"Core" outside of a coil

[exnihiloest]

...
If we can increase the flux surrounding a coil by providing a higher permeability pathway of sufficient size, can we force that flux (which is conservative) through the smaller space of low permeability air at the center of the coil - or will the reluctance of that air be so great so as to prevent an increase of flux in the circuit?
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Very clear synthesis. And under this form, it suggests me a way to explain why the effect of the outside ferrite is weak.
Would it be possible that:
- a small leakage flux escapes the ferrite and loops far away in space (thin line)
- the main part of the coil flux passes through the ferrite and loops partly through the coil (thick red line) and partly outside the ferrite (thick brown line) in a reverse direction comparing to the leakage flux.  [update after experiment: the flux represented by the thick brown line doesn't exist, almost all the flux from the coil is looped in the ferrite]
See the attachment (coil inside, not represented).

In this case, the flux through the coil should be less than through the ferrite, explaining the weaker increase of the inductance in comparison with the ferrite inside the coil.
This would also explain that the flux in the ferrite is now logically almost the same in both experiments with the ferrite outside or inside, which was the main point to be questioned.

This sounds rather strange but if we think in the same way with a static field, it is clearer. Imagine a permanent magnet inside the ferrite, with axial poles. The magnet magnetizes the ferrite and makes it looking as a permanent magnet of same polarity.
Now I'm not yet really convinced by my hypothesis because how could the flux in the ferrite be stronger than inside the coil that is the field source?

[BEP]

Very interesting question indeed. Evidently, there must be a limit to how much can be forced inside regardless of what is happening outside. 

Would it be possible that:
- a small leakage flux escapes the ferrite and loops far away in space (thin line)
- the main part of the coil flux passes through the ferrite and loops partly through the coil (thick red line) and partly outside the ferrite (thick brown line) in a reverse direction comparing to the leakage flux.

In this case, the flux through the coil should be less than through the ferrite, explaining the weaker increase of the inductance in comparison with the ferrite inside the coil.
This would also explain that the flux in the ferrite is now logically almost the same in both experiments with the ferrite outside or inside, which was the main point to be questioned.

This sounds rather strange but if we think in the same way with a static field, it is clearer. Imagine a permanent magnet inside the ferrite, with axial poles. The magnet magnetizes the ferrite and makes it looking as a permanent magnet of same polarity.
Now I'm not yet really convinced by my hypothesis because how could the flux in the ferrite be stronger than inside the coil that is the field source?

Your hypothesis?

Perhaps you should read my answer, again?

[exnihiloest]

I re-read it, and it seems not more relevant than the first time I read it.

[exnihiloest]

A new simple test:
A coil inside the ferrite and a coil wound outside, i.e. the cylindrical ferrite is between the two coils. The generator is connected to the inside coil.
The signal measured on the outside coil is very weak (at least 20 times weaker than when the 2 coils are simply coupled without ferrite).

The flux crossing the outside coil is the flux in the inside coil+the flux in the ferrite. We must conclude that they are equal and reverse: this means that almost all the flux from the inside coil is really looped in the ferrite.

Another independent coil probe, parallel to the ferrite cylinder, doesn't detect a significant signal. So my previous idea was not correct: the flux that I represented by the thick brown line doesn't exist.

Now we know that the flux from the inside coil is almost totally looped in the outside ferrite. So the situation is the same as with the inside ferrite: the flux is conservative but why the effect on the inductance is not the same in both cases remains unexplained.

[poynt99]

Ex,

As I mentioned before, I believe the flux in both directions cancels inside the ferrite when it is situated outside the coil.

[Harvey]

The total flux (Φ) may be identical. However the flux density (B) may be considerably less in the outside loop because of the increased area of the exterior core. B = Φ/A

In addition to this, the entire magnetic circuit has some value of maximum reluctance which limits the flux similar to the way a resistor limits the current in an electrical circuit.

And even further, the coil inductance also limits the flux based on the time rate of change of current in your coil. Since the inductance is linked to the magnetic path, the two are interactive.

Just as the spokes of a wheel are closer at the hub than at the rim, flux density is greater in the center than around the outside.

To get the same results in both tests, I would suspect the best approach would be to choose the desired inductance and provide the geometry (and permeability) that satisfies the same flux density for both areas, internal and external to meet the inductance goal.

[BEP]

I re-read it, and it seems not more relevant than the first time I read it.

Ah! Why am I not surprised?

Never the less, the answer I supplied is the reason inductive devices are not designed as you have in your experiment. I seriously doubt those same designers worry about the closed loops of the magnetic circuit being non-conservative.

Forgive me, but I see your experiment as if a scientist is holding a bucket of water with many holes in the bottom while he puzzles over why the water level drops.

Yes, indeed, the high permeability of the ferrite will act as a lower reluctance path for the magnetic loops. This does not mean all of these loops will take that path. The very high reluctance portion of the circuit (between the ends of the coil and the ends of the outer core ferrite) provide an area where the loops take an equal preference of increasing the distance between them.

Magnets do not repel only when like poles face each other. They also repel when like 'equators' (bad terminology but should be clear) face each other. All that is required is the smallest of gaps. You have a huge distance allowing leakage. It is no different than a loosely wound coil over a sensible core causing magnetic leakage.

The above is only one half of the problem you see. The other half is exactly as .99 has described. In a central core the magnetic circuit direction is only one direction (simplified by not involving Lenz).

In any outer core there are a minimum of two magnetic circuit paths. The net magnetic is almost null. The only reason it isn't null is because the larger diameter of the outer perimeter presents a greater path than the inner diameter.

You should be able to link that minute 7% change to the difference between the inner and outer diameters of the outer core 

Here is an idea to ponder....

Make an outer core that is of Mobius form. This would provide the same path surface area for inner an outer diameters and should result in no effect on the inner coil.....

Wait a minute!  Isn't that why non-inductive resistors and capacitors use that form?   

[exnihiloest]

Ex,

As I mentioned before, I believe the flux in both directions cancels inside the ferrite when it is situated outside the coil.

Hi Poynt99,
There is only one flux direction in the ferrite, the opposite direction being in the air. I agree that in both cases, ferrite inside or outside, the flux in both directions (air/ferrite) cancels. This is well known for a coil with an inside core, all its flux is looped in space around and my last experiment confirms it is also the case with an outside ferrite: flux passing in air through the inside coil = flux in opposite direction in the ferrite, nothing outside.
The last question that remained was: why the change of the inductance due to the ferrite is not the same in both cases? See Harvey's reply and mine to him (likely not a question of ferrite position but of the air path).

[exnihiloest]

The total flux (Φ) may be identical. However the flux density (B) may be considerably less in the outside loop because of the increased area of the exterior core. B = Φ/A

In addition to this, the entire magnetic circuit has some value of maximum reluctance which limits the flux similar to the way a resistor limits the current in an electrical circuit.

And even further, the coil inductance also limits the flux based on the time rate of change of current in your coil. Since the inductance is linked to the magnetic path, the two are interactive.

Just as the spokes of a wheel are closer at the hub than at the rim, flux density is greater in the center than around the outside.

To get the same results in both tests, I would suspect the best approach would be to choose the desired inductance and provide the geometry (and permeability) that satisfies the same flux density for both areas, internal and external to meet the inductance goal.

Hi Harvey
I synthesize what I understand now from your answer that enlightened me. We have two magnetic circuits. The first one with the ferrite inside the coil is constituted for one way by the ferrite cylinder and for the return by the entire air space outside and around the coil. The second one with the ferrite outside of the coil is constituted for one way by the air inside the coil and for the return by the same ferrite cylinder now around the coil.
Each magnetic circuit is far from saturation. Not the point. Signals are weak enough for not saturating the ferrite, and air is not saturable.
I agree with you that the flux is limited by the value of maximum reluctance. I think that we can accept without calculating that the reluctance of the second circuit is higher due to the lower crossed section of the air path inside the coil. From Φ=L*I we must conclude that a lower Φ is the consequence of a lower L and so the phenomenon is explained: it is not the ferrite outside or inside that explains the difference (I'm pleased  ), but the consequent change of the section of the associated air path.

The same experiment by using a ferrite toroid having a big hole and wide diameter in order to severely increase the inside air path should clearly reduce the inductance change when coil inside and outside. I will try to confirm if time permits.

[poynt99]

If you do this experiment up in FEMM, you should be able to determine why the difference.