Hi, I have some trouble understanding my book's derivation of Ampere's law. I have attached the derivation, and would like to ask the following. In equation 5.47 they throw away the first term because, ∇xJ=0. I don't understand why that is. Their argument is that J does not depend on the coordinates (x,y,z), but I don't see why that is. What if you wanted the magnetic field inside the mass distribution?