Multipole expansion

  • Thread starter h0dgey84bc
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  • #1
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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
 

Answers and Replies

  • #2
Meir Achuz
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The variable u=(L/r)
 
  • #3
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thanks clem
 

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