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Author Topic: "Core" outside of a coil  (Read 28986 times)
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Why a coil has a different behavior when a magnetic core is place inside and when it is placed outside? By "outside core", I mean a hollow magnetic cylinder in which a coreless coil is placed (see attachment).

I led the following experiment:
- A LC circuit is tuned to a resonant frequency of 600 Khz. The coil has a large diameter in order to place a ferrite cylinder inside. This cylinder acts as a ferrite rod. When I put this ferrite core in the coil, the resonant frequency is lowered down to 378 Khz, which means a variation of -37% of the frequency.
- Another LC circuit is also tuned to a resonant frequency of 600 Khz. The coil is of smaller diameter so that it can take place inside the same ferrite cylinder. When I put the cylinder around the coil, the resonant frequency is lowered down to 557 Khz, which means a variation of only -7% of the frequency.

In both cases, the field lines can pass through the ferrite, either through the "inside core" for the first case or the "outside core" in the second case. The magnetic circuit in which the field lines are looped is constituted in both cases of a half pass in air and a half pass in ferrite. There is the same flux inside and outside of the coil because the flux is supposed to be conservative. So why the ferrite effect in the second case is less than in the first one?


   
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Hi exnihiloest,

I assume your smaller diameter coil has got less self inductance than the large one.  This means the small coil needs a higher value capacitor to get resonance at 600kHz than the large coil does.
Now the detuning effect of the cylinder core for the small coil can only be less than for the large coil from the resonant frequency point of view because a smaller inductance is able to change its L value in a smaller percentage than the large one.  The L/C ratio is smaller for the small coil case, hence the influence of the core on the L is also less.

Gyula
   
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Thanks for the reply, Gyula.
I had chosen coils of similar inductance. For the same value of capacity, the small coil oscillates on 840 Khz and the larger on 600 Khz.

Nevertheless, well done: I had to adjust the capacity as you said (I use a variable capacitor), and this can be the cause of a biased experiment.
So to take into account your relevant remark, here is the result of the same experiment with the small coil, but by keeping the same capacity as for the larger one:
- without core: 843 Khz
- with the "outside core": 780 Khz
The variation is: 7,47%.
Therefore the weakness of the inductance change can't be explained this way although we see you are right when you say that the detuning is less when the capacity is more.

The mystery remains.  :)
I have noticed for a long time this phenomenon of the weak effect of the presence of an external magnetic material, but it appears to me abnormal only today, after thoughts about the "Non-conservative Fields Experiment" seen in the other thread.

   

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It's not as complicated as it may seem...
Ex,

It's the same phenomenon with the Lewin experiment; the B field intensity is much larger within the diameter of the coil, than outside of it.

The electric field set up from the changing B field INSIDE the coil is co-axial with the coil, therefore it is in the perfect position to induce an emf in the coil.

The less intense B field returning OUTSIDE the coil is not co-axial with the coil, therefore the weaker electric fields produced outside the coil are not able to induce as much emf, if any at all.
   
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Poynt beats me into it.  The field lines is much more dense within the coil than outside the coil. 


   
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Hi ex,

Ok, my assumption of the differing inductances was a possibility,  now I have a go otherwise:  I tend to accept what poynt99 wrote and the reason is that inside the coil if you consider any single turn, the fields of any single turn "sees" the inserted core twice.  How I mean, see this link on a normal solenoid, without core, Fig. 2, explanation is above Fig.2:
http://plasma.kulgun.net/sol_page/

Gyula
   
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Ex,

It's the same phenomenon with the Lewin experiment; the B field intensity is much larger within the diameter of the coil, than outside of it.

The electric field set up from the changing B field INSIDE the coil is co-axial with the coil, therefore it is in the perfect position to induce an emf in the coil.

The less intense B field returning OUTSIDE the coil is not co-axial with the coil, therefore the weaker electric fields produced outside the coil are not able to induce as much emf, if any at all.

This conclusion is not correct. The emf is not proportional to the B field only, the emf is proportional to the flux crossing (wikipedia). Inside the coil, the surface is less than outside, and the B field intensity is more. Outside of the coil, the surface is much larger, B is not constant and we have to integrate B on an infinite surface. Nothing here implies that the flux should be more inside than outside the coil.
It is the same thing with a river: the intensity of the current (= the B field) can be very strong when the water flows in the narrow pipe of a barrage to rotate a generator, but the flow is the same as further downstream when the river is wide (same number of m3/h/by unit of crossed surface)

In my experiment, the ferrite outside of the coil should channelize the outside flux because it represents an easier path for the magnetic flux than air. As it is the same ferrite in both cases when it is inside or outside, we should expect for the same effect because we have the same flux through the same surface.
So the explanation must be more complicated (or more simple  :( ).


   

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It's not as complicated as it may seem...
Not correct Ex.

This is also from Wicki

Quote
Outside

Magnetic field created by a solenoid (cross-sectional view) described using field lines.

A similar argument can be applied to the loop a to conclude that the field outside the solenoid is radially uniform or constant. This last result, which holds strictly true only near the centre of the solenoid where the field lines are parallel to its length, is important in as much as it shows that the flux density outside is practically zero since the radii of the field outside the solenoid will tend to infinity.

An intuitive argument can also be used to show that the flux density outside the solenoid is actually zero. Magnetic field lines only exist as loops, they cannot diverge from or converge to a point like electric field lines can (see Gauss's law for magnetism). The magnetic field lines follow the longitudinal path of the solenoid inside, so they must go in the opposite direction outside of the solenoid so that the lines can form a loop. However, the volume outside the solenoid is much greater than the volume inside, so the density of magnetic field lines outside is greatly reduced. Now recall that the field outside is constant. In order for the total number of field lines to be conserved, the field outside must go to zero as the solenoid gets longer.

   
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Hi ex,

Ok, my assumption of the differing inductances was a possibility,  now I have a go otherwise:  I tend to accept what poynt99 wrote and the reason is that inside the coil if you consider any single turn, the fields of any single turn "sees" the inserted core twice.  How I mean, see this link on a normal solenoid, without core, Fig. 2, explanation is above Fig.2:
http://plasma.kulgun.net/sol_page/

Gyula

If you represent the flux with lines, why should it be less lines outside than inside?
Only the density of lines crossing a unit of surface is higher inside than outside, not the number of lines, therefore the flux is the same, it is just crossing a wider surface outside than inside.
But with a ferrite core outside, the ferrite curves the field lines so that they concentrate in the ferrite material, and this is the only interest of my experiment (to try to concentrate the same flux outside than inside. Where is the cause of the failure, I don't yet know):


("The magnetic field is concentrated through the ferrite rod").

   

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It's not as complicated as it may seem...
   
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Not correct Ex.

I'm correct. You misinterpreted what is written.

Quote
Quote
... the flux density outside is practically zero...

If you don't specify through which outside surface it is zero, you say nothing. If you consider the surface of an infinite disk lying in a plane parallel to the plane of the turns, all the outside field lines have to cross this surface to loop from a end of the coil to the other end.
All courses say the same: the flux is conservative. You cannot expect to prove the contrary of the academic knowledge by using its own matter. Only experiments.


   

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It's not as complicated as it may seem...
Quote
However, the volume outside the solenoid is much greater than the volume inside, so the density of magnetic field lines outside is greatly reduced

Why are you making this so hard on yourself? How can it be made any more clear?
   
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To avoid a big confusion:

"The field outside is weak and divergent": yes it is! The field, not the flux!

Magnetic flux is conservative, but magnetic field is not.

It is the consequence of the null divergence of the magnetic field, formalized by the following Maxwell's equation:



   

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It's not as complicated as it may seem...
The flux density inside the coil is >> the flux density outside the coil.

Therefore, since your core is not infinitely large, much less total flux passes through the core vs. when the core is inside the coil.

That is the reason the core has much less effect at increasing L when it is outside the coil, vs. inside.
   
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...
Therefore, since your core is not infinitely large, much less total flux passes through the core vs. when the core is inside the coil.

That is the reason the core has much less effect at increasing L when it is outside the coil, vs. inside.


The flux that passes through surfaces in media of different permeabilities depends on the permeabilty. The higher the permeability, the more the flux. As already said, a ferrite material deviates a magnetic flux because its permeability is much higher than air. It will conduct more flux, at the detriment of the flux in the air.
Your answer is probably the right one (Okkham's razor), but it cannot be affirmed so easily: the part of the flux that is catched by the outside ferrite has to be evaluated (difficult problem). It is amazing that the outside ferrite doesn't capture more flux:
- firstly because in my setup the ends of the coil are completely inside the ferrite, at 1 cm from the ends of the ferrite cylinder so that the field lines should curved towards the ferrite as soon as they leave the ends of the coil
- secondly because the drastic effect of a ferrite rod antenna of an AM receiver is well known, it strongly curved the field lines, greatly increasing the flux inside, so we could be expecting for the same effect here.

   

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It's not as complicated as it may seem...
You are right of course. Most of the returning flux should go through the outside core, vs. the air.

It would seem that the coil's self inductance is primarily determined by the total flux through its center, and the u of the core.

Here is an experiment that may prove this:

Compare the percentage Fo changes with both the inner and outer core while bringing a magnet close to the coil/core in each case.
   

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It's not as complicated as it may seem...
One other possibility is this:

When the core is outside the coil, the core might be "shared" (almost equally) by both the inside and outside flux (opposite directions), such that the end result is close to a net zero flux change inside the core.

When the core is inside the coil, "sharing" does not occur, and the core is influenced mostly in the direction of the B field inside the coil.
   
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Ex,

Here is an answer that should trigger disagreement. Never the less, it is accepted in transformer design.

The outer core has less influence on the inner coil because the outer core sees both directions of flux lines (inner Gaussian surface and outside the coil), where the inner core sees only the inner Gaussian surface.

It is very understandable that all lines found in the inner core should also pass through the outer core. This is not the case. Field lines prefer to be conducted through the outer core but they also act to separate themselves from adjacent field lines. In-short.... the outer core allows too much flux leakage.

It isn't a question of conservation. It is a question of leakage. If the ends of the coil were covered by the outside ferrite there would be less leakage. To prevent the leakage and the cancellation effect between inner and outer field lines, the central core would require a complete path to the outer core, as is done in SMPS's.

Of course, magnetic fields do not affect other magnetic fields so I will assume your comment on my explanation will be negative.


>Edit..

Credit where credit is due: .99 covered most of my answer before this post. I just didn't see it before I posted this one.
Yes, the net B in the outer core is less since both directions pass through that core.


I don't understand Flux vs. Field, one being conservative and the other not. The field is gradients of flux. The gradients are an aspect or result of the magnet or coil but both the field and flux are properties of space. How can one be conservative and the other not?
Maybe it is my semantics again. I'll read up on it.
 

 
« Last Edit: 2012-03-05, 20:24:35 by WaveWatcher »
   
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Hi Exnihiloest,

The answer is in the geometry and the permeability of the two materials i.e. air and ferromagnetic core.

Because the flux is conserved, there must be a value of flux outside the solenoid that exactly matches the value inside the solenoid - A one to one match for every line of flux.

However, the occupied space of those values is radically different, therefore we are discussing the concentration within a given volume, not the total quantity.

The inside area is a finite space.

The outside area is confined only by the boundaries of the universe (if such exist) and is therefore considered infinite.

So, depending on the thickness and permeability of your exterior core, only a small fraction of the actual exterior flux is routed through that material. Of course it is possible to find a value of permeability and thickness that could contain all (or nearly so) of the exterior flux and then the two experiments would be nearly identical.

The formulae for determining inductance is as varied as the geometry: http://en.wikipedia.org/wiki/Inductor#Inductance_formulae

But one important aspect relates to the formula Φ = BA = µNπr²i / ℓ where the total flux (Φ) is shown to increase if either the flux density (B) or the area (A) are increased as it is the product of the two. And since the flux density is dependent on the relative permeability of the interior core (µ) in the formula B = µNi / ℓ  we expect more flux when there is higher permeability in the core e.g. ferromagnetic core vs air. Alternatively, we could write it as B = Φ/A

So the middle of the solenoid is a finite area that we can use in our calculations. But once we leave that defined volume these formulas become difficult as A would represent the universe (or at least a measurable volume magnitudes larger than the solenoid center) and we are looking for a cross sectional area where the flux is normal to it.

Hope that helps  ;)
   
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EX,

I would suggest an experiment where you use only one coil size, but you insert two different ferrites.     One smaller diameter ferrite that goes snuggly on the inside of the coil,  and one that goes snuggly on the outside of the coil.   But most importantly, make sure the wall thickness of the ferrite cylinders is the same.      

I think that is what you are aiming for with this inquiry, and I'll say this:    if the thickness of the ferrite cylinders is  much less then the diameter of the coil,  say 10 times smaller,  you will find that the inductance is the SAME in either case.  or is it?    lol   :-\

EM

PS,  here's a picture to make sure you understand what I'm saying.  
« Last Edit: 2012-03-06, 02:31:03 by EMdevices »
   

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It's not as complicated as it may seem...
EM,

I think Ex has already done your experiment (see first post). In the case where the core is outside the coil, the core has very little affect on the coil inductance, and hence Fo of the oscillator.
   

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Aren't we fortunate that the inductance of a
coil is little affected by external material?

Think how the design of many electronic devices
would have been made much more difficult if
external influences had significant effect.

Whoever established the "laws" of magnetics
certainly had our technological advancement
in mind...


---------------------------
For there is nothing hidden that will not be disclosed, and nothing concealed that will not be known or brought out into the open.
   
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. . . if the thickness of the ferrite cylinders is  much less then the diameter of the coil,  say 10 times smaller,  you will find that the inductance is the SAME in either case.  or is it?    lol   :-\ . . .

Because of the nature of the solenoid, the internal flux has a higher concentration (density) than the external flux. So it will require a thicker or higher permeability material (or both) on the outside to achieve the same results even though the exterior has a greater cross sectional area as a flux path. ( See http://en.wikipedia.org/wiki/Magnetic_circuit#Microscopic_origins_of_reluctance )

 8)
   
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Hi Exnihiloest,

The answer is in the geometry and the permeability of the two materials i.e. air and ferromagnetic core.

Because the flux is conserved, there must be a value of flux outside the solenoid that exactly matches the value inside the solenoid - A one to one match for every line of flux.

However, the occupied space of those values is radically different, therefore we are discussing the concentration within a given volume, not the total quantity.

The inside area is a finite space.

The outside area is confined only by the boundaries of the universe (if such exist) and is therefore considered infinite.

So, depending on the thickness and permeability of your exterior core, only a small fraction of the actual exterior flux is routed through that material. Of course it is possible to find a value of permeability and thickness that could contain all (or nearly so) of the exterior flux and then the two experiments would be nearly identical.

The formulae for determining inductance is as varied as the geometry: http://en.wikipedia.org/wiki/Inductor#Inductance_formulae

Hi Harvey,

I well understand your reply and I think it is the likely explanation which is qualitatively in perfect agreement with the laws of electromagnetism. Nevertheless I would like to check it quantitatively because a question remains.
If there is no magnetic material and we chose a particular surface outside of the coil, we have some flux crossing it. If the air is replaced by a material of high magnetic permeability, the flux through the same area will be strongly increased. This is traditionally represented by field lines curving towards the magnetic material, resulting in more lines crossing the same area.  It is the principle used in a ferrite rod AM antenna: for the same flux, the crossed section in air is much wider than in the rod, and this allows the antenna to work as if its geometrical dimensions were 10 to 30 times larger.

Small ferrite rod antennae have replaced old big loop. Same effet for this:

And this:


We all have a mental image of the field lines of a coil, extending until infinity all over the space around from one end of the coil to the other one. But if we replace air outside of the coil with a magnetic material, the image has to be modified: the presence of the material changes the space properties around the coil and the magnetic flux preferably follows the sections of higher permeability (consequence of the principle of least action). And so when the permeability of a surrounding medium is not uniform, we have not at all the same flux crossing the same arbitrary area, we have much more flux through to the sections of higher permeability that bend the field lines. Your reply shows clearly that you know that, but this point must emphasized. The quantity of flux must be calculated otherwise it is not concluding:
The infinity of the space around a coil is not a sufficient reason to suppose that the most of magnetic flux would not take the ferrite path.

"The magnetic field is concentrated through the ferrite rod"

I’m aware that inside the coil, the cross section is the same either with air or with a magnetic material, and of course we cannot expect for the same effect outside of the coil even though an external magnetic material attracts the flux.
But I wonder why ferrite outside of a coil that is completely embedded in it, changes the resonant frequency by only 7% while we would be expecting for much more because of the ability of the high permeability material to “suck” the magnetic flux at the detriment of the flux in air. Although the change of the coil inductance is more than 7% because it is the resonant frequency square that is proportional to the inductance, it is not much and it is considerably much less than with the ferrite inside the coil.
The difference of the effect between ferrite inside and outside is not astonishing but the order of magnitude of the difference is. It puzzles me and motivates for further tests.
My first test has flaws:
-   There is a 2mm gap between the external circumference of the ferrite cylinder and  the outside coil
-   There is a 1mm gap between the internal circumference of the ferrite cylinder and the inside coil
-   The inside coil is thick with several  layers of turns, and so it has a not constant diameter, while the outside coil is thin

I will wound a wire directly outside and inside the ferrite cylinder, without gap, and see what will be going on.

Quote
But one important aspect relates to the formula Φ = BA = µNπr²i / ℓ where the total flux (Φ) is shown to increase if either the flux density (B) or the area (A) are increased as it is the product of the two. And since the flux density is dependent on the relative permeability of the interior core (µ) in the formula B = µNi / ℓ  we expect more flux when there is higher permeability in the core e.g. ferromagnetic core vs air. Alternatively, we could write it as B = Φ/A

So the middle of the solenoid is a finite area that we can use in our calculations. But once we leave that defined volume these formulas become difficult as A would represent the universe (or at least a measurable volume magnitudes larger than the solenoid center) and we are looking for a cross sectional area where the flux is normal to it.

Hope that helps  ;)

I agree with these formulae and the difficulty of real calculus for any area, anywhere, and with any permeability. This is the question  to be experimentally verified. The flux being supposed conservative, the same action upon a section of same flux should not depend on the location of the section that we deal with, whether it is inside or outside.


« Last Edit: 2012-03-06, 10:59:14 by exnihiloest »
   
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I see.

So really then, we are asking:

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?

Very interesting question indeed. Evidently, there must be a limit to how much can be forced inside regardless of what is happening outside.  O0

 8)
   
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