Using the expression from Coulomb's law, we get the total field at r by using an integral to sum the field at r due to the infinitesimal charge at each other point s in space, to give E ( r ) = 1 4 π π ε ε 0 ∫ ∫ ρ ρ ( s ) ( r − − s ) | r − − s | 3 d 3 s where ρ is the charge density. If we take the divergence of both sides of this equation with respect to r, and use the known theorem