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Display information for equation id:math.2101.14 on revision:2101

* Page found: Magnetische Multipole (eq math.2101.14)

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Magnetische Multipole Eq: math.2101.14

Hash: c068c753414c0f9f1a6d13719db45893

TeX (original user input):

\begin{align}
& {{\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}=0 \\
& \Rightarrow {{\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) \right] \\
\end{align}

TeX (checked):

{\begin{aligned}&{{\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}}=0\\&\Rightarrow {{\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)\right]\\\end{aligned}}

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MathML (6.864 KB / 535 B) :

\begin{aligned} \nabla_{r \overset{´}{}} [x_{k} \overset{´}{} (\bar{r} \bar{r} \overset{´}{}) \bar{j}] = [(\bar{r} \bar{r} \overset{´}{}) j_{k} + x_{k} \overset{´}{} (\bar{r} \bar{j}) + x_{k \overset{´}{}} (\bar{r} \bar{r} \overset{´}{}) \nabla_{r \overset{´}{}} \cdot \bar{j}] \\ \nabla_{r \overset{´}{}} \cdot \bar{j} = 0 \\ \Rightarrow \nabla_{r \overset{´}{}} [x_{k} \overset{´}{} (\bar{r} \bar{r} \overset{´}{}) \bar{j}] = [(\bar{r} \bar{r} \overset{´}{}) j_{k} + x_{k} \overset{´}{} (\bar{r} \bar{j})] \end{aligned}

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