I've been reading some E&M text and came across an interesting electrostatic problem that went something like "find the net force that the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere". The answer is (3Q^2) / (64*[tex]\pi[/tex][tex]\epsilon[/tex]*R^2). Where Q is the total charge on the sphere, R is the radius, and [tex]\epsilon[/tex] is the permitivity of free space. This is a rather beautiful problem, and an interesting theoretical exercise would be to apply it to the earth and figure out just how strong, roughly, the earth is resisting the separation, due to the electric force, of it's northern and southern hemisphere's. My question: what is a nice way to guess the charge on the earth? The only variable in the solution to the problem that gives me any trouble is the charge. I am not sure if it is necessary to even consider whether or not most of the charge is gathered along the surface or rather if it is speckled throughout the volume. The reason I am not sure if it is necessary is because I don't think the estimation will be off more than a factor of 10 if we consider the earth as a uniformly charged sphere and not a conductor. The work to build a spherical conductor is about 3/5 or 4/5 the work to build a spherical insulator which means the difference between the forces which pushes the hemispheres apart in both cases cannot be much different. Reiteration of question: what is a nice way to guess the charge on the earth?