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Display information for equation id:math.2182.0 on revision:2182
* Page found: Inhomogene Maxwellgleichungen im Vakuum (eq math.2182.0)
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Hash: cddb0a503474620dc123d9775bb60fef
TeX (original user input):
\begin{align}
& {{\varepsilon }_{0}}\nabla \cdot \bar{E}=\rho \\
& \Leftrightarrow {{\partial }_{1}}{{E}^{1}}+{{\partial }_{2}}{{E}^{2}}+{{\partial }_{3}}{{E}^{3}}=\frac{1}{{{\varepsilon }_{0}}c}c\rho \\
& \Leftrightarrow {{\partial }_{1}}{{F}^{10}}+{{\partial }_{2}}{{F}^{20}}+{{\partial }_{3}}{{F}^{30}}=\frac{1}{{{\varepsilon }_{0}}c}{{j}^{0}} \\
& \Leftrightarrow {{\partial }_{\nu }}{{F}^{\nu 0}}=\frac{1}{{{\varepsilon }_{0}}c}{{j}^{0}} \\
& wegen{{\partial }_{0}}{{F}^{00}}=0 \\
& auch{{\partial }_{i}}{{F}^{i0}}=\frac{1}{{{\varepsilon }_{0}}c}{{j}^{0}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\varepsilon }_{0}}\nabla \cdot {\bar {E}}=\rho \\&\Leftrightarrow {{\partial }_{1}}{{E}^{1}}+{{\partial }_{2}}{{E}^{2}}+{{\partial }_{3}}{{E}^{3}}={\frac {1}{{{\varepsilon }_{0}}c}}c\rho \\&\Leftrightarrow {{\partial }_{1}}{{F}^{10}}+{{\partial }_{2}}{{F}^{20}}+{{\partial }_{3}}{{F}^{30}}={\frac {1}{{{\varepsilon }_{0}}c}}{{j}^{0}}\\&\Leftrightarrow {{\partial }_{\nu }}{{F}^{\nu 0}}={\frac {1}{{{\varepsilon }_{0}}c}}{{j}^{0}}\\&wegen{{\partial }_{0}}{{F}^{00}}=0\\&auch{{\partial }_{i}}{{F}^{i0}}={\frac {1}{{{\varepsilon }_{0}}c}}{{j}^{0}}\\\end{aligned}}
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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"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi mathvariant="normal">∇</mi><mo stretchy="false">⋅</mo><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><mi>ρ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇔</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo stretchy="false">+</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><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"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>c</mi></mrow></mrow></mfrac></mrow><mi>c</mi><mi>ρ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇔</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>10</mn></mrow></msup><mo stretchy="false">+</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>20</mn></mrow></msup><mo stretchy="false">+</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>30</mn></mrow></msup><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"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>c</mi></mrow></mrow></mfrac></mrow><msup><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇔</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>ν</mi><mn>0</mn></mrow></mrow></msup><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"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>c</mi></mrow></mrow></mfrac></mrow><msup><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>w</mi><mi>e</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>00</mn></mrow></msup><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>a</mi><mi>u</mi><mi>c</mi><mi>h</mi><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mn>0</mn></mrow></mrow></msup><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"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>c</mi></mrow></mrow></mfrac></mrow><msup><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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