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Display information for equation id:math.1199.171 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.171)

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TeX (original user input):

W=\frac{{{\varepsilon }_{0}}}{2}\int_{{{R}^{3}}}^{{}}{\Phi (\bar{r})\nabla \cdot \bar{E}{{d}^{3}}r}=\frac{{{\varepsilon }_{0}}}{2}\left[ \int_{{{R}^{3}}}^{{}}{\nabla \cdot \left( \Phi (\bar{r})\bar{E} \right){{d}^{3}}r}-\int_{{{R}^{3}}}^{{}}{\left( \nabla \Phi (\bar{r}) \right)\cdot \bar{E}{{d}^{3}}r} \right]

TeX (checked):

W={\frac {{\varepsilon }_{0}}{2}}\int _{{R}^{3}}^{}{\Phi ({\bar {r}})\nabla \cdot {\bar {E}}{{d}^{3}}r}={\frac {{\varepsilon }_{0}}{2}}\left[\int _{{R}^{3}}^{}{\nabla \cdot \left(\Phi ({\bar {r}}){\bar {E}}\right){{d}^{3}}r}-\int _{{R}^{3}}^{}{\left(\nabla \Phi ({\bar {r}})\right)\cdot {\bar {E}}{{d}^{3}}r}\right]

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MathML (3.11 KB / 447 B) :

W=ε02R3Φ(r¯)E¯d3r=ε02[R3(Φ(r¯)E¯)d3rR3(Φ(r¯))E¯d3r]
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>W</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>&#x03B5;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><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 mathvariant="normal">&#x2207;</mi><mo>&#x22C5;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>&#x03B5;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x2207;</mi><mo>&#x22C5;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi></mrow><mo>&#x2212;</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</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><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x22C5;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mstyle></mrow></math>

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

Identifiers

  • W
  • ε0
  • R
  • Φ
  • r¯
  • E¯
  • r
  • ε0
  • R
  • Φ
  • r¯
  • E¯
  • r
  • R
  • Φ
  • r¯
  • E¯
  • r

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