Prove that in a region free of electric charge, the value of the potential
at a point is equal to its average over any sphere centered at that point.
V(r) = 1/(4piR^2) Integral(V * da)
The Attempt at a Solution
I defined a point outside the region where a point charge is located. At a random point inside the potential is kq/r. The point charge has the coordinate H,alpha(angle),gamma(angle).Now I made my auxiliary sphere and using that same point where the charge is located I got the Integral of 1/(4pi4r^2) q/(4piepsiolonsubnot) R^2 sin(phi) (H^2 +R^2 -2HR(cosalphacosthetasinalphasintheta+sinthetasinalphasingammasinphi+cosgammacosphi_^1/2 but I cannot integrate it.