Let say we have charged conductor M and we know its potential energy function Vm(r) when M is isolated from any charges. We also have charged conductor N with potential energy function Vn(r) when it is isolated. Now we put objects M and N close together, the charges on their surfaces redistribute. I am interested in potential energy at every point in space, can I still add potential energy functions (Vm + Vn) to find that? I'd like to think that it is possible to add functions like that, but I can't find a way of proving it mathematically yet. Any ideas of how to show this?