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Dirac Delta function and Divergence

  1. Nov 5, 2013 #1
    1. The problem statement, all variables and given/known data

    The Potential V(r) is given: A*e^(-lambda*r)/r, A and lambda are constants
    From this potential, I have to calculate: E(r), Rho(r) -- charge density, and Q -- total charge.


    2. Relevant equations



    3. The attempt at a solution

    I know that E(r) is simply minus gradient of V(r), which is lambda*A*e^(-lambda*r)/r + A*e^(-lambda*r)/r^2. And, the rho will be equal to divergence of E times emissivity constant, according to the Gauss' Law and Divergence theorem. However, I'm having trouble calculating the divergence of E(r). Apparently, I have to use the Dirac Delta Function, but I'm simply lost from here. Please help me out.

    Thank you,
     
  2. jcsd
  3. Nov 6, 2013 #2

    BruceW

    User Avatar
    Homework Helper

    hmm. Just have a go at calculating the divergence of E(r). Clearly, something slightly strange will happen at r=0. But for r>0 you can see what happens without worrying about Dirac Delta functions.
     
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