sci.physics.electromag

On Tue, 19 Feb 2008, aether22@gmail.com wrote:

> 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.

Sure, a consequence of the geometry. Field due to an infinitesimal current
element falls off as 1/r^2, field due to an infinite straight wire falls
off as 1/r. Thus, from either of these, the field at the centre of the
coil falls off as 1/r, r now being the coil radius (length of coil * 1/r^2
in the first case, a loop, seen from the centre, being equivalent to an
infinite wire in the 2nd).

> 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.
[cut]
> 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.

So, a significantly different geometry. Basically, the field now looks
like that produced by an infinitely long solenoid, which only depends on
turns/metre and the current, not the radius of the winding.

There's a geometric analogy along the lines of infinite wire vs loop. Note
that the field due to an infinite sheet of current is uniform. Wrap it
into a loop, and the field inside in uniform.

In practice, you're not going to have an infinite current sheet, or the
equivalent infinite solenoid, but you can wrap it into a toroid or around
a permeable core.

While at it, consider the magnetic moment of a closed loop. If you make
the field within the loop uniform, how does the field depend on the loop
(or coil) radius?

But I don't need to tell you this, since you already note at least the
kernel of the answer:

> note 2: I have found that diameter has little effect in longer coils
> so the coils may need to be kept shorter than pictured.

--
Timo