝐷 ¯ 𝐻 ¯ 𝑗 missing-subexpression ˙ ¯ 𝐵 ¯ 𝐸 missing-subexpression absent 𝑡 ¯ 𝐷 ¯ 𝐵 1 subscript 𝜇 0 ¯ 𝐵 ¯ 𝐵 ¯ 𝑗 ¯ 𝐵 subscript 𝜀 𝑜 ¯ 𝐸 ¯ 𝐸 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\frac{\partial}{% \partial t}\left(\bar{D}\times\bar{B}\right)=\dot{\bar{D}}\times\bar{B}+\bar{D% }\times\dot{\bar{B}}\\ &\displaystyle\dot{\bar{D}}=\nabla\times\bar{H}-\bar{j}\\ &\displaystyle\dot{\bar{B}}=-\nabla\times\bar{E}\\ &\displaystyle\Rightarrow\frac{\partial}{\partial t}\left(\bar{D}\times\bar{B}% \right)=-\frac{1}{{{\mu}_{0}}}\bar{B}\times\left(\nabla\times\bar{B}\right)-% \bar{j}\times\bar{B}-{{\varepsilon}_{o}}\bar{E}\times\left(\nabla\times\bar{E}% \right)\\ \end{aligned}}}

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MathML (experimentell; keine Bilder) rendering

MathML (4.571 KB / 524 B) :

t(D¯×B¯)=D¯˙×B¯+D¯×B¯˙D¯˙=×H¯j¯B¯˙=×E¯t(D¯×B¯)=1μ0B¯×(×B¯)j¯×B¯εoE¯×(×E¯)

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Calculated based on the variables occurring on the entire Impulsbilanz page

Identifiers

  • t
  • D¯
  • B¯
  • D¯˙
  • B¯
  • D¯
  • B¯˙
  • D¯˙
  • H¯
  • j¯
  • B¯˙
  • E¯
  • t
  • D¯
  • B¯
  • μ0
  • B¯
  • B¯
  • j¯
  • B¯
  • εo
  • E¯
  • E¯

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