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Display information for equation id:math.2099.27 on revision:2099

* Page found: Magnetische Multipole (eq math.2099.27)

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\Rightarrow \bar{m}=\frac{1}{2}\oint\limits_{L}{{}}{{d}^{3}}r\acute{\ }\left( \bar{r}\acute{\ }\times \bar{j}(\bar{r}\acute{\ }) \right)=\frac{I}{2}\oint\limits_{L}{{}}\bar{r}\acute{\ }\times d\bar{s}\acute{\ }=I\int_{F}^{{}}{{}}d\bar{f}\acute{\ }=IF\bar{n}

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⇒ m ¯ = 1 2 ⁢ ∮ L d 3 ⁢ r ⁢ ´ ⁢ ( r ¯ ⁢ ´ × j ¯ ⁢ ( r ¯ ⁢ ´ ) ) = I 2 ⁢ ∮ L r ¯ ⁢ ´ × 𝑑 s ¯ ⁢ ´ = I ⁢ ∫ F 𝑑 f ¯ ⁢ ´ = I ⁢ F ⁢ n ¯ ⇒ absent ¯ 𝑚 1 2 subscript contour-integral 𝐿 superscript 𝑑 3 𝑟 ´ absent ¯ 𝑟 ´ absent ¯ 𝑗 ¯ 𝑟 ´ absent 𝐼 2 subscript contour-integral 𝐿 ¯ 𝑟 ´ absent differential-d ¯ 𝑠 ´ absent 𝐼 subscript 𝐹 differential-d ¯ 𝑓 ´ absent 𝐼 𝐹 ¯ 𝑛 {\displaystyle{\displaystyle\Rightarrow\bar{m}=\frac{1}{2}\oint\limits_{L}{{}}% {{d}^{3}}r\acute{\ }\left(\bar{r}\acute{\ }\times\bar{j}(\bar{r}\acute{\ })% \right)=\frac{I}{2}\oint\limits_{L}{{}}\bar{r}\acute{\ }\times d\bar{s}\acute{% \ }=I\int_{F}{{}}d\bar{f}\acute{\ }=IF\bar{n}}}

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⇒m¯=12∮Ld3r´(r¯´×j¯(r¯´))=I2∮Lr¯´×ds¯´=I∫Fdf¯´=IFn¯

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