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Asymptotic behavior quadrupole potential

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the asymptotic behavior of a quadrupole consisting of a -2 charge at the origin and +1 charges at z = +/- 1.

    2. Relevant equations

    -

    3. The attempt at a solution

    You can construct the Coulomb potentials for these three charges and show that for large r, they all go as 1/r. The problem is that if you add them together, for large r, the -2 cancels the 2*1, so for large r you actually get 0/r. This makes the potential go to zero more quickly than 1/r, and 1/r doesn't seem like a fitting description of the asymptotic behavior. How do I go about incorporating this?
     
  2. jcsd
  3. Apr 14, 2010 #2

    gabbagabbahey

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    Taylor expand your expression for the total potential about the point 1/r=0
     
  4. Apr 14, 2010 #3
    Yup, that worked. Thanks.
     
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