I'm solving a problem numerically where I have some charge density above an infinite, grounded conducting plane and want to determine the electrical potential at a given point. My intuition says that this is not simply given by the potential of the charge density above the plane, since this will also attract charges of opposite sign to the grounded plane. To solve the problem I employ the method of Images such that the same charge density with opposite sign is found below the conducting plane. I then wish to calculate the electric potential. To do so I use Poissons equation: ∇2φ = -ρ/ε From this I can find the charge density by inverting the laplacian, which I have in matrix form (remember all this is done numerically, my density is a vector of values). The problem with doing so is that I get the exact same potential, as I would if I had just ignored the mirror charge distribution and worked with only the original charge distribution (which I guess is not so surprising). But I am pretty sure this is wrong. If you for example do the problem with a point charge above the grouned plane it is easy to see, that the mirrored charge will affect the potential. What am I doing wrong?