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Display information for equation id:math.2133.33 on revision:2133

* Page found: Multipolstrahlung (eq math.2133.33)

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TeX (original user input): 

\begin{align}
& \bar{B}\left( \bar{r},t \right)=\nabla \times \bar{A}\left( \bar{r},t \right)\approx \frac{{{\mu }_{\acute{\ }0}}}{4\pi }\nabla \times \frac{1}{r}\dot{\bar{p}}\left( t-\frac{r}{c} \right)=\frac{{{\mu }_{\acute{\ }0}}}{4\pi c}\frac{1}{{{r}^{2}}}\left[ \ddot{\bar{p}}\left( t-\frac{r}{c} \right)\times \bar{r} \right]+O\left( \frac{1}{{{r}^{2}}} \right) \\
& \bar{E}\left( \bar{r},t \right)=-\nabla \Phi \left( \bar{r},t \right)-\dot{\bar{A}}\left( \bar{r},t \right)=\frac{1}{4\pi {{\varepsilon }_{0}}{{c}^{2}}}\frac{1}{{{r}^{3}}}\left[ \ddot{\bar{p}}\left( t-\frac{r}{c} \right)\times \bar{r} \right]\times \bar{r}+O\left( \frac{1}{{{r}^{2}}} \right) \\
\end{align}

TeX (checked): 

{\begin{aligned}&{\bar {B}}\left({\bar {r}},t\right)=\nabla \times {\bar {A}}\left({\bar {r}},t\right)\approx {\frac {{\mu }_{{\acute {\ }}0}}{4\pi }}\nabla \times {\frac {1}{r}}{\dot {\bar {p}}}\left(t-{\frac {r}{c}}\right)={\frac {{\mu }_{{\acute {\ }}0}}{4\pi c}}{\frac {1}{{r}^{2}}}\left[{\ddot {\bar {p}}}\left(t-{\frac {r}{c}}\right)\times {\bar {r}}\right]+O\left({\frac {1}{{r}^{2}}}\right)\\&{\bar {E}}\left({\bar {r}},t\right)=-\nabla \Phi \left({\bar {r}},t\right)-{\dot {\bar {A}}}\left({\bar {r}},t\right)={\frac {1}{4\pi {{\varepsilon }_{0}}{{c}^{2}}}}{\frac {1}{{r}^{3}}}\left[{\ddot {\bar {p}}}\left(t-{\frac {r}{c}}\right)\times {\bar {r}}\right]\times {\bar {r}}+O\left({\frac {1}{{r}^{2}}}\right)\\\end{aligned}}

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B¯(r¯,t)=∇×A¯(r¯,t)≈μ´04π∇×1rp¯˙(t−rc)=μ´04πc1r2[p¯¨(t−rc)×r¯]+O(1r2)E¯(r¯,t)=−∇Φ(r¯,t)−A¯˙(r¯,t)=14πε0c21r3[p¯¨(t−rc)×r¯]×r¯+O(1r2)
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data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2248;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>&#x03BC;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mn>0</mn></mrow></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>&#x03C0;</mi></mrow></mrow></mfrac></mrow><mi mathvariant="normal">&#x2207;</mi><mo>&#x00D7;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow 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data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>¨</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x00D7;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>+</mo><mi>O</mi><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"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></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>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>&#x2212;</mo><mi mathvariant="normal">&#x2207;</mi><mi mathvariant="normal">&#x03A6;</mi><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>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></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>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><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><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>¨</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x00D7;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>&#x00D7;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>+</mo><mi>O</mi><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 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Calculated based on the variables occurring on the entire Multipolstrahlung page

Identifiers

  • B¯
  • r¯
  • t
  • A¯
  • r¯
  • t
  • μ
  • ´
  • π
  • r
  • p¯˙
  • t
  • r
  • c
  • μ
  • ´
  • π
  • c
  • r
  • p¯¨
  • t
  • r
  • c
  • r¯
  • O
  • r
  • E¯
  • r¯
  • t
  • Φ
  • r¯
  • t
  • A¯˙
  • r¯
  • t
  • π
  • ε0
  • c
  • r
  • p¯¨
  • t
  • r
  • c
  • r¯
  • r¯
  • O
  • r

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