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Display information for equation id:math.1199.921 on revision:1199
* Page found: Elektrodynamik Schöll (eq math.1199.921)
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TeX (original user input):
\nabla \cdot \bar{E}=-\frac{\partial }{\partial t}\nabla \cdot \bar{A}\left( \bar{r},t \right)-\nabla \cdot \nabla \Phi =\frac{1}{{{c}^{2}}}\frac{{{\partial }^{2}}}{\partial {{t}^{2}}}\Phi -\Delta \Phi =-\#\Phi =\frac{1}{{{\varepsilon }_{0}}}\left( \rho +{{\rho }_{p}} \right)=\frac{1}{{{\varepsilon }_{0}}}\left( \rho -\nabla \cdot \bar{P} \right)
TeX (checked):
\nabla \cdot {\bar {E}}=-{\frac {\partial }{\partial t}}\nabla \cdot {\bar {A}}\left({\bar {r}},t\right)-\nabla \cdot \nabla \Phi ={\frac {1}{{c}^{2}}}{\frac {{\partial }^{2}}{\partial {{t}^{2}}}}\Phi -\Delta \Phi =-\#\Phi ={\frac {1}{{\varepsilon }_{0}}}\left(\rho +{{\rho }_{p}}\right)={\frac {1}{{\varepsilon }_{0}}}\left(\rho -\nabla \cdot {\bar {P}}\right)
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mi mathvariant="normal">∇</mi><mi mathvariant="normal">Φ</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mi mathvariant="normal">Φ</mi><mo>−</mo><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Φ</mi><mo>=</mo><mo>−</mo><mo>#</mo><mi mathvariant="normal">Φ</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ρ</mi><mo>+</mo><msub><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mi>p</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ρ</mi><mo>−</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>P</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>
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