1. The problem statement, all variables and given/known data A conducting sphere of charge Q and radius A is located at a distance D from the sphere's center to an infinite, grounded, conducting plane. Ultimately, I would like to find the capacitance, but that is simple once I find the potential. So the question isow does one determine the potential of this system using the method of images? The hint given is that the solution is a very nasty infinite series. 2. Relevant equations Miscellaneous electrostatic equations, Method of Images 3. The attempt at a solution Initially we have an infinite grounded conducting plane with no net charge and a potential = 0 everywhere. We place this plane in the YZ plane. Then we bring in our charged conducting sphere, placing it at distance D from the plane. Obviously the charges on the sphere will no longer be homogeneously distributed. The method of images states that any stationary charge distribution near a grounded conducting plane can be treated by introducing an oppositely charged mirror image (sphere). The charged sphere behaves as though all of its charge is concentrated at the center, as does its mirror sphere... This is where I take a step that I am somewhat unsure of... If this is the case, then the situation is similar to that of a charged sphere and a point charge, except the boundary conditions are that V=0 at the plane (or when rvector = dvector = |d|ihat, or more simply, when rvector dot dvector= |d|) In this scenario, the mirror sphere behaves like a point charge, which I call q' = -Q. There is an image charge induced in the real sphere of q'' by the image sphere/charge, at a distance d' from the center of the real sphere. So, I know that [[EQ 1]]V = Vground + (4*pi*epsilon0)-1 (Q - q'')(|rvector|-1, But this is for a charged sphere and a point charge! Can I make the assumption that the image sphere will beave like a point charge? Not quite, I'm sure! So I churn through copious amounts of vector algebra and the like, and I discover that from the solution for the grounded sphere & point charge is gives us: q'' = (AQ)/(2D), and d' = (A^2)/(2D) And then I can substitute into [[EQ 1]]: V(rvector) = k( -Q/(|rvector - 2d*ihat|) + (aQ)/(2d(|rvector - (a^2)/(2d)*ihat| + (Q(1-(a/(2d))))/(|rvector|) (where k = (4 * pi * epsilon0)-1 This is only a valid solution when V(rvector dot dvector = d ) (because that would represent the surface of the grounded plane) Mucking about with some more math, I discover I am missing a term: (-Q(a^3))/(4(d^3)|rvector - (a^2)/(2d) * ihat|) I'm can see a pattern *trying* to emerge, but I'm not 100% sure how to morph this into an infinite series... Any pointers? Can I treat this situation the way that I have? Are my Boundary Conditions correct? Also, is there an equation editor I can use to make expressing these less cumbersome?