sci.physics.electromag

The basis of the problem is this.
Common sense and coil calculators (and even real world experiuments I
did looooong ago) all assure me that 2 identical hoop coils where the
only difference is the diameter should produce very different magnetic
field strengths (densities) when an identical current is passed.

The tighter coil produces a higher gauss than the same number of
Ampere turns in a larger dia. coil.

The next fact that can't be denied is that a coil wound on a highly
magnetically permeable toroid should have no significant readily
measurible magnetic flux outside the toroid provided the core has not
been saturated. (I am well aware that infact strong magnetic fields do
exist outside the toroid but due to superposition they are not readily
detected by magnetic means)

These 2 facts collide in a seeming impossibility however, if you have
(to keep it easy) 2 square toroid forms (a normal E I bar transformer
with the middle of the E removed) and you wind a single layer coil of
say 100 turns on (the outside vertical leg of) each of these toroid
forms and pass a current through there should not be an observible
external magnetic field from either of these toroids. see fig 1.

If we now place the 2 coils next to each other (as in fig 2) we should
not expect any drop in the gauss in either core since neither produced
a net external magnetic field.

Now consider fig 3, we have a show down (largest gauss wins) between a
tight coil over one core or a larger looser coil (of the same number
of ampere turns) over 2 cores, the tighter coil should win, easy
right?

Now in fig 4 we have the same only we have another core we have placed
next to the tight coil, which one wins now?
Since we have alrewady established that the tight cores shouldn't
interfere with each other the 2 tight cores should win.

But by now surely you can see the paradox, the only difference between
the 2 tight coils and the one loose one is the windings between the 2
tight coiled cores, but these shouldn't create any net magnetic field,
fig 5 helps illistrate this issue.

Anyone wanna take a crack at this, either explaining the paradox or at
least telling me in each case if you agree with the winner I've
chosen.

Or run it through a 3D magnetic simulation program?

Or at least agree it's a head scratcher!?!?

figs here:
http://www.imagedump.com/index.cgi?pick=get&tp=527437

note: in my browser I need to scroll horizontally to the right to see
the picture.
note 2: I have found that diameter has little effect in longer coils
so the coils may need to be kept shorter than pictured.