I've been trying to get my head arround this problem for several days now, and while I deemed it relatively simple at first it turns out that I can't figure out the BCs on a conductor, to which we apply a potential U. In the simplified version of the problem, there is a rectangular conductor with resistance ρ to two opposing sites of which (call them A and C) we impose a given voltage 0 to U₀. Question remains: What are the boundary conditions on sides B and D? I don't want to influence the topic at this point so I won't really state what I thought could be done, I just say that no matter what BC I imagined, I could not ultimately justify it without requiring further assumptions than the given data. Addition: I should add that the conductor is interfaced into a circuit at sides A and C, so a current flows through it.