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Display information for equation id:math.2143.14 on revision:2143

* Page found: Magnetisierung (eq math.2143.14)

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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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data-mjx-texclass="OPEN">[</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mfrac></mrow><msub><mover><mover><mi>p</mi><mo>¯</mo></mover><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><mi mathvariant="normal">∇</mi><mo stretchy="false">×</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mfrac></mrow><msub><mover><mi>m</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mover><mi>p</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mspace width="1em"></mspace><mi>e</mi><mi>l</mi><mi>e</mi><mi>k</mi><mi>t</mi><mi>r</mi><mi>D</mi><mi>i</mi><mi>p</mi><mi>o</mi><mi>l</mi><mi>m</mi><mi>o</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mover><mi>m</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mspace width="1em"></mspace><mi>m</mi><mi>a</mi><mi>g</mi><mi>n</mi><mi>e</mi><mi>t</mi><mi>D</mi><mi>i</mi><mi>p</mi><mi>o</mi><mi>l</mi><mi>m</mi><mi>o</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><msub><mover><mi>A</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi></mrow></mrow></mfrac></mrow><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mfrac></mrow><msub><mover><mover><mi>p</mi><mo>¯</mo></mover><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo stretchy="false">×</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mfrac></mrow><msub><mover><mi>M</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Magnetisierung page

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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