Magnetic field Cancellation in AC wires (How?)

[HAgdn]

Homework Statement

How do magnetic fields cancel in AC wires? (common wire with hot and neutral)

Relevant Equations

This question has no involved equations

Why do the magnetic fields in-between the wires does not seem to cancel? Even those outside each wire? (the fields do are not in opposite direction). Yet most of the people I have talked to until now says that such magnetic fields do cancel? I am confused...

 

[Cutter Ketch]

Is this homework, or are you just asking?

 

[HAgdn]

Is this homework, or are you just asking?

Just asking

 

[Cutter Ketch]

Look at your sketch. Yes, the fields are the same direction between the wires, but the fields extend out further. The field below the top wire is into the board. A little lower and it is still into the board including the region below the bottom wire. So in the region above both wires and the region below both wires the fields are in opposite directions. If the wires are very close together, the fields are also essentially equal and cancel.

We don’t officially care about the region between the wires as nothing will be located between the wires. However, minimizing that space and putting the wires together is important for best cancellation of the field away from the wires. In fact you can relate the strength of the field away from the wires to the area of the loop made by the wires. As that area can never be exactly zero, we often further minimize the field by twisting the wires so that there are a series of tiny loops with the residual field pointing opposite directions from each loop.

 

[HAgdn]

... so it's just a matter of having a larger view...

 

[Cutter Ketch]

... so it's just a matter of having a larger view...

Right. Actually, it’s much easier to see in cross section. Draw the field of each wire as an ever expanding set of concentric circles. The two sets of circles almost but don’t quite cancel everywhere