Asymptotic behavior quadrupole potential

[NanakiXIII]

Homework Statement

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

Homework Equations

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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?

 

[gabbagabbahey]

Taylor expand your expression for the total potential about the point 1/r=0

 

[NanakiXIII]

Yup, that worked. Thanks.