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Display information for equation id:math.2084.8 on revision:2084
* Page found: Die elektrostatische Feldenergie (eq math.2084.8)
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Hash: 93b9ccacbde8eb987f6b18f189d81c42
TeX (original user input):
W=\frac{1}{2}\int_{{}}^{{}}{\Phi (\bar{r})\rho (\bar{r}){{d}^{3}}r}=\frac{1}{8\pi {{\varepsilon }_{0}}}\int_{{}}^{{}}{{}}{{d}^{3}}r\int_{{}}^{{}}{{}}{{d}^{3}}r\acute{\ }\frac{\rho (\bar{r})\rho (\bar{r}\acute{\ })}{|\bar{r}-\bar{r}\acute{\ }|}
TeX (checked):
W={\frac {1}{2}}\int _{}^{}{\Phi ({\bar {r}})\rho ({\bar {r}}){{d}^{3}}r}={\frac {1}{8\pi {{\varepsilon }_{0}}}}\int _{}^{}{}{{d}^{3}}r\int _{}^{}{}{{d}^{3}}r{\acute {\ }}{\frac {\rho ({\bar {r}})\rho ({\bar {r}}{\acute {\ }})}{|{\bar {r}}-{\bar {r}}{\acute {\ }}|}}
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<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"><mi>W</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"><mn>2</mn></mrow></mfrac></mrow><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>Φ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mi>ρ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi></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>8</mn><mi>π</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>ρ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mi>ρ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">|</mo></mrow></mrow></mfrac></mrow></mstyle></mrow></math>
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