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Display information for equation id:math.2133.37 on revision:2133

* Page found: Multipolstrahlung (eq math.2133.37)

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TeX (original user input): 

\begin{align}
& \bar{S}=\bar{E}\times \bar{H}=\frac{-1}{{{\mu }_{0}}}\bar{B}\times \bar{E}=\frac{-c}{{{\mu }_{0}}r}\bar{B}\times \left( \bar{B}\times \bar{r} \right)=\frac{-c}{{{\mu }_{0}}r}\left[ \left( \bar{B}\cdot \bar{r} \right)\bar{B}-{{B}^{2}}\bar{r} \right] \\
& \left( \bar{B}\cdot \bar{r} \right)=0 \\
& \Rightarrow \bar{S}=\frac{c}{{{\mu }_{0}}r}{{B}^{2}}\bar{r} \\
\end{align}

TeX (checked): 

{\begin{aligned}&{\bar {S}}={\bar {E}}\times {\bar {H}}={\frac {-1}{{\mu }_{0}}}{\bar {B}}\times {\bar {E}}={\frac {-c}{{{\mu }_{0}}r}}{\bar {B}}\times \left({\bar {B}}\times {\bar {r}}\right)={\frac {-c}{{{\mu }_{0}}r}}\left[\left({\bar {B}}\cdot {\bar {r}}\right){\bar {B}}-{{B}^{2}}{\bar {r}}\right]\\&\left({\bar {B}}\cdot {\bar {r}}\right)=0\\&\Rightarrow {\bar {S}}={\frac {c}{{{\mu }_{0}}r}}{{B}^{2}}{\bar {r}}\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (32.48 KB / 3.656 KB) :

S ¯ = E ¯ × H ¯ = - 1 μ 0 ⁢ B ¯ × E ¯ = - c μ 0 ⁢ r ⁢ B ¯ × ( B ¯ × r ¯ ) = - c μ 0 ⁢ r ⁢ [ ( B ¯ ⋅ r ¯ ) ⁢ B ¯ - B 2 ⁢ r ¯ ] ( B ¯ ⋅ r ¯ ) = 0 ⇒ S ¯ = c μ 0 ⁢ r ⁢ B 2 ⁢ r ¯ missing-subexpression ¯ 𝑆 ¯ 𝐸 ¯ 𝐻 1 subscript 𝜇 0 ¯ 𝐵 ¯ 𝐸 𝑐 subscript 𝜇 0 𝑟 ¯ 𝐵 ¯ 𝐵 ¯ 𝑟 𝑐 subscript 𝜇 0 𝑟 delimited-[] ⋅ ¯ 𝐵 ¯ 𝑟 ¯ 𝐵 superscript 𝐵 2 ¯ 𝑟 missing-subexpression ⋅ ¯ 𝐵 ¯ 𝑟 0 missing-subexpression ⇒ absent ¯ 𝑆 𝑐 subscript 𝜇 0 𝑟 superscript 𝐵 2 ¯ 𝑟 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\bar{S}=\bar{E}% \times\bar{H}=\frac{-1}{{{\mu}_{0}}}\bar{B}\times\bar{E}=\frac{-c}{{{\mu}_{0}}% r}\bar{B}\times\left(\bar{B}\times\bar{r}\right)=\frac{-c}{{{\mu}_{0}}r}\left[% \left(\bar{B}\cdot\bar{r}\right)\bar{B}-{{B}^{2}}\bar{r}\right]\\ &\displaystyle\left(\bar{B}\cdot\bar{r}\right)=0\\ &\displaystyle\Rightarrow\bar{S}=\frac{c}{{{\mu}_{0}}r}{{B}^{2}}\bar{r}\\ \end{aligned}}}

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MathML (experimentell; keine Bilder) rendering

MathML (4.125 KB / 477 B) :

S¯=E¯×H¯=−1μ0B¯×E¯=−cμ0rB¯×(B¯×r¯)=−cμ0r[(B¯⋅r¯)B¯−B2r¯](B¯⋅r¯)=0⇒S¯=cμ0rB2r¯

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Calculated based on the variables occurring on the entire Multipolstrahlung page

Identifiers

  • S¯
  • E¯
  • H¯
  • μ0
  • B¯
  • E¯
  • c
  • μ0
  • r
  • B¯
  • B¯
  • r¯
  • c
  • μ0
  • r
  • B¯
  • r¯
  • B¯
  • B
  • r¯
  • B¯
  • r¯
  • S¯
  • c
  • μ0
  • r
  • B
  • r¯

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