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\section{Kontinuitätsgleichung}  $$rot\vec{H}=\vec{J}+\frac{\partial}{\partial t}\vec{D}$$  $$\rightarrow \begin{equation}  rot\vec{H}=\vec{J}+\frac{\partial}{\partial t}\vec{D}  \end{equation}  \begin{equation}  \rightarrow  div(rot\vec{H})=div\vec{J}+\underbrace{div(\frac{\partial}{\partial t}\vec{D})}$$  $$\rightarrow t}\vec{D})}  \end{equation}  \begin{equation}  \rightarrow  div\vec{J}=-\frac{\partial}{\partial t}\rho$$  $$div\vec{J}+\frac{\partial\rho}{\partial t}=0$$  $$\int\limits t}\rho  \end{equation}  \begin{equation}  div\vec{J}+\frac{\partial\rho}{\partial t}=0  \end{equation}  \begin{equation}  \int\limits  _V div\vec{J}dV=-\frac{dQ}{dt}$$ div\vec{J}dV=-\frac{dQ}{dt}  \end{equation}  \subsection{Grenzbedingung}  $$Div\vec{J}+\frac{\partial\rho \begin{equation}  Div\vec{J}+\frac{\partial\rho  _I}{\partial t}=0$$ t}=0  \end{equation}