I know the ampere's law but I want an explanation on why it exist in that way, consider a wire where flows current, i know that when an observer is in relative motion to the current there is a magnetic field but why in this geometric configuration and not in another? What about the electric field outside? I guess is zero unless we don't move at the same velocity on the current so that our frame of reference is solidal with it, then the electromagnetic field is just electric field, is that TRUE? I mean, if we see current flowing all the field is magnetic, if we don't see current all the field is gonna be electric due to Lorentz contraction law and all that stuff right? Why the magnetic field outside a wire obeys to the right hand rule?