1. The problem statement, all variables and given/known data Consider a pair of spheres of radius R with uniform charge densities ρ > 0 and −ρ located respectively at ~r+ = (0, 0, d/2) and ~r− = (0, 0, −d/2), with d < R. a)Find the electric field at all points in the region of overlap of the spheres for arbitrary d < R. 2. Relevant equations Coulomb's law Gauss's law (integral and differential form) ∇E = (1/∈_0)ρ is the differential form. 3. The attempt at a solution I haven't made it very far into the problem. I'm still trying to set it up. I believe at some point I will have to integrate from -d/2 to d/2, but that can't happen until I set up the proper equation. Now, I have to find the flux through the overlapping region while there is a uniform charge density, ρ and -ρ. One idea I had was to integrate the divergence of the electric field over the volume, each sphere. This would put me into a triple integral in spherical coordinates and I want to say integrate R^2*dr from -d/2 to d/2 and proceed with integrating sinΘdΘ from 0 to π and dΦ from 0 to 2π. P.S. I kind of thought all of this out while I was posting.