- testwiki

General

Display information for equation id:math.1439.170 on revision:1439

* Page found: Elektromagnetische Wellen (eq math.1439.170)

Occurrences on the following pages:

Multipolstrahlung Eq: math.2133.33

Hash: ff3b290d103c89286f067dd87167d17f

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}}

LaTeXML (experimental; uses MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimental; no images) rendering

MathML (5.531 KB / 635 B) :

\begin{matrix} \bar{B} (\bar{r}, t) = \nabla \times \bar{A} (\bar{r}, t) \approx \frac{μ_{\overset{´}{} 0}}{4 π} \nabla \times \frac{1}{r} \dot{\bar{p}} (t - \frac{r}{c}) = \frac{μ_{\overset{´}{} 0}}{4 π c} \frac{1}{r^{2}} [\ddot{\bar{p}} (t - \frac{r}{c}) \times \bar{r}] + O (\frac{1}{r^{2}}) \\ \bar{E} (\bar{r}, t) = - \nabla Φ (\bar{r}, t) - \dot{\bar{A}} (\bar{r}, t) = \frac{1}{4 π ε_{0} c^{2}} \frac{1}{r^{3}} [\ddot{\bar{p}} (t - \frac{r}{c}) \times \bar{r}] \times \bar{r} + O (\frac{1}{r^{2}}) \end{matrix}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mover><mi>B</mi><mo>¯</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mi mathvariant="normal">∇</mi><mo stretchy="false">×</mo><mover><mi>A</mi><mo>¯</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">≈</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mn>0</mn></mrow></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi></mrow></mrow></mfrac></mrow><mi mathvariant="normal">∇</mi><mo stretchy="false">×</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><mover><mover><mi>p</mi><mo>¯</mo></mover><mo>˙</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo stretchy="false">−</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 stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mn>0</mn></mrow></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi><mi>c</mi></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>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mover><mover><mi>p</mi><mo>¯</mo></mover><mo>¨</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo stretchy="false">−</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 stretchy="false">×</mo><mover><mi>r</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">+</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 class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi mathvariant="normal">∇</mi><mi>Φ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">−</mo><mover><mover><mi>A</mi><mo>¯</mo></mover><mo>˙</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</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>π</mi><msub><mi>ε</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><mover><mover><mi>p</mi><mo>¯</mo></mover><mo>¨</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo stretchy="false">−</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 stretchy="false">×</mo><mover><mi>r</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">×</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">+</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 class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$\bar{B}$

$\bar{r}$

$t$

$\bar{A}$

$\bar{r}$

$t$

$μ$

$\overset{´}{}$

$π$

$r$

$\dot{\bar{p}}$

$t$

$r$

$c$

$μ$

$\overset{´}{}$

$π$

$c$

$r$

$\ddot{\bar{p}}$

$t$

$r$

$c$

$\bar{r}$

$O$

$r$

$\bar{E}$

$\bar{r}$

$t$

$Φ$

$\bar{r}$

$t$

$\dot{\bar{A}}$

$\bar{r}$

$t$

$π$

$ε_{0}$

$c$

$r$

$\ddot{\bar{p}}$

$t$

$r$

$c$

$\bar{r}$

$\bar{r}$

$O$

$r$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search