# Gauss's law, determing average volume charge density

#### Breedlove

1. The problem statement, all variables and given/known data
In the air over a particular region at an altitude of 500 m above the ground, the electric field is 120 N/C directed downward. At 600 m above the ground, the electric field is 100 N/C downward. What is the average volume charge density in the layer of air between these two elevations? Is it positive or negative?

2. Relevant equations
$$\Phi$$net=$$\stackrel{Q}{\epsilon}$$
$$\rho$$=$$\stackrel{Q}{v}$$
$$\Phi$$=$$\int$$E(dot)dA

3. The attempt at a solution
I substituted $$\rho$$V for Q in
$$\Phi$$net=$$\stackrel{Q}{\epsilon}$$
and then set that equal to EA from $$\Phi$$=$$\int$$E(dot)dA, and solved for $$\rho$$, getting $$\rho$$=E/(h$$\epsilon$$)
h is coming from A/V

Am I going about this the right way? My next step would be to find $$\rho$$ at both elevations and average them. Are the steps that I have taken this far correct?

Oh, and anything that looks like a superscript or subscript is just an error on my part, I didn't mean for the equations to look like they had them. I'm still pretty new with it.
Thanks!

#### Vuldoraq

Looks like a good way to go about the calculation. As a safety check make sure your units on both sides of your equation are consistent, that way you know when your definitely on the wrong track! (P.S. I think your units are good in this case).

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