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Display information for equation id:math.2099.12 on revision:2099

* Page found: Magnetische Multipole (eq math.2099.12)

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TeX (original user input): 

\int_{{}}^{{}}{{{d}^{3}}r\acute{\ }}{{j}_{k}}(\bar{r}\acute{\ })=\int_{{}}^{{}}{{{d}^{3}}r\acute{\ }}{{\nabla }_{r\acute{\ }}}\cdot \left[ {{x}_{k}}\acute{\ }\bar{j}(\bar{r}\acute{\ }) \right]=\oint\limits_{S\infty }{d\bar{f}}\left[ {{x}_{k}}\acute{\ }\bar{j}(\bar{r}\acute{\ }) \right]=0

TeX (checked): 

\int _{}^{}{{{d}^{3}}r{\acute {\ }}}{{j}_{k}}({\bar {r}}{\acute {\ }})=\int _{}^{}{{{d}^{3}}r{\acute {\ }}}{{\nabla }_{r{\acute {\ }}}}\cdot \left[{{x}_{k}}{\acute {\ }}{\bar {j}}({\bar {r}}{\acute {\ }})\right]=\oint \limits _{S\infty }{d{\bar {f}}}\left[{{x}_{k}}{\acute {\ }}{\bar {j}}({\bar {r}}{\acute {\ }})\right]=0

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MathML (22.09 KB / 2.888 KB) :

∫ d 3 ⁢ r ⁢ ´ ⁢ j k ⁢ ( r ¯ ⁢ ´ ) = ∫ d 3 ⁢ r ⁢ ´ ⁢ ∇ r ⁢ ´ ⋅ [ x k ⁢ ´ ⁢ j ¯ ⁢ ( r ¯ ⁢ ´ ) ] = ∮ S ⁢ ∞ 𝑑 f ¯ ⁢ [ x k ⁢ ´ ⁢ j ¯ ⁢ ( r ¯ ⁢ ´ ) ] = 0 superscript 𝑑 3 𝑟 ´ absent subscript 𝑗 𝑘 ¯ 𝑟 ´ absent ⋅ superscript 𝑑 3 𝑟 ´ absent subscript ∇ 𝑟 ´ absent delimited-[] subscript 𝑥 𝑘 ´ absent ¯ 𝑗 ¯ 𝑟 ´ absent subscript contour-integral 𝑆 differential-d ¯ 𝑓 delimited-[] subscript 𝑥 𝑘 ´ absent ¯ 𝑗 ¯ 𝑟 ´ absent 0 {\displaystyle{\displaystyle\int{{{d}^{3}}r\acute{\ }}{{j}_{k}}(\bar{r}\acute{% \ })=\int{{{d}^{3}}r\acute{\ }}{{\nabla}_{r\acute{\ }}}\cdot\left[{{x}_{k}}% \acute{\ }\bar{j}(\bar{r}\acute{\ })\right]=\oint\limits_{S\infty}{d\bar{f}}% \left[{{x}_{k}}\acute{\ }\bar{j}(\bar{r}\acute{\ })\right]=0}}

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MathML (3.585 KB / 476 B) :

∫d3r´jk(r¯´)=∫d3r´∇r´⋅[xk´j¯(r¯´)]=∮S∞df¯[xk´j¯(r¯´)]=0

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Calculated based on the variables occurring on the entire Magnetische Multipole page

Identifiers

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