1. The problem statement, all variables and given/known data An infinite plane at z=0 is divided into two: the right half of it (y>0) is held at potential zero and the left half of it is held at potential \phi_0 . Over this surface lies a point charge q at (0,y_0,z_0) . Use Green's function to calculate the potential at z>0. 3. The attempt at a solution I'd appreciate it if someone could take a look at my attempt at solution as I'm not sure whether what I've gotten to is right or wrong. Mainly because I also have to calculate other things that require taking the derivative of this expression (surface charge density and force acting on the charge). Also, I couldn't calculate the integral (Wolfram won't read it for some reason) which makes it even more suspicious. If you plug it into some program and you get an answer, please, let me know. Thanks in advance! P.S: I've noticed earlier that someone had replied to my older post which has been deleted and I couldn't reply at the time and I can't recall what had been said. If you read this and want to share again, please do.