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* Page found: Magnetisierung (eq math.2144.17)

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TeX (original user input): 

\begin{align}
& \bar{A}\left( \bar{r},t \right)=\frac{1}{\Delta V}\int_{\Delta V}^{{}}{{}}{{d}^{3}}s{{{\bar{A}}}_{m}}\left( \bar{r}+\bar{s},t \right) \\
& =\frac{{{\mu }_{0}}}{4\pi }\frac{1}{\Delta V}\int_{\Delta V}^{{}}{{}}{{d}^{3}}s\int_{{}}^{{}}{{}}{{d}^{3}}r\acute{\ }\left[ \frac{1}{\left| \bar{r}+\bar{s}-\bar{r}\acute{\ } \right|}{{{\dot{\bar{p}}}}_{m}}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}+\bar{s}-\bar{r}\acute{\ } \right|}{c} \right)+{{\nabla }_{r}}\times \left( \frac{1}{\left| \bar{r}+\bar{s}-\bar{r}\acute{\ } \right|}{{{\bar{M}}}_{m}}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}+\bar{s}-\bar{r}\acute{\ } \right|}{c} \right) \right) \right] \\
& ==\frac{{{\mu }_{0}}}{4\pi }\int_{{}}^{{}}{{}}{{d}^{3}}r\acute{\ }\left[ \frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}\dot{\bar{P}}\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}\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}}\left({\bar {r}},t\right)={\frac {1}{\Delta V}}\int _{\Delta V}^{}{}{{d}^{3}}s{{\bar {A}}_{m}}\left({\bar {r}}+{\bar {s}},t\right)\\&={\frac {{\mu }_{0}}{4\pi }}{\frac {1}{\Delta V}}\int _{\Delta V}^{}{}{{d}^{3}}s\int _{}^{}{}{{d}^{3}}r{\acute {\ }}\left[{\frac {1}{\left|{\bar {r}}+{\bar {s}}-{\bar {r}}{\acute {\ }}\right|}}{{\dot {\bar {p}}}_{m}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}+{\bar {s}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)+{{\nabla }_{r}}\times \left({\frac {1}{\left|{\bar {r}}+{\bar {s}}-{\bar {r}}{\acute {\ }}\right|}}{{\bar {M}}_{m}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}+{\bar {s}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\right)\right]\\&=={\frac {{\mu }_{0}}{4\pi }}\int _{}^{}{}{{d}^{3}}r{\acute {\ }}\left[{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{\dot {\bar {P}}}\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}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\right)\right]\\\end{aligned}}

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A¯(r¯,t)=1ΔV∫ΔVd3sA¯m(r¯+s¯,t)=μ04π1ΔV∫ΔVd3s∫d3r´[1|r¯+s¯−r¯´|p¯˙m(r¯´,t−|r¯+s¯−r¯´|c)+∇r×(1|r¯+s¯−r¯´|M¯m(r¯´,t−|r¯+s¯−r¯´|c))]==μ04π∫d3r´[1|r¯−r¯´|P¯˙(r¯´,t−|r¯−r¯´|c)+∇r×(1|r¯−r¯´|M¯(r¯´,t−|r¯−r¯´|c))]
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Calculated based on the variables occurring on the entire Magnetisierung page

Identifiers

  • A¯
  • r¯
  • t
  • Δ
  • V
  • Δ
  • V
  • s
  • A¯m
  • r¯
  • s¯
  • t
  • μ0
  • π
  • Δ
  • V
  • Δ
  • V
  • s
  • r
  • ´
  • r¯
  • s¯
  • r¯
  • ´
  • p¯˙m
  • r¯
  • ´
  • t
  • r¯
  • s¯
  • r¯
  • ´
  • c
  • r
  • r¯
  • s¯
  • r¯
  • ´
  • M¯m
  • r¯
  • ´
  • t
  • r¯
  • s¯
  • r¯
  • ´
  • c
  • μ0
  • π
  • r
  • ´
  • r¯
  • r¯
  • ´
  • P¯˙
  • r¯
  • ´
  • t
  • r¯
  • r¯
  • ´
  • c
  • r
  • r¯
  • r¯
  • ´
  • M¯
  • r¯
  • ´
  • t
  • r¯
  • r¯
  • ´
  • c

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