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Display information for equation id:math.2126.46 on revision:2126

* Page found: Freie Wellenausbreitung im Vakuum (eq math.2126.46)

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Freie Wellenausbreitung im Vakuum Eq: math.2126.46

Hash: 7d87efc2cb7340a9abc705e3fdb5d8ac

TeX (original user input):

\begin{align}
& \nabla \times \bar{E}(\bar{r},t)+\dot{\bar{B}}=0 \\
& \Rightarrow \left( i\bar{k}\times {{{\bar{E}}}_{0}}-i\varpi {{{\bar{B}}}_{0}} \right){{e}^{i\left( \bar{k}\bar{r}-\varpi t \right)}}=0 \\
& \varpi =c\left| {\bar{k}} \right| \\
& \Rightarrow {{{\bar{B}}}_{0}}=\frac{1}{c}\frac{{\bar{k}}}{\left| {\bar{k}} \right|}\times {{{\bar{E}}}_{0}}:=\frac{1}{c}\bar{n}\times {{{\bar{E}}}_{0}} \\
\end{align}

TeX (checked):

{\begin{aligned}&\nabla \times {\bar {E}}({\bar {r}},t)+{\dot {\bar {B}}}=0\\&\Rightarrow \left(i{\bar {k}}\times {{\bar {E}}_{0}}-i\varpi {{\bar {B}}_{0}}\right){{e}^{i\left({\bar {k}}{\bar {r}}-\varpi t\right)}}=0\\&\varpi =c\left|{\bar {k}}\right|\\&\Rightarrow {{\bar {B}}_{0}}={\frac {1}{c}}{\frac {\bar {k}}{\left|{\bar {k}}\right|}}\times {{\bar {E}}_{0}}:={\frac {1}{c}}{\bar {n}}\times {{\bar {E}}_{0}}\\\end{aligned}}

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MathML (3.906 KB / 561 B) :

\begin{aligned} \nabla \times \bar{E} (\bar{r}, t) + \dot{\bar{B}} = 0 \\ \Rightarrow (i \bar{k} \times {\bar{E}}_{0} - i ϖ {\bar{B}}_{0}) e^{i (\bar{k} \bar{r} - ϖ t)} = 0 \\ ϖ = c | \bar{k} | \\ \Rightarrow {\bar{B}}_{0} = \frac{1}{c} \frac{\bar{k}}{| \bar{k} |} \times {\bar{E}}_{0} : = \frac{1}{c} \bar{n} \times {\bar{E}}_{0} \end{aligned}

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Identifiers

$\bar{E}$

$\bar{r}$

$t$

$\dot{\bar{B}}$

$i$

$\bar{k}$

${\bar{E}}_{0}$

$i$

$ϖ$

${\bar{B}}_{0}$

$e$

$i$

$\bar{k}$

$\bar{r}$

$ϖ$

$t$

$ϖ$

$c$

$\bar{k}$

${\bar{B}}_{0}$

$c$

$\bar{k}$

$\bar{k}$

${\bar{E}}_{0}$

$c$

$\bar{n}$

${\bar{E}}_{0}$

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