- #1
MMS
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Homework Statement
Find the electric potential of a ring of radius R that is charged uniformly with a linear charge density λ.
Homework Equations
The Attempt at a Solution
I wasn't sure which section to post this in but I finally landed here. It isn't really a problem that I'm troubled solving. Rather, it's something in the solution given I'm troubled understanding.
Here's the full solution: http://docdro.id/lhpIgyS
First off, I believe they messed up a little substituting Y_lm (not Y*_lm) as the exponent is exp(-i*m*phi) rather than exp(i*m*phi).
However, What's really bugging me is what they did after picking phi=0 and using the delta in (8).
I'm really not sure what went there. It seems as if they used some sort of orthogonality expression, I'm assuming that of spherical harmonics. If they did do so, I can't see what manipulations they did to get 2*pi*delta_m0.
It hints that m'=0 but there is no m' here. Also, assuming there was, they picked it to be 0 because of the azimuthal symmetry?
Moreover, if they did use the orthogonality expression of spherical harmonics, why is there no delta_ll'?
Thanks in advance.