1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Multipole expansion

  1. Dec 10, 2008 #1

    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?

  2. jcsd
  3. Dec 10, 2008 #2


    User Avatar
    Science Advisor

    The variable u=(L/r)
  4. Dec 11, 2008 #3
    thanks clem
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook