the final equation ∇XB(x) = μ0j(x) But this means that the curl of the magnetic field at any point is proportional to the current density at that point. But take the case of a long straight wire carrying current. The magnetic field surrounding the wire is circular and hence its curl is everywhere constant in value. But that means that the current density is everywhere constant in value, even at a million miles away from the wire. what's with that?