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* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1444.51)

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\begin{align}
& {{{\bar{A}}}_{m}}\left( \bar{r},t \right)=\frac{{{\mu }_{0}}}{4\pi }\sum\limits_{i}{{}}\left[ \frac{1}{\left| \bar{r}-{{{\bar{r}}}_{i}} \right|}{{{\dot{\bar{p}}}}_{i}}\left( t-\frac{\left| \bar{r}-{{{\bar{r}}}_{i}} \right|}{c} \right)+\nabla \times \left( \frac{1}{\left| \bar{r}-{{{\bar{r}}}_{i}} \right|}{{{\bar{m}}}_{i}}\left( t-\frac{\left| \bar{r}-{{{\bar{r}}}_{i}} \right|}{c} \right) \right) \right] \\
& {{{\bar{p}}}_{i}}\left( t-\frac{\left| \bar{r}-{{{\bar{r}}}_{i}} \right|}{c} \right)\quad elektrDipolmoment \\
& {{{\bar{m}}}_{i}}\left( t-\frac{\left| \bar{r}-{{{\bar{r}}}_{i}} \right|}{c} \right)\quad magnetDipolmoment \\
& \Rightarrow {{{\bar{A}}}_{m}}\left( \bar{r},t \right)=\frac{{{\mu }_{0}}}{4\pi }\int_{{}}^{{}}{{}}{{d}^{3}}r\acute{\ }\left[ \frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}{{{\dot{\bar{p}}}}_{m}}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \right)+{{\nabla }_{r}}\times \left( \frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}{{{\bar{M}}}_{m}}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \right) \right) \right] \\
\end{align}

TeX (checked): 

{\begin{aligned}&{{\bar {A}}_{m}}\left({\bar {r}},t\right)={\frac {{\mu }_{0}}{4\pi }}\sum \limits _{i}{}\left[{\frac {1}{\left|{\bar {r}}-{{\bar {r}}_{i}}\right|}}{{\dot {\bar {p}}}_{i}}\left(t-{\frac {\left|{\bar {r}}-{{\bar {r}}_{i}}\right|}{c}}\right)+\nabla \times \left({\frac {1}{\left|{\bar {r}}-{{\bar {r}}_{i}}\right|}}{{\bar {m}}_{i}}\left(t-{\frac {\left|{\bar {r}}-{{\bar {r}}_{i}}\right|}{c}}\right)\right)\right]\\&{{\bar {p}}_{i}}\left(t-{\frac {\left|{\bar {r}}-{{\bar {r}}_{i}}\right|}{c}}\right)\quad elektrDipolmoment\\&{{\bar {m}}_{i}}\left(t-{\frac {\left|{\bar {r}}-{{\bar {r}}_{i}}\right|}{c}}\right)\quad magnetDipolmoment\\&\Rightarrow {{\bar {A}}_{m}}\left({\bar {r}},t\right)={\frac {{\mu }_{0}}{4\pi }}\int _{}^{}{}{{d}^{3}}r{\acute {\ }}\left[{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{{\dot {\bar {p}}}_{m}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)+{{\nabla }_{r}}\times \left({\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{{\bar {M}}_{m}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\right)\right]\\\end{aligned}}

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A ¯ m ⁢ ( r ¯ , t ) = μ 0 4 ⁢ π ⁢ ∑ i [ 1 | r ¯ - r ¯ i | ⁢ p ¯ ˙ i ⁢ ( t - | r ¯ - r ¯ i | c ) + ∇ × ( 1 | r ¯ - r ¯ i | ⁢ m ¯ i ⁢ ( t - | r ¯ - r ¯ i | c ) ) ] p ¯ i ⁢ ( t - | r ¯ - r ¯ i | c )   e ⁢ l ⁢ e ⁢ k ⁢ t ⁢ r ⁢ D ⁢ i ⁢ p ⁢ o ⁢ l ⁢ m ⁢ o ⁢ m ⁢ e ⁢ n ⁢ t m ¯ i ⁢ ( t - | r ¯ - r ¯ i | c )   m ⁢ a ⁢ g ⁢ n ⁢ e ⁢ t ⁢ D ⁢ i ⁢ p ⁢ o ⁢ l ⁢ m ⁢ o ⁢ m ⁢ e ⁢ n ⁢ t ⇒ A ¯ m ⁢ ( r ¯ , t ) = μ 0 4 ⁢ π ⁢ ∫ d 3 ⁢ r ⁢ ´ ⁢ [ 1 | r ¯ - r ¯ ⁢ ´ | ⁢ p ¯ ˙ m ⁢ ( r ¯ ⁢ ´ , t - | r ¯ - r ¯ ⁢ ´ | c ) + ∇ r × ( 1 | r ¯ - r ¯ ⁢ ´ | ⁢ M ¯ m ⁢ ( r ¯ ⁢ ´ , t - | r ¯ - r ¯ ⁢ ´ | c ) ) ] missing-subexpression subscript ¯ 𝐴 𝑚 ¯ 𝑟 𝑡 subscript 𝜇 0 4 𝜋 subscript 𝑖 delimited-[] 1 ¯ 𝑟 subscript ¯ 𝑟 𝑖 subscript ˙ ¯ 𝑝 𝑖 𝑡 ¯ 𝑟 subscript ¯ 𝑟 𝑖 𝑐 ∇ 1 ¯ 𝑟 subscript ¯ 𝑟 𝑖 subscript ¯ 𝑚 𝑖 𝑡 ¯ 𝑟 subscript ¯ 𝑟 𝑖 𝑐 missing-subexpression subscript ¯ 𝑝 𝑖 𝑡 ¯ 𝑟 subscript ¯ 𝑟 𝑖 𝑐 𝑒 𝑙 𝑒 𝑘 𝑡 𝑟 𝐷 𝑖 𝑝 𝑜 𝑙 𝑚 𝑜 𝑚 𝑒 𝑛 𝑡 missing-subexpression subscript ¯ 𝑚 𝑖 𝑡 ¯ 𝑟 subscript ¯ 𝑟 𝑖 𝑐 𝑚 𝑎 𝑔 𝑛 𝑒 𝑡 𝐷 𝑖 𝑝 𝑜 𝑙 𝑚 𝑜 𝑚 𝑒 𝑛 𝑡 missing-subexpression ⇒ absent subscript ¯ 𝐴 𝑚 ¯ 𝑟 𝑡 subscript 𝜇 0 4 𝜋 superscript 𝑑 3 𝑟 ´ absent delimited-[] 1 ¯ 𝑟 ¯ 𝑟 ´ absent subscript ˙ ¯ 𝑝 𝑚 ¯ 𝑟 ´ absent 𝑡 ¯ 𝑟 ¯ 𝑟 ´ absent 𝑐 subscript ∇ 𝑟 1 ¯ 𝑟 ¯ 𝑟 ´ absent subscript ¯ 𝑀 𝑚 ¯ 𝑟 ´ absent 𝑡 ¯ 𝑟 ¯ 𝑟 ´ absent 𝑐 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle{{{\bar{A}}}_{m}}% \left(\bar{r},t\right)=\frac{{{\mu}_{0}}}{4\pi}\sum\limits_{i}{{}}\left[\frac{% 1}{\left|\bar{r}-{{{\bar{r}}}_{i}}\right|}{{{\dot{\bar{p}}}}_{i}}\left(t-\frac% {\left|\bar{r}-{{{\bar{r}}}_{i}}\right|}{c}\right)+\nabla\times\left(\frac{1}{% \left|\bar{r}-{{{\bar{r}}}_{i}}\right|}{{{\bar{m}}}_{i}}\left(t-\frac{\left|% \bar{r}-{{{\bar{r}}}_{i}}\right|}{c}\right)\right)\right]\\ &\displaystyle{{{\bar{p}}}_{i}}\left(t-\frac{\left|\bar{r}-{{{\bar{r}}}_{i}}% \right|}{c}\right)\quad elektrDipolmoment\\ &\displaystyle{{{\bar{m}}}_{i}}\left(t-\frac{\left|\bar{r}-{{{\bar{r}}}_{i}}% \right|}{c}\right)\quad magnetDipolmoment\\ &\displaystyle\Rightarrow{{{\bar{A}}}_{m}}\left(\bar{r},t\right)=\frac{{{\mu}_% {0}}}{4\pi}\int{{}}{{d}^{3}}r\acute{\ }\left[\frac{1}{\left|\bar{r}-\bar{r}% \acute{\ }\right|}{{{\dot{\bar{p}}}}_{m}}\left(\bar{r}\acute{\ },t-\frac{\left% |\bar{r}-\bar{r}\acute{\ }\right|}{c}\right)+{{\nabla}_{r}}\times\left(\frac{1% }{\left|\bar{r}-\bar{r}\acute{\ }\right|}{{{\bar{M}}}_{m}}\left(\bar{r}\acute{% \ },t-\frac{\left|\bar{r}-\bar{r}\acute{\ }\right|}{c}\right)\right)\right]\\ \end{aligned}}}

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A¯m(r¯,t)=μ04π∑i[1|r¯−r¯i|p¯˙i(t−|r¯−r¯i|c)+∇×(1|r¯−r¯i|m¯i(t−|r¯−r¯i|c))]p¯i(t−|r¯−r¯i|c)elektrDipolmomentm¯i(t−|r¯−r¯i|c)magnetDipolmoment⇒A¯m(r¯,t)=μ04π∫d3r´[1|r¯−r¯´|p¯˙m(r¯´,t−|r¯−r¯´|c)+∇r×(1|r¯−r¯´|M¯m(r¯´,t−|r¯−r¯´|c))]

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