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Chris Spencer edited Theory.tex
about 10 years ago
Commit id: e9fa4ed1f91804fc9b5041bb290b863ec7d6300a
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\section{Theory}
Gaus's Law is in free space is \[\nabla\cdot\vec{E}=\frac{\rho}{\epsilon_0}\]. In a plasma $\epsilon_0$ becomes a tensor for $\epsilon$ and the relation becomes \[\nabla\cdot(\epsilon\vec{E})=\rho\] and noting that
$\vec{E}=-\nabla\phi$, $\vec{E}=-\nabla\phi$ and tensor
$\kappa=\tensor{\epsilon}\epsilon_0$ $\kappa=\tensor{\epsilon}\epsilon_0$, Gaus's Law can be rewritten as \[vec{D}=\epsilon_0(tensor)\kappa\cdot\vec{E}\]