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Display information for equation id:math.1199.756 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.756)

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\begin{align}
& \left( \bar{r}\bar{r}\acute{\ } \right)\bar{j}\left( \bar{r}\acute{\ },\tau  \right)=\frac{1}{2}\left( \bar{r}\acute{\ }\times \bar{j} \right)\times \bar{r}+\frac{1}{2}\left[ \left( \bar{r}\bar{r}\acute{\ } \right)\bar{j}+\left( \bar{r}\bar{j} \right)\bar{r}\acute{\ } \right] \\
& und \\
& {{\nabla }_{r\acute{\ }}}\left[ {{x}_{k}}\acute{\ }\left( \bar{r}\bar{r}\acute{\ } \right)\bar{j} \right]=\left[ \left( \bar{r}\bar{r}\acute{\ } \right){{j}_{k}}+{{x}_{k}}\acute{\ }\left( \bar{r}\bar{j} \right)+{{x}_{k\acute{\ }}}\left( \bar{r}\bar{r}\acute{\ } \right){{\nabla }_{r\acute{\ }}}\cdot \bar{j} \right] \\
& {{\nabla }_{r\acute{\ }}}\cdot \bar{j}=-\frac{\partial }{\partial \tau }\rho \left( \bar{r}\acute{\ },\tau  \right) \\
\end{align}

TeX (checked): 

{\begin{aligned}&\left({\bar {r}}{\bar {r}}{\acute {\ }}\right){\bar {j}}\left({\bar {r}}{\acute {\ }},\tau \right)={\frac {1}{2}}\left({\bar {r}}{\acute {\ }}\times {\bar {j}}\right)\times {\bar {r}}+{\frac {1}{2}}\left[\left({\bar {r}}{\bar {r}}{\acute {\ }}\right){\bar {j}}+\left({\bar {r}}{\bar {j}}\right){\bar {r}}{\acute {\ }}\right]\\&und\\&{{\nabla }_{r{\acute {\ }}}}\left[{{x}_{k}}{\acute {\ }}\left({\bar {r}}{\bar {r}}{\acute {\ }}\right){\bar {j}}\right]=\left[\left({\bar {r}}{\bar {r}}{\acute {\ }}\right){{j}_{k}}+{{x}_{k}}{\acute {\ }}\left({\bar {r}}{\bar {j}}\right)+{{x}_{k{\acute {\ }}}}\left({\bar {r}}{\bar {r}}{\acute {\ }}\right){{\nabla }_{r{\acute {\ }}}}\cdot {\bar {j}}\right]\\&{{\nabla }_{r{\acute {\ }}}}\cdot {\bar {j}}=-{\frac {\partial }{\partial \tau }}\rho \left({\bar {r}}{\acute {\ }},\tau \right)\\\end{aligned}}

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(r¯r¯´)j¯(r¯´,τ)=12(r¯´×j¯)×r¯+12[(r¯r¯´)j¯+(r¯j¯)r¯´]und∇r´[xk´(r¯r¯´)j¯]=[(r¯r¯´)jk+xk´(r¯j¯)+xk´(r¯r¯´)∇r´⋅j¯]∇r´⋅j¯=−∂∂τρ(r¯´,τ)
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Calculated based on the variables occurring on the entire Elektrodynamik Schöll page

Identifiers

  • r¯
  • r¯
  • ´
  • j¯
  • r¯
  • ´
  • τ
  • r¯
  • ´
  • j¯
  • r¯
  • r¯
  • r¯
  • ´
  • j¯
  • r¯
  • j¯
  • r¯
  • ´
  • u
  • n
  • d
  • r
  • ´
  • xk
  • ´
  • r¯
  • r¯
  • ´
  • j¯
  • r¯
  • r¯
  • ´
  • jk
  • xk
  • ´
  • r¯
  • j¯
  • x
  • k
  • ´
  • r¯
  • r¯
  • ´
  • r
  • ´
  • j¯
  • r
  • ´
  • j¯
  • τ
  • ρ
  • r¯
  • ´
  • τ

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