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Display information for equation id:math.2110.7 on revision:2110
* Page found: Maxwell- Gleichungen im Vakuum (eq math.2110.7)
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TeX (original user input):
\begin{align}
& 0=\frac{\partial }{\partial t}\left( {{\varepsilon }_{0}}{{\nabla }_{r}}\cdot \bar{E}-\rho \right)={{\varepsilon }_{0}}{{\nabla }_{r}}\cdot \dot{\bar{E}}-\dot{\rho }=\frac{{{\varepsilon }_{0}}}{{{a}_{2}}}\nabla \cdot \left( \nabla \times \bar{B}-{{\mu }_{0}}\bar{j} \right)-\dot{\rho } \\
& \frac{{{\varepsilon }_{0}}}{{{a}_{2}}}\nabla \cdot \nabla \times \bar{B}=0 \\
& \Rightarrow \frac{{{\varepsilon }_{0}}}{{{a}_{2}}}\nabla \cdot \left( {{\mu }_{0}}\bar{j} \right)-\dot{\rho }=0 \\
& \Rightarrow {{a}_{2}}={{\varepsilon }_{0}}{{\mu }_{0}} \\
\end{align}
TeX (checked):
{\begin{aligned}&0={\frac {\partial }{\partial t}}\left({{\varepsilon }_{0}}{{\nabla }_{r}}\cdot {\bar {E}}-\rho \right)={{\varepsilon }_{0}}{{\nabla }_{r}}\cdot {\dot {\bar {E}}}-{\dot {\rho }}={\frac {{\varepsilon }_{0}}{{a}_{2}}}\nabla \cdot \left(\nabla \times {\bar {B}}-{{\mu }_{0}}{\bar {j}}\right)-{\dot {\rho }}\\&{\frac {{\varepsilon }_{0}}{{a}_{2}}}\nabla \cdot \nabla \times {\bar {B}}=0\\&\Rightarrow {\frac {{\varepsilon }_{0}}{{a}_{2}}}\nabla \cdot \left({{\mu }_{0}}{\bar {j}}\right)-{\dot {\rho }}=0\\&\Rightarrow {{a}_{2}}={{\varepsilon }_{0}}{{\mu }_{0}}\\\end{aligned}}
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