This is an interesting problem! Consider a cube with charges 'q' situated at its corners(a total of 8). Determine the point of stable equilibrium in this cube. My Answer: An off hand guess would be the point at the center of the cube, as though a positive charge at the center is suspended in midair. A point of stable equilibrium is a point of local minimum in the potential energy. Here the potetial energy of 'q' is 'V'. But, we know that Laplace's equation do not allow a local minima for V. So where would be the point of equilibrium be located?