# Dispersion relations and Plasma

## Homework Statement

The dispersion relation for a plasma is given by

$$k^{2}=\frac{\omega^{2}}{c^{2}}(1-\frac{\omega^{2}_{p}}{\omega^{2}})$$

$$\omega^{2}_{p}\:= \frac{Ne^{2}}{m_{e}\epsilon_{0}}$$

Where N is the electron density

During re enrty of a spacecraft there was a radio blackout of all frequencies up to 10^10 Hz because it was surrounded by a plasma. Calculate the electron density in the plasma surrounding the spacecraft.

Sensitive equipment detected EM radio waves at 10^9 Hz at an amplitude of 10% of that before re entry. Calculate the thickness of the plasma.

Given above

## The Attempt at a Solution

Got the first part easily enough, by substituting in the expression for $$\omega^{2}_{p}$$, then solving $$\frac{Ne^{2}}{\omega^{2}m_{e}\epsilon_{0}}=1$$ for N to get N= 1.24x10^18. I don't really have any idea about how to go about the second part, I can't find anything about it in my textbook (I S Grant & W R Phillips Electromagnetism) or on the old googles

Any help would be much appreciated! Thanks

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