In § {Activity: A Uniformly Charged Ring}, you will have found an integral expression for the electrostatic potential due to a uniform ring of charge. Some things you may have needed to pay attention to are:

1. Draw a picture!
2. How thick is the ring? What shape is its cross section? Should it be described by a volume charge density? In the absence of further information, the only thing you can do is idealize the ring as a line charge.
3. In equation (1) of § {Potentials from Continuous Charge Distributions} the charge density is described as a volume charge density. You must change this equation to accommodate a line charge.
4. How should the differential volume element $d\tau'$ be changed to accommodate the fact that the charge density represents a line charge?
5. Where should the origin be? What coordinate system should you choose?
6. How can you simplify the differential element in your chosen coordinate system?
7. How can you simplify the expression for $|\rr-\rrp|$ in your chosen coordinate system?

Putting several of these steps together, the equation \begin{eqnarray*} V(\rr) = \Int_{\hbox{ring}} {1\over 4\pi\epsilon_0} {\rho(\rrp)\,d\tau'\over|\rr-\rrp|} \end{eqnarray*} becomes \begin{eqnarray*} V(r, \phi, z) = {\lambda\over 4\pi\epsilon_0} \Int_0^{2\pi} {R\,d\phi'\over\sqrt{r^2+R^2-2rR\cos(\phi-\phi')+z^2}} \end{eqnarray*}