How to Calculate the Volume Charge Density of Earth's Atmosphere?

[pyroknife]

Homework Statement

In a particular region of Earth's atmosphere, the electric field above Earth's surface has been measured to be 147 N/C downward at an altitude of 260 m and 165 N/C downward at an altitude of 410 m. Calculate the volume charge density of the atmosphere, assuming it to be uniform between 260 and 410 m. (Hint: You may neglect the curvature of Earth. Why?)

Homework Equations

volume charge density = Q/V

I tried doing E=kq/r^2 for the 147 N/C and 260m altitude. -147=(9*10^9)(q)/(260)^2_ and got -0.0011 C. I divided that by volume (4/3*pi*260^3) which gave me -1.5e-11, but that wasn't right.I really have no idea how to even start this. Why did they give me 2 sets of altitude and E field?

 

[Spinnor]

Are you learning Gauss's law?

 

[pyroknife]

yes, our prof just gave us like 20 different equations and never showed us how to use a single one.

 

[Spinnor]

yes, our prof just gave us like 20 different equations and never showed us how to use a single one.

Ouch! I think this problem calls for Gauss' Law which you will want to learn forward and backwards. Then do every relevant problem in your text that has answers so you make sure you understand it. The following sketch might help and if there are mistakes I hope they are pointed out.

 

[pyroknife]

it worked thanks. But how come Volume=150A, isn't volume (4/3)*pi*r^3 which would be 150(1/3)*A?