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Chris Spencer edited Theory.tex
about 10 years ago
Commit id: b99f519ada08b50e2dc4a555ffbe777801bed222
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diff --git a/Theory.tex b/Theory.tex
index da83eec..79273c8 100644
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\[\kappa_{xy}=\kappa_{yx}=\frac{i\omega_{ce}\omega_{ce}^2}{\omega^2-\omega_{ce}^2}\]
\[\kappa_{\parallel}=1-\frac{\omega_{pe}^2}{\omega^2}\]
Need to define an oscillating point charge in this system. Define $\rho$ from Gaus's law as \[\rho=qe^{-i\omega t}\sigma(\vec{r})\]
where $\sigma(\vec{r})$ is the delta function at $\vec{r}$ at zero. Use fourier analysis on Gaus's law and note that
$E=-\gradient\phi$ $E=-\grad\phi$