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Multipole expansion

  1. Dec 10, 2008 #1
    Hi,

    I'm just working through some electrodynamics notes, and am a bit stuck following a particular Taylor expansion, the author starts with:

    [itex] \frac{1}{R_1}=\frac{1}{r} [1+(\frac{l}{r})^2-2\frac{l}{r}cos(\theta)]^-0.5[/itex]

    Which he then says by assuming l<<r and expanding we get:

    [itex] \frac{1}{R_1}=\frac{1}{r} [1+(\frac{l}{r})cos(\theta)+\frac{1}{2}(\frac{l}{r})^2(3cos(\theta)^2-1)+ \frac{1}{2}(\frac{l}{r})^3(5cos(\theta)^2-3cos(\theta)) ].... [/itex]

    Just a bit lost at how to do this, what variables am I expanding wrt?

    thanks
     
  2. jcsd
  3. Dec 10, 2008 #2

    clem

    User Avatar
    Science Advisor

    The variable u=(L/r)
     
  4. Dec 11, 2008 #3
    thanks clem
     
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