1. The problem statement, all variables and given/known data A long copper pipe, with it's axis on the z axis, is cut in half and the two halves are insulated. One half is held at 0V, the other at 9V. Find the potential everywhere in space. 2. Relevant equations [tex]\nabla^2V=0[/tex] 3. The attempt at a solution Alright. This is a laplace's equation problem in two dimensions, since the potential should be independent of z because the pipe is infinite. Using separation of variables( [tex]V=R\Phi[/tex]) the solution to the two dimensional Laplace's EQ in cylindrical coordinates is: [tex]R(r)=ar^k+br^-k[/tex] [tex]\Phi(\phi)=A\sin(k\phi) + B\cos(k\phi)[/tex] w/ [tex]V=R(r)\Phi(\phi)[/tex] I am getting confused when I try to apply boundary conditions to this problem. Here is what I think the boundary conditions should be: 1) V should go to zero as r goes to infinity. (I don't think this is right, since the pipe is infinite, but I am not sure.) 2)V=0 for phi between 0 and pi, r=radius of pipe 3)V=9 for phi between 0 and 2pi, r=radius of pipe. I can't figure out how to actually use these to eliminate any of the constants. Any help and hints would be greatly appreciated.