A cubical box (sides of length a) consists of five metal plates, which are welded together and grounded. The top is made of a separate sheet of metal, insulated from the others, and held at a constant potential Vo. Can you predict what the the potential at the center of the cube is without explicitly solving Laplace's equation? Provide a rigorous mathematical justification for your answer.

A cubical box (sides of length a) consists of five metal plates, which are welded together and grounded. The top is made of a separate sheet of metal, insulated from the others, and held at a constant potential Vo. Can you predict what the the potential at the center of the cube is without explicitly solving Laplace's equation? Provide a rigorous mathematical justification for your answer.