It should cancel, but the only way to produce that field is to run a canceling current down the wire, so that's really the trivial solution.

What is a wire carry the the same AC current is the opposite direction why placed next to it. Lets assume very very thin wires.

Edited March 24, 201510 yr by CasualKilla

What is a wire carry the the same AC current is the opposite direction why placed next to it. Lets assume very very thin wires.

In the far-field limit, there will be no magnetic field. Close to the wires there will be, i.e. when the distance is not small compared to the wire size and separation.

 

This is the very reason you use twisted pair or coaxial wiring.