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Gauss's law, determing average volume charge density

  1. Mar 1, 2009 #1
    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
    [tex]\Phi[/tex]net=[tex]\stackrel{Q}{\epsilon}[/tex]
    [tex]\rho[/tex]=[tex]\stackrel{Q}{v}[/tex]
    [tex]\Phi[/tex]=[tex]\int[/tex]E(dot)dA

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

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

    Thanks for whatever help you can offer! :smile:

    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!
     
  2. jcsd
  3. Mar 1, 2009 #2
    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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