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Display information for equation id:math.1199.45 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.45)

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Hash: 504494fbf9ce1adb0a423ffa4fc4ace7

TeX (original user input):

\begin{align}
& \bar{E}(\bar{r})=\frac{1}{4\pi {{\varepsilon }_{0}}}\sum\limits_{i}^{{}}{{}}\frac{{{q}_{i}}}{|\bar{r}-{{{\bar{r}}}_{i}}{{|}^{3}}}\left( \bar{r}-{{{\bar{r}}}_{i}} \right)=-\nabla \Phi (\bar{r}) \\
& \Phi (\bar{r}):=\frac{1}{4\pi {{\varepsilon }_{0}}}\sum\limits_{i}^{{}}{{}}\frac{{{q}_{i}}}{|\bar{r}-{{{\bar{r}}}_{i}}|} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\bar {E}}({\bar {r}})={\frac {1}{4\pi {{\varepsilon }_{0}}}}\sum \limits _{i}^{}{}{\frac {{q}_{i}}{|{\bar {r}}-{{\bar {r}}_{i}}{{|}^{3}}}}\left({\bar {r}}-{{\bar {r}}_{i}}\right)=-\nabla \Phi ({\bar {r}})\\&\Phi ({\bar {r}}):={\frac {1}{4\pi {{\varepsilon }_{0}}}}\sum \limits _{i}^{}{}{\frac {{q}_{i}}{|{\bar {r}}-{{\bar {r}}_{i}}|}}\\\end{aligned}}

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MathML (3.605 KB / 532 B) :

E¯(r¯)=14πε0iqi|r¯r¯i|3(r¯r¯i)=Φ(r¯)Φ(r¯):=14πε0iqi|r¯r¯i|
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mo>=</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="ORD"><mn>4</mn><mi>&#x03C0;</mi><msub><mi>&#x03B5;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>|</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2212;</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><msup><mo>|</mo><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2212;</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>&#x2212;</mo><mi mathvariant="normal">&#x2207;</mi><mi mathvariant="normal">&#x03A6;</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi mathvariant="normal">&#x03A6;</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mi>:</mi><mo>=</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="ORD"><mn>4</mn><mi>&#x03C0;</mi><msub><mi>&#x03B5;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>|</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2212;</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>|</mo></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Elektrodynamik Schöll page

Identifiers

  • E¯
  • r¯
  • π
  • ε0
  • i
  • qi
  • r¯
  • r¯i
  • r¯
  • r¯i
  • Φ
  • r¯
  • Φ
  • r¯
  • π
  • ε0
  • i
  • qi
  • r¯
  • r¯i

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