Hello, 1. The problem statement, all variables and given/known data I am trying to solve Laplace's equation for the setup shown in the attachment, where f(x)=9sin(2πx)+3x and g(x)=10sin(πy)+3y. I have managed to solve it for the setup without the rectangle (PEC), and am now trying to solve ∇2[itex]\phi[/itex]=0 for that inner rectangle in order to then apply superposition and sum up the solutions. 2. Relevant equations 3. The attempt at a solution Since the inner rectangle is a perfect conductor, the electric field inside must be zero. Hence the potential must be constant, right (as E=-∇[itex]\phi[/itex])? d1=1/4 and d2=1/3, hence the boundary conditions are: [itex]\phi[/itex](x,y=0)=?, [itex]\phi[/itex](x=1/4,y)=?, [itex]\phi[/itex] (x,y=1/3)=?, [itex]\phi[/itex](x=0,y)=?. Now how should I proceed? Should all these potentials indeed be equated to constants or ought I to use something linear, such as (Ax+B)(Cy+D)?