Doubts on Ampère's Law and Coaxial Cables

[xareu]

I have a doubt about Ampère's that keeps me awake at night haha, but I think that for a more knowledgeable person it may seem pretty obvious. I've seen in several books that, in a coaxial cable with equal and opposed currents in the core and shield, the magnetic field outside the outer conductor is zero, after using Ampères Law (the summation of the currents in a loop around the whole cable, with opposite currents, is 0, assuming that in this particular arrangement H and dl have the same direction). Leaving apart the calculation, for me it's difficult to visualize it in the points which lay very close to the outer conductor. How can the field be zero there?
In the same cable, but with no current in the core conductor, only in the screen, is there field in the region from the centre to the shield?

 

[Dale]

In the same cable, but with no current in the core conductor, only in the screen, is there field in the region from the centre to the shield?

No, the field would be 0 in that region.