Lucky,
Break it down. In normal operation, which conductors are the current carrying conductors and, at any instant in time, what is the direction and magnitude of each current?
Then, apply the right hand rule to show the magnetic field direction. (Imagine the hitchhiker's extended right hand thumb symbol, the four fingers curled toward the palm like you have a roll of quarters under your fingers). Your thumb points in the direction of the current, your fingers show the direction of the magnetic field.
on GFI boxes we wrap the ground wire around the hot and neutral to identify the line side.
The hot and the neutral are the current carrying conductors.
The current "in" on the black is equal to the current "out" on the white, they are just going in opposite directions. The current in a wire makes a magnetic field of equal strength to the magnetic field from the current of the other wire, but, (use the right hand rule) the fields are exactly in opposition. The two magnetic fields sum to exactly zero.
The EGC (as you say, "ground") that is tightly wrapped around the hot and neutral does not "see" any magnetic field. Nothing happens here.
we tightly wrap the switch leg wire around the ground and hot wire with 2 wraps right up against the front of the box and tuck away the wires for drywall.
Here, the hot and switched leg are the current carrying conductors.
The current "in" on the hot is equal to the current "out" on the switched leg.
The hot and switched leg are physically running parallel to each other except in the short distance where the two wraps occur. Where parallel, the net magnetic field present is always zero, during normal operation of the circuit (See the right hand rule exercise for the GFI wire wrapping/marking above.) Nothing happens in the parallel part of the wiring.
The little area of the two wraps is a little more complex. The two wraps of the switched leg represent an air core electromagnet of two turns and creates a magnetic field at 90? to the magnetic field created by the hot conductor within the center of the air core.
These two magnetic fields don't "see" each other so they don't add or subtract.
Use the right hand rule (above) to show yourself the direction of the magnetic lines of force coming off of a given wire. It will probably be easiest to start with the straight "hot" wire inside the wraps. Imagine the magnetic lines of force coming off the hot wire . . . you'll note that they are in the direction of the wraps of the switched leg.
As the magnetic field of the hot expands and collapses it induces a current in the wrap, the switched leg, at 90? to the run of the wire. This is basically an eddy current going from side to side of the cross section of the conductor. This current doesn't go down the length of the conductor.
Conversely, the magnetic field created by the wraps of the switched leg, while twice as strong as the field created by the straight hot wire, is also inducing a current in the hot wire that is flowing across the cross section of the conductor, not down the length of the run of the hot wire.
End result, where parallel, zero induction, where wrapped, trapped eddy current.
Now, the two wraps of the switched leg is also an air core inductor. The current in the inductor, as it increases and decreases, creates an inflating and collapsing magnetic field that the inductor itself is within. The changing magnetic field induces a "back EMF" in the wire of the inductor that is the "impedance" that is the reactive inductance. This effect is to "choke" the change of the current strength and direction.
Also, in the confines of the two wraps, the two magnetic fields present, at right angle to each other, are creating two currents in the "ground" wire. Those two currents are at right angles to each other, within the "ground". One of the currents is in the direction of the run of the "ground".
Which one?
The current induced from the hot wire that is running parallel to the ground, but only for the magnetic coupling occurring within the confines of the two wraps. The tighter the wraps, the smaller the area. The smaller the area the fewer lines of magnetic force involved. The fewer lines of magnetic force, the lower the current induced. Within the confines of the two wraps, the hot and ground, in effect, form the windings of a 1:1 air core transformer with one turn in each winding. The flux density that can be created is minuscule. That is, really tiny, so tiny as to be of no engineering importance to the macro scale of the general lighting circuit.
For 3ways we do the same thing, wrapping the common wire, whether it be hot or switch leg.
Same as the switch above.
