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Display information for equation id:math.2123.12 on revision:2123

* Page found: Eichinvarianz (eq math.2123.12)

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Eichinvarianz Eq: math.2123.12

Hash: 20c923fc8f8b0d9a64852c1b988cf8fb

TeX (original user input):

\begin{align}
& \nabla \cdot \bar{B}=0 \\
& \Rightarrow \exists \bar{A}\left( \bar{r},t \right)\Rightarrow \nabla \times \bar{A}\left( \bar{r},t \right)=\bar{B} \\
& \nabla \times \bar{E}=-\frac{\partial }{\partial t}\bar{B}=-\nabla \times \frac{\partial }{\partial t}\bar{A}\left( \bar{r},t \right)\Rightarrow \nabla \times \left( \bar{E}+\frac{\partial }{\partial t}\bar{A}\left( \bar{r},t \right) \right)=0 \\
& \Rightarrow \exists \Phi \left( \bar{r},t \right)\Rightarrow \bar{E}+\frac{\partial }{\partial t}\bar{A}\left( \bar{r},t \right)=-\nabla \Phi \left( \bar{r},t \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&\nabla \cdot {\bar {B}}=0\\&\Rightarrow \exists {\bar {A}}\left({\bar {r}},t\right)\Rightarrow \nabla \times {\bar {A}}\left({\bar {r}},t\right)={\bar {B}}\\&\nabla \times {\bar {E}}=-{\frac {\partial }{\partial t}}{\bar {B}}=-\nabla \times {\frac {\partial }{\partial t}}{\bar {A}}\left({\bar {r}},t\right)\Rightarrow \nabla \times \left({\bar {E}}+{\frac {\partial }{\partial t}}{\bar {A}}\left({\bar {r}},t\right)\right)=0\\&\Rightarrow \exists \Phi \left({\bar {r}},t\right)\Rightarrow {\bar {E}}+{\frac {\partial }{\partial t}}{\bar {A}}\left({\bar {r}},t\right)=-\nabla \Phi \left({\bar {r}},t\right)\\\end{aligned}}

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\begin{aligned} \nabla \cdot \bar{B} = 0 \\ \Rightarrow \exists \bar{A} (\bar{r}, t) \Rightarrow \nabla \times \bar{A} (\bar{r}, t) = \bar{B} \\ \nabla \times \bar{E} = - \frac{\partial}{\partial t} \bar{B} = - \nabla \times \frac{\partial}{\partial t} \bar{A} (\bar{r}, t) \Rightarrow \nabla \times (\bar{E} + \frac{\partial}{\partial t} \bar{A} (\bar{r}, t)) = 0 \\ \Rightarrow \exists Φ (\bar{r}, t) \Rightarrow \bar{E} + \frac{\partial}{\partial t} \bar{A} (\bar{r}, t) = - \nabla Φ (\bar{r}, t) \end{aligned}

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Identifiers

$\bar{B}$

$\bar{A}$

$\bar{r}$

$t$

$\bar{A}$

$\bar{r}$

$t$

$\bar{B}$

$\bar{E}$

$t$

$\bar{B}$

$t$

$\bar{A}$

$\bar{r}$

$t$

$\bar{E}$

$t$

$\bar{A}$

$\bar{r}$

$t$

$Φ$

$\bar{r}$

$t$

$\bar{E}$

$t$

$\bar{A}$

$\bar{r}$

$t$

$Φ$

$\bar{r}$

$t$

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