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Display information for equation id:math.2139.28 on revision:2139

* Page found: Polarisation (eq math.2139.28)

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TeX (original user input): 

{{\Phi }_{m}}\left( \bar{r},t \right)=-\frac{1}{4\pi {{\varepsilon }_{0}}}\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }{{\nabla }_{r}}\left\{ \frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}{{{\bar{P}}}_{m}}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \right) \right\}

TeX (checked): 

{{\Phi }_{m}}\left({\bar {r}},t\right)=-{\frac {1}{4\pi {{\varepsilon }_{0}}}}\int _{{R}^{3}}^{}{}{{d}^{3}}r{\acute {\ }}{{\nabla }_{r}}\left\{{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{{\bar {P}}_{m}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\right\}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (22.323 KB / 2.875 KB) :

Φ m ⁢ ( r ¯ , t ) = - 1 4 ⁢ π ⁢ ε 0 ⁢ ∫ R 3 d 3 ⁢ r ⁢ ´ ⁢ ∇ r ⁡ { 1 | r ¯ - r ¯ ⁢ ´ | ⁢ P ¯ m ⁢ ( r ¯ ⁢ ´ , t - | r ¯ - r ¯ ⁢ ´ | c ) } subscript Φ 𝑚 ¯ 𝑟 𝑡 1 4 𝜋 subscript 𝜀 0 subscript superscript 𝑅 3 superscript 𝑑 3 𝑟 ´ absent subscript ∇ 𝑟 1 ¯ 𝑟 ¯ 𝑟 ´ absent subscript ¯ 𝑃 𝑚 ¯ 𝑟 ´ absent 𝑡 ¯ 𝑟 ¯ 𝑟 ´ absent 𝑐 {\displaystyle{\displaystyle{{\Phi}_{m}}\left(\bar{r},t\right)=-\frac{1}{4\pi{% {\varepsilon}_{0}}}\int_{{{R}^{3}}}{{}}{{d}^{3}}r\acute{\ }{{\nabla}_{r}}\left% \{\frac{1}{\left|\bar{r}-\bar{r}\acute{\ }\right|}{{{\bar{P}}}_{m}}\left(\bar{% r}\acute{\ },t-\frac{\left|\bar{r}-\bar{r}\acute{\ }\right|}{c}\right)\right\}}}

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MathML (3.276 KB / 507 B) :

Φm(r¯,t)=−14πε0∫R3d3r´∇r{1|r¯−r¯´|P¯m(r¯´,t−|r¯−r¯´|c)}

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Calculated based on the variables occurring on the entire Polarisation page

Identifiers

  • Φm
  • r¯
  • t
  • π
  • ε0
  • R
  • r
  • ´
  • r
  • r¯
  • r¯
  • ´
  • P¯m
  • r¯
  • ´
  • t
  • r¯
  • r¯
  • ´
  • c

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