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Transformationsverhalten der Ströme und Felder Eq: math.2174.36

Hash: d9857059bb5be59ab4ac363d0e4a3da0

TeX (original user input):

\begin{align}
& B{{\acute{\ }}^{1}}=\frac{1}{c}F{{\acute{\ }}^{32}}=\frac{1}{c}{{U}^{3}}_{\lambda }{{U}^{2}}_{\kappa }{{F}^{\lambda \kappa }}=\frac{1}{c}{{F}^{32}}={{B}^{1}} \\
& B{{\acute{\ }}^{2}}=\frac{1}{c}F{{\acute{\ }}^{13}}=\frac{1}{c}{{U}^{1}}_{\lambda }{{U}^{3}}_{\kappa }{{F}^{\lambda \kappa }}=\frac{1}{c}{{U}^{1}}_{\kappa }{{F}^{\kappa 3}}=-\frac{\beta \gamma }{c}{{F}^{03}}+\frac{\gamma }{c}{{F}^{13}}=\gamma \left( {{B}^{2}}+\frac{v}{{{c}^{2}}}{{E}^{3}} \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&B{{\acute {\ }}^{1}}={\frac {1}{c}}F{{\acute {\ }}^{32}}={\frac {1}{c}}{{U}^{3}}_{\lambda }{{U}^{2}}_{\kappa }{{F}^{\lambda \kappa }}={\frac {1}{c}}{{F}^{32}}={{B}^{1}}\\&B{{\acute {\ }}^{2}}={\frac {1}{c}}F{{\acute {\ }}^{13}}={\frac {1}{c}}{{U}^{1}}_{\lambda }{{U}^{3}}_{\kappa }{{F}^{\lambda \kappa }}={\frac {1}{c}}{{U}^{1}}_{\kappa }{{F}^{\kappa 3}}=-{\frac {\beta \gamma }{c}}{{F}^{03}}+{\frac {\gamma }{c}}{{F}^{13}}=\gamma \left({{B}^{2}}+{\frac {v}{{c}^{2}}}{{E}^{3}}\right)\\\end{aligned}}

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\begin{aligned} B {\overset{´}{}}^{1} = \frac{1}{c} F {\overset{´}{}}^{32} = \frac{1}{c} {U^{3}}_{λ} {U^{2}}_{κ} F^{λ κ} = \frac{1}{c} F^{32} = B^{1} \\ B {\overset{´}{}}^{2} = \frac{1}{c} F {\overset{´}{}}^{13} = \frac{1}{c} {U^{1}}_{λ} {U^{3}}_{κ} F^{λ κ} = \frac{1}{c} {U^{1}}_{κ} F^{κ 3} = - \frac{β γ}{c} F^{03} + \frac{γ}{c} F^{13} = γ (B^{2} + \frac{v}{c^{2}} E^{3}) \end{aligned}

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Identifiers

$B$

$\overset{´}{}$

$c$

$F$

$\overset{´}{}$

$c$

$U_{λ}$

$U_{κ}$

$F$

$λ$

$κ$

$c$

$F$

$B$

$B$

$\overset{´}{}$

$c$

$F$

$\overset{´}{}$

$c$

$U_{λ}$

$U_{κ}$

$F$

$λ$

$κ$

$c$

$U_{κ}$

$F$

$κ$

$β$

$γ$

$c$

$F$

$γ$

$c$

$F$

$γ$

$B$

$v$

$c$

$E$

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