1. The problem statement, all variables and given/known data Essentially it gives the potential above the xy-plane as and I am tasked with verifying it satisfies laplace's equation, determining the electric field, and describing the charge distribution on the plane. 2. Relevant equations then 3. The attempt at a solution As far as I can tell it does not satisfy laplace's equation because when I take the gradient of the potential twice I get which is non-zero. So taking the second equation up there I found and using the third I found . In the case of the electric field I would assume the field in the x direction wouldn't matter (or at least shouldn't be there) because it is parallel to the field, but I'm not really sure if I'm doing this correctly.