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Display information for equation id:math.2144.14 on revision:2144

* Page found: Magnetisierung (eq math.2144.14)

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TeX (original user input): 

\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)=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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Identifiers

  • A¯m
  • r¯
  • t
  • μ0
  • π
  • i
  • r¯
  • r¯i
  • p¯˙i
  • t
  • r¯
  • r¯i
  • c
  • 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
  • μ0
  • π
  • r
  • ´
  • r¯
  • r¯
  • ´
  • p¯˙m
  • r¯
  • ´
  • t
  • r¯
  • r¯
  • ´
  • c
  • r
  • r¯
  • r¯
  • ´
  • M¯m
  • r¯
  • ´
  • t
  • r¯
  • r¯
  • ´
  • c

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