2.67 product of rho and φ ** consider a charge distribution rho1(r) and the potential φ1(r) due to it. consider another charge distribution rho2(r) and the potential φ2(r) due to it. both distributions have finite extent, but are other- wise arbitrary and need not have anything to do with each other. show that rho1φ2 dv = rho2φ1 dv, where the integrals are taken over all space. solve this in two different ways as follows. (a) consider the two collections of charges to be rigid objects that can be moved around. start with them initially located very far apart, and then bring them together. how much work does this require? imagine moving collection 1 toward collection 2, and then the other way around. (b) consider the integral e1e2 dv over all space, where e1 and e2 are the electric fields due to the two distributions. by using the vector identity ∇ · (e1φ2) = (∇ · e1)φ2 + e1 · ∇φ2 (and similarly with the 1s and 2s switched), rewrite the integral e1e2 dv in two different ways.