A square sheet has a uniform surface charge densityσσ. Letting the electric potential ϕϕ be zero at infinite distance from the square, denote by ϕ0 the potential at the center of the square and by ϕ1 the potential at a corner. Determine the ratio .
The answer can be found with very little calculation by combining a dimensional argument with superposition. (Think about the potential at the center of a square with the same charge density and with twice the edge length.)
