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Display information for equation id:math.2118.7 on revision:2118

* Page found: Impulsbilanz (eq math.2118.7)

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Impulsbilanz Eq: math.2119.7

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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\begin{matrix} \bar{E} \times (\nabla \times \bar{E}) = \nabla \cdot {(1) \frac{1}{2} (\bar{E} \cdot \bar{E}) - \bar{E} \otimes \bar{E}} + \bar{E} (\nabla \cdot \bar{E}) = \nabla \cdot {(1) \frac{1}{2} (\bar{E} \cdot \bar{E}) - \bar{E} \otimes \bar{E}} + \bar{E} \frac{ρ}{ε_{0}} \\ \Rightarrow \frac{\partial}{\partial t} (\bar{D} \times \bar{B}) + \nabla \cdot {(1) \frac{1}{2} (ε_{0} E^{2} + \frac{1}{μ_{0}} B^{2}) - ε_{0} \bar{E} \otimes \bar{E} - \frac{1}{μ_{0}} \bar{B} \otimes \bar{B}} = - (\bar{E} ρ + \bar{j} \times \bar{B}) \end{matrix}

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Identifiers

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$\bar{E}$

$ρ$

$ε_{0}$

$t$

$\bar{D}$

$\bar{B}$

$ε_{0}$

$E$

$μ_{0}$

$B$

$ε_{0}$

$\bar{E}$

$\bar{E}$

$μ_{0}$

$\bar{B}$

$\bar{B}$

$\bar{E}$

$ρ$

$\bar{j}$

$\bar{B}$

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