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Display information for equation id:math.1199.1053 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.1053)

Occurrences on the following pages:

Wellenausbreitung in Materie Eq: math.2160.3

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}

TeX (checked):

{\begin{aligned}&\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{aligned}}

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MathML (5.349 KB / 535 B) :

\begin{aligned} ρ = 0 \\ \nabla \times \bar{E} + \dot{\bar{B}} = 0 \\ \nabla \times \bar{B} - μ_{0} μ ε ε_{0} \dot{\bar{E}} = μ_{0} μ \bar{j} = μ_{0} μ σ \bar{E} \\ \nabla \cdot \bar{E} = 0 \\ \nabla \cdot \bar{B} = 0 \\ \Rightarrow \nabla \times (\nabla \times \bar{E}) = \nabla (\nabla \cdot \bar{E}) - Δ \bar{E} = - Δ \bar{E} = - \nabla \times \dot{\bar{B}} = - μ_{0} μ σ \dot{\bar{E}} - μ_{0} μ ε ε_{0} \ddot{\bar{E}} \\ Δ \bar{E} = μ_{0} μ σ \dot{\bar{E}} + μ_{0} μ ε ε_{0} \ddot{\bar{E}} \end{aligned}

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Identifiers

$ρ$

$\bar{E}$

$\dot{\bar{B}}$

$\bar{B}$

$μ_{0}$

$μ$

$ε$

$ε_{0}$

$\dot{\bar{E}}$

$μ_{0}$

$μ$

$\bar{j}$

$μ_{0}$

$μ$

$σ$

$\bar{E}$

$\bar{E}$

$\bar{B}$

$\bar{E}$

$\bar{E}$

$Δ$

$\bar{E}$

$Δ$

$\bar{E}$

$\dot{\bar{B}}$

$μ_{0}$

$μ$

$σ$

$\dot{\bar{E}}$

$μ_{0}$

$μ$

$ε$

$ε_{0}$

$\ddot{\bar{E}}$

$Δ$

$\bar{E}$

$μ_{0}$

$μ$

$σ$

$\dot{\bar{E}}$

$μ_{0}$

$μ$

$ε$

$ε_{0}$

$\ddot{\bar{E}}$

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