h0dgey84bc
Dec10-08, 12:28 PM
Hi,
I'm just working through some electrodynamics notes, and am a bit stuck following a particular Taylor expansion, the author starts with:
\frac{1}{R_1}=\frac{1}{r} [1+(\frac{l}{r})^2-2\frac{l}{r}cos(\theta)]^-0.5
Which he then says by assuming l<<r and expanding we get:
\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)) ]....
Just a bit lost at how to do this, what variables am I expanding wrt?
thanks
I'm just working through some electrodynamics notes, and am a bit stuck following a particular Taylor expansion, the author starts with:
\frac{1}{R_1}=\frac{1}{r} [1+(\frac{l}{r})^2-2\frac{l}{r}cos(\theta)]^-0.5
Which he then says by assuming l<<r and expanding we get:
\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)) ]....
Just a bit lost at how to do this, what variables am I expanding wrt?
thanks