Why do two opposing currents cancel each other out perfectly in Ampere's Law?

[PsychonautQQ]

Homework Statement

http://grephysics.net/ans/9277/9

I'm confused why these two currents cancel each other out perfectly when the distance they are being measured from is closer to the outside current than the inside current...

Like if the magnetic induction is proportional to the distance from the current,, then wouldn't the outside currents induced magnetic field be a little bit bigger than the inner currents?

edit: I just realized a potential flaw in my logic... since the outer part goes completely around the inner part,, on average both of the currents are the same distance away from the point P?

 

[Dick]

Homework Statement

http://grephysics.net/ans/9277/9

I'm confused why these two currents cancel each other out perfectly when the distance they are being measured from is closer to the outside current than the inside current...

Like if the magnetic induction is proportional to the distance from the current,, then wouldn't the outside currents induced magnetic field be a little bit bigger than the inner currents?

edit: I just realized a potential flaw in my logic... since the outer part goes completely around the inner part,, on average both of the currents are the same distance away from the point P?

Sort of. Just use Ampere's law and the symmetry of the currents.