Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.2141.22 on revision:2141

* Page found: Polarisation (eq math.2141.22)

(force rerendering)

Occurrences on the following pages:

Hash: 7bb3910342d5f550e2e338b72db94f25

TeX (original user input): 

\begin{align}
& \Phi \left( \bar{r},t \right)=\frac{1}{\Delta V}\int_{\Delta V}^{{}}{{}}{{d}^{3}}s{{\Phi }_{m}}\left( \bar{r}+\bar{s},t \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{1}{\Delta V}\int_{\Delta V}^{{}}{{}}{{d}^{3}}s\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }\frac{{{\rho }_{m}}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}+\bar{s}-\bar{r}\acute{\ } \right|}{c} \right)}{\left| \bar{r}+\bar{s}-\bar{r}\acute{\ } \right|} \\
& \bar{r}\acute{\ }\acute{\ }:=\bar{r}\acute{\ }-\bar{s} \\
& \Phi \left( \bar{r},t \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{1}{\Delta V}\int_{\Delta V}^{{}}{{}}{{d}^{3}}s\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }\acute{\ }\frac{{{\rho }_{m}}\left( \bar{r}\acute{\ }\acute{\ }+\bar{s},t-\frac{\left| \bar{r}-\bar{r}\acute{\ }\acute{\ } \right|}{c} \right)}{\left| \bar{r}-\bar{r}\acute{\ }\acute{\ } \right|} \\
& =\frac{1}{4\pi {{\varepsilon }_{0}}}\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }\acute{\ }\frac{1}{\left| \bar{r}-\bar{r}\acute{\ }\acute{\ } \right|}\frac{1}{\Delta V}\int_{\Delta V}^{{}}{{}}{{d}^{3}}s{{\rho }_{m}}\left( \bar{r}\acute{\ }\acute{\ }+\bar{s},t-\frac{\left| \bar{r}-\bar{r}\acute{\ }\acute{\ } \right|}{c} \right) \\
\end{align}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (112.087 KB / 10.117 KB) :

Φ ⁢ ( r ¯ , t ) = 1 Δ ⁢ V ⁢ ∫ Δ ⁢ V d 3 ⁢ s ⁢ Φ m ⁢ ( r ¯ + s ¯ , t ) = 1 4 ⁢ π ⁢ ε 0 ⁢ 1 Δ ⁢ V ⁢ ∫ Δ ⁢ V d 3 ⁢ s ⁢ ∫ R 3 d 3 ⁢ r ⁢ ´ ⁢ ρ m ⁢ ( r ¯ ⁢ ´ , t - | r ¯ + s ¯ - r ¯ ⁢ ´ | c ) | r ¯ + s ¯ - r ¯ ⁢ ´ | r ¯ ⁢ ´ ⁢ ´ := r ¯ ⁢ ´ - s ¯ Φ ⁢ ( r ¯ , t ) = 1 4 ⁢ π ⁢ ε 0 ⁢ 1 Δ ⁢ V ⁢ ∫ Δ ⁢ V d 3 ⁢ s ⁢ ∫ R 3 d 3 ⁢ r ⁢ ´ ⁢ ´ ⁢ ρ m ⁢ ( r ¯ ⁢ ´ ⁢ ´ + s ¯ , t - | r ¯ - r ¯ ⁢ ´ ⁢ ´ | c ) | r ¯ - r ¯ ⁢ ´ ⁢ ´ | = 1 4 ⁢ π ⁢ ε 0 ⁢ ∫ R 3 d 3 ⁢ r ⁢ ´ ⁢ ´ ⁢ 1 | r ¯ - r ¯ ⁢ ´ ⁢ ´ | ⁢ 1 Δ ⁢ V ⁢ ∫ Δ ⁢ V d 3 ⁢ s ⁢ ρ m ⁢ ( r ¯ ⁢ ´ ⁢ ´ + s ¯ , t - | r ¯ - r ¯ ⁢ ´ ⁢ ´ | c ) missing-subexpression Φ ¯ 𝑟 𝑡 1 Δ 𝑉 subscript Δ 𝑉 superscript 𝑑 3 𝑠 subscript Φ 𝑚 ¯ 𝑟 ¯ 𝑠 𝑡 1 4 𝜋 subscript 𝜀 0 1 Δ 𝑉 subscript Δ 𝑉 superscript 𝑑 3 𝑠 subscript superscript 𝑅 3 superscript 𝑑 3 𝑟 ´ absent subscript 𝜌 𝑚 ¯ 𝑟 ´ absent 𝑡 ¯ 𝑟 ¯ 𝑠 ¯ 𝑟 ´ absent 𝑐 ¯ 𝑟 ¯ 𝑠 ¯ 𝑟 ´ absent missing-subexpression assign ¯ 𝑟 ´ absent ´ absent ¯ 𝑟 ´ absent ¯ 𝑠 missing-subexpression Φ ¯ 𝑟 𝑡 1 4 𝜋 subscript 𝜀 0 1 Δ 𝑉 subscript Δ 𝑉 superscript 𝑑 3 𝑠 subscript superscript 𝑅 3 superscript 𝑑 3 𝑟 ´ absent ´ absent subscript 𝜌 𝑚 ¯ 𝑟 ´ absent ´ absent ¯ 𝑠 𝑡 ¯ 𝑟 ¯ 𝑟 ´ absent ´ absent 𝑐 ¯ 𝑟 ¯ 𝑟 ´ absent ´ absent missing-subexpression absent 1 4 𝜋 subscript 𝜀 0 subscript superscript 𝑅 3 superscript 𝑑 3 𝑟 ´ absent ´ absent 1 ¯ 𝑟 ¯ 𝑟 ´ absent ´ absent 1 Δ 𝑉 subscript Δ 𝑉 superscript 𝑑 3 𝑠 subscript 𝜌 𝑚 ¯ 𝑟 ´ absent ´ absent ¯ 𝑠 𝑡 ¯ 𝑟 ¯ 𝑟 ´ absent ´ absent 𝑐 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\Phi\left(\bar{r},t% \right)=\frac{1}{\Delta V}\int_{\Delta V}{{}}{{d}^{3}}s{{\Phi}_{m}}\left(\bar{% r}+\bar{s},t\right)=\frac{1}{4\pi{{\varepsilon}_{0}}}\frac{1}{\Delta V}\int_{% \Delta V}{{}}{{d}^{3}}s\int_{{{R}^{3}}}{{}}{{d}^{3}}r\acute{\ }\frac{{{\rho}_{% m}}\left(\bar{r}\acute{\ },t-\frac{\left|\bar{r}+\bar{s}-\bar{r}\acute{\ }% \right|}{c}\right)}{\left|\bar{r}+\bar{s}-\bar{r}\acute{\ }\right|}\\ &\displaystyle\bar{r}\acute{\ }\acute{\ }:=\bar{r}\acute{\ }-\bar{s}\\ &\displaystyle\Phi\left(\bar{r},t\right)=\frac{1}{4\pi{{\varepsilon}_{0}}}% \frac{1}{\Delta V}\int_{\Delta V}{{}}{{d}^{3}}s\int_{{{R}^{3}}}{{}}{{d}^{3}}r% \acute{\ }\acute{\ }\frac{{{\rho}_{m}}\left(\bar{r}\acute{\ }\acute{\ }+\bar{s% },t-\frac{\left|\bar{r}-\bar{r}\acute{\ }\acute{\ }\right|}{c}\right)}{\left|% \bar{r}-\bar{r}\acute{\ }\acute{\ }\right|}\\ &\displaystyle=\frac{1}{4\pi{{\varepsilon}_{0}}}\int_{{{R}^{3}}}{{}}{{d}^{3}}r% \acute{\ }\acute{\ }\frac{1}{\left|\bar{r}-\bar{r}\acute{\ }\acute{\ }\right|}% \frac{1}{\Delta V}\int_{\Delta V}{{}}{{d}^{3}}s{{\rho}_{m}}\left(\bar{r}\acute% {\ }\acute{\ }+\bar{s},t-\frac{\left|\bar{r}-\bar{r}\acute{\ }\acute{\ }\right% |}{c}\right)\\ \end{aligned}}}

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (13.685 KB / 749 B) :

Φ(r¯,t)=1ΔV∫ΔVd3sΦm(r¯+s¯,t)=14πε01ΔV∫ΔVd3s∫R3d3r´ρm(r¯´,t−|r¯+s¯−r¯´|c)|r¯+s¯−r¯´|r¯´´:=r¯´−s¯Φ(r¯,t)=14πε01ΔV∫ΔVd3s∫R3d3r´´ρm(r¯´´+s¯,t−|r¯−r¯´´|c)|r¯−r¯´´|=14πε0∫R3d3r´´1|r¯−r¯´´|1ΔV∫ΔVd3sρm(r¯´´+s¯,t−|r¯−r¯´´|c)

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Polarisation page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“