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Display information for equation id:math.1199.332 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.332)

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TeX (original user input): 

\begin{align}
& \Delta \bar{A}(\bar{r})=\frac{{{\mu }_{0}}}{4\pi }\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }{{\Delta }_{r}}\cdot \left( \frac{\bar{j}(\bar{r}\acute{\ })}{\left| \bar{r}-\bar{r}\acute{\ } \right|} \right)=\frac{{{\mu }_{0}}}{4\pi }\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }\bar{j}(\bar{r}\acute{\ }){{\Delta }_{r}}\cdot \left( \frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|} \right) \\
& =\frac{{{\mu }_{0}}}{4\pi }\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }\bar{j}(\bar{r}\acute{\ })\delta \left( \bar{r}-\bar{r}\acute{\ } \right)=-{{\mu }_{0}}\bar{j}(\bar{r}) \\
\end{align}

TeX (checked): 

{\begin{aligned}&\Delta {\bar {A}}({\bar {r}})={\frac {{\mu }_{0}}{4\pi }}\int _{{R}^{3}}^{}{}{{d}^{3}}r{\acute {\ }}{{\Delta }_{r}}\cdot \left({\frac {{\bar {j}}({\bar {r}}{\acute {\ }})}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}\right)={\frac {{\mu }_{0}}{4\pi }}\int _{{R}^{3}}^{}{}{{d}^{3}}r{\acute {\ }}{\bar {j}}({\bar {r}}{\acute {\ }}){{\Delta }_{r}}\cdot \left({\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}\right)\\&={\frac {{\mu }_{0}}{4\pi }}\int _{{R}^{3}}^{}{}{{d}^{3}}r{\acute {\ }}{\bar {j}}({\bar {r}}{\acute {\ }})\delta \left({\bar {r}}-{\bar {r}}{\acute {\ }}\right)=-{{\mu }_{0}}{\bar {j}}({\bar {r}})\\\end{aligned}}

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ΔA¯(r¯)=μ04π∫R3d3r´Δr⋅(j¯(r¯´)|r¯−r¯´|)=μ04π∫R3d3r´j¯(r¯´)Δr⋅(1|r¯−r¯´|)=μ04π∫R3d3r´j¯(r¯´)δ(r¯−r¯´)=−μ0j¯(r¯)
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Calculated based on the variables occurring on the entire Elektrodynamik Schöll page

Identifiers

  • Δ
  • A¯
  • r¯
  • μ0
  • π
  • R
  • r
  • ´
  • Δr
  • j¯
  • r¯
  • ´
  • r¯
  • r¯
  • ´
  • μ0
  • π
  • R
  • r
  • ´
  • j¯
  • r¯
  • ´
  • Δr
  • r¯
  • r¯
  • ´
  • μ0
  • π
  • R
  • r
  • ´
  • j¯
  • r¯
  • ´
  • δ
  • r¯
  • r¯
  • ´
  • μ0
  • j¯
  • r¯

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