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  • Elektromagnetische Felder

    Preamble

    This paper concludes the most important equations and solving algorithms of the RWTH course Elektromagnetische Felder 1.

    Maxwell Gleichungen

    Maxwellgleichungen in integraler Form

    \[\oint \limits _{C}\vec{H} d\vec{r}=\int\limits _{F} (\vec{J}+\frac{\partial}{\partial{t}}\vec{D})d\vec{F}\]

    \[\oint \limits _{C}\vec{E} d\vec{r}=-\int\limits _{F}\frac{\partial}{\partial{t}}\vec{B}d\vec{F}\]

    \[\oint\limits _F \vec{D} d\vec{F}=\int\limits_{V}\rho dV\]

    \[\oint\limits _F \vec{B} d\vec{F}=0\]

    Maxwellgleichungen in differentieller Form

    \[rot \vec{H}=\vec{J}+\frac{\partial}{\partial t}\vec{D}\]

    \[Rot\vec{H}=\vec{J_F}\]

    \[rot \vec{E}=-\frac{\partial}{\partial t}\vec{B}\]

    \[Rot \vec{E}=0\]

    \[div \vec{D}=\rho\]

    \[Div \vec{D}=\rho _F\]

    \[div\vec{B}=0\]

    \[Div\vec{B}=0\]

    Grenzbedingungen

    \[Div \vec{B} := \vec{n_{12}}\cdot(\vec{B_2}-\vec{B_1})=0 \quad\rightarrow\quad B_{norm1}=B_{norm2}\]

    \[Rot \vec{E}:= \vec{n_{12}}\times(\vec{E_2}-\vec{E_1})=\vec{0}\quad\rightarrow\quad E_{tan1}=E_{tan2}\]