A cubical box (sides of length a) consists of five metal plates, which are welded togeth...

A cubical box (sides of length a) consists of five metal plates, which are welded together and grounded (Fig. 3.23). The top is made of a separate sheet of metal, insulated from the others, and held at a constant potential V₀. Find the potential inside the box. [What should the potential at the center (a/2, a/2, a/2) be? Check numerically that your formula is consistent with this value.]¹¹