Firstly, sorry for asking a physics question here, but on physics stackexchange, the moment they smell a hint of homework-like questions they click on "close" without even reading the problem...
So i'm supposed to calculate the behavior of the electrostatic potential $V$ at large distances $|r| \gg a$ for the following linear charge density along a ring of radius $a$:
$$\rho(r,\psi, z) = \frac{q}{2\pi a}\cos(n\psi )\delta(z)\delta(r-a)$$
where $n=0,1,2,....$
So what I'm supposed to do, is calculate the following integral:
$$V(r)=\frac{1}{4\pi \epsilon_0}\left(\frac{1}{r} \int\rho(r')d\tau'+\frac{1}{r^2}\int r'\cos\alpha \rho(r')d\tau'+\cdots\right)$$
(where the first term is called a monopole term, second dipole..)
Question 1: what is that $n$ inside the cosine term for? Am I supposed to just plug numbers in? e.g. for the mono-term, use different $n$ numbers?
Question 2: the dirac delta term $\delta z$ requires $z=0$ otherwise the charge density is $0$? So I'm supposed to only integrate the $x,y$ plane, is that correct? And this brings me back to question 1, since i'm integrating from $0$ to $2\pi$ on the $\theta$ term, the whole thing is $0$?