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Electric Fields, Flux, Gauss' Law

  1. Sep 12, 2011 #1
    1. The problem statement, all variables and given/known data
    The Electric field E produced by an unknown charge distribution p (rho) is E(r)= (constant)*((exp(-ar))/r^2)*(r_hat).
    a.) Use Gauss' law in differential for to determine p(rho)
    b.) Find the total charge q_tot by directly integrating p(rho), and show that it is 0.
    c.) Find q_tot again, except this time use Gauss' law in integral form.
    d.) Make a sketch of p(rho)

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 12, 2011 #2

    vela

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    According to the forum rules, you need to show some effort at working the problem yourself before you can receive help.
     
  4. Sep 12, 2011 #3
    Hey! Sorry for that... I did some work but I got stuck.

    I used divergence E = p/e0

    a.) div E = (-a/r^2 - 2/r^3) * exp(-a*r) = p/e0. So I know what p is.
    b.) Then I tried to integrate over p(rho) to get q_tot

    q_tot = Integral [pdV]
    I got --> exp(-a*r)/r^2 - 2*exp(-a*r)/r^3 = q_tot

    I'm still trying to figure out what is this surface
     
  5. Sep 12, 2011 #4
    Sorry for that!! I put down the work I had
     
  6. Sep 12, 2011 #5

    vela

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    You calculated the divergence incorrectly. Look up the formula for the divergence in spherical coordinates. Your book should have a list of the various vector operators for different coordinate systems.
    It's not a surface; it's a volume. What is dV in spherical coordinates? What limits should you be integrating over?

    Please show more details of your work.
     
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