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Display information for equation id:math.1443.176 on revision:1443

* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1443.176)

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TeX (original user input): 

\begin{align}
& {{m}_{K}}{{{\ddot{\bar{r}}}}_{k}}={{{\bar{F}}}_{K}}+{{Q}_{K}}{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right)=-\frac{{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}\left( {{{\bar{r}}}_{k}}-{{{\bar{r}}}_{e}} \right)+{{Q}_{K}}{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right)=-\frac{{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}\left( {{{\bar{r}}}_{k}}-{{{\bar{r}}}_{e}} \right)+Ze{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right) \\
& Z{{m}_{e}}{{{\ddot{\bar{r}}}}_{e}}=-{{{\bar{F}}}_{K}}+{{Q}_{e}}{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right)=\frac{{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}\left( {{{\bar{r}}}_{k}}-{{{\bar{r}}}_{e}} \right)+{{Q}_{e}}{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right)=\frac{{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}\left( {{{\bar{r}}}_{k}}-{{{\bar{r}}}_{e}} \right)-Ze{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right) \\
\end{align}

TeX (checked): 

{\begin{aligned}&{{m}_{K}}{{\ddot {\bar {r}}}_{k}}={{\bar {F}}_{K}}+{{Q}_{K}}{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)=-{\frac {{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}}\left({{\bar {r}}_{k}}-{{\bar {r}}_{e}}\right)+{{Q}_{K}}{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)=-{\frac {{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}}\left({{\bar {r}}_{k}}-{{\bar {r}}_{e}}\right)+Ze{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)\\&Z{{m}_{e}}{{\ddot {\bar {r}}}_{e}}=-{{\bar {F}}_{K}}+{{Q}_{e}}{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)={\frac {{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}}\left({{\bar {r}}_{k}}-{{\bar {r}}_{e}}\right)+{{Q}_{e}}{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)={\frac {{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}}\left({{\bar {r}}_{k}}-{{\bar {r}}_{e}}\right)-Ze{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)\\\end{aligned}}

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mKr¯¨k=F¯K+QKE¯a(r¯ ´k,t)=−Z2e24πε0R3(r¯k−r¯e)+QKE¯a(r¯ ´k,t)=−Z2e24πε0R3(r¯k−r¯e)+ZeE¯a(r¯ ´k,t)Zmer¯¨e=−F¯K+QeE¯a(r¯ ´k,t)=Z2e24πε0R3(r¯k−r¯e)+QeE¯a(r¯ ´k,t)=Z2e24πε0R3(r¯k−r¯e)−ZeE¯a(r¯ ´k,t)
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data-mjx-pseudoscript="true">´</mo></mover><mi>k</mi></mrow></mrow></msub><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>Z</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></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>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>K</mi></mrow></msub><msub><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>k</mi></mrow></mrow></msub><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>Z</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></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>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><mi>Z</mi><mi>e</mi><msub><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>k</mi></mrow></mrow></msub><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>Z</mi><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><msub><mover><mover><mi>r</mi><mo>¯</mo></mover><mo>¨</mo></mover><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">−</mo><msub><mover><mi>F</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>K</mi></mrow></msub><mo stretchy="false">+</mo><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><msub><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>k</mi></mrow></mrow></msub><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"><mrow data-mjx-texclass="ORD"><msup><mi>Z</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></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>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><msub><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>k</mi></mrow></mrow></msub><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"><mrow data-mjx-texclass="ORD"><msup><mi>Z</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></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>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">−</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">−</mo><mi>Z</mi><mi>e</mi><msub><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>k</mi></mrow></mrow></msub><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Materie in elektrischen und magnetischen Feldern page

Identifiers

  • mK
  • r¯¨k
  • F¯K
  • QK
  • E¯a
  • r¯
  •  ´
  • k
  • t
  • Z
  • e
  • π
  • ε0
  • R
  • r¯k
  • r¯e
  • QK
  • E¯a
  • r¯
  •  ´
  • k
  • t
  • Z
  • e
  • π
  • ε0
  • R
  • r¯k
  • r¯e
  • Z
  • e
  • E¯a
  • r¯
  •  ´
  • k
  • t
  • Z
  • me
  • r¯¨e
  • F¯K
  • Qe
  • E¯a
  • r¯
  •  ´
  • k
  • t
  • Z
  • e
  • π
  • ε0
  • R
  • r¯k
  • r¯e
  • Qe
  • E¯a
  • r¯
  •  ´
  • k
  • t
  • Z
  • e
  • π
  • ε0
  • R
  • r¯k
  • r¯e
  • Z
  • e
  • E¯a
  • r¯
  •  ´
  • k
  • t

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