Originally Posted by bshanteau

Yes, the magnetic field is additive, but it is additive for current in two wires flowing in the same direction (and subtractive for current flowing in opposite direction).

Now apply that principle to quadrupole loops. This is a detail from Caltrans Standard Plan ES-5B showing the winding detail for what they call a Type Q loop:



Loops run on radio frequency AC current, but assume for the moment that the current is flowing in the direction of the S and F arrows. If you follow the the S arrow, you will see that it points up in the left wire, down in the center wire, and up again in the right wire. Thus the current is flowing up in the left and right wires and down in the center wires. The total current in the center wires is double that in the upper and lower wires, meaning that the magnetic field is double also. That is why the center wires are the "sweet spot" for quadrupole loops.

Also, the S and F arrows in the lead-in wires are pointing in opposite directions, making the net current in the lead-in zero.