I've been thinking about this problem and would like some clarification regarding the value of the divergence at a theoretical point charge. My logic so far: Because the integral over all space(in spherical coordinates) around the point charge is finite(4pi), then the divergence at r=0 must be nonzero. If we can say that the dirac-delta function is a good physical model for the point charge then the Divergence is infinite at r=0 and zero elsewhere. A property of the dirac-delta function is that when you integrate it picks out the value of the function at the location of the spike. With the integral value being 4pi, it would make sense that divergence is equal to 4pi at the origin. So back to my question. Would the divergence be infinite at r=0 or equal to 4pi?