1. The problem statement, all variables and given/known data A box shaped rectangular metal cavity of sides a, b and c along the x, y and z axes, respectively, has one corner at the origin. Of the six sides, all are grounded except the one at x=a and the one at y=b which are held at potentials of V1 and V2 , respectively. Find the potential V(x,y,z) everywhere inside the cavity. There are 6 boundary conditions, I think I've got them all correct: i.) V(a, y, z)=V1 ii.)V(x, b, z)=V2 iii.)V(x, y, c)=0 iv.)V(x ,y, 0)=0 v.)V(0, y, z)=0 vi.)V(x, 0, z)=0 2. Relevant equations ## \Delta V = 0 ## 3. The attempt at a solution I know how to approach this, we assume the potential can take the form V(x,y,z)= X(x)Y(y)Z(z), twice differentiate with respect to each spatial coordinate and plug it into the Laplace equation. From there we get three ODEs, which are each equal to a constant. This is where I get stuck. I know the choice of these constants, in particular their signs, is dependent on the boundary conditions. I'm stuck at this point, I don't know which sign to choose for each constant such that A+B+C=0, since the form of each separated solution will change based on these constants. Previous problems I've done involved one of the sides of the box going to infinity, so it was easy to choose constants to satisfy V->0 as a coordinate went to infinity.