Thread: Relative permeability of different magnets

1. Relative permeability of different magnets

Hi guys,

I'm trying to understand how the different polepiece materials can affect the coil inductance of a pickup, for example:

I have a singlecoil 43AWG, with ~6950 turns, 6.7K DC Resistance that has:

Inductance of 3.30H with low carbon steel polepieces
Inductance of 1.74H with magnetized Alnico V polepieces
Inductance of 1.40H without any polepiece (air coil)

So my questions are:
1) Is there a way to calculate how a polepiece material will affect the coil inductance starting from the air coil inductance? (In this example, what would be the coil inductance if we put Alnico II polepieces?)
2) Is this related to the relative permeability of the different materials?, if so, where can I find a table with the different relative permeabilities for each material?
3) Does anyone knows if the inductance of a coil can be calculated in FEMM (or any other FEM software) defining the coil dimesions + number of turns + defining the material properties of the coil core?

Thanks a lot!

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2. The calculation you would want to do is not simple. Higher permeability results in higher inductance, but only up to a point, using short cores and an "open" magnetic circuit as pickups do. Note that steel is a lot higher permeability than any Alnico, but the difference in inductance is only about a factor of two.

Measurement is the easiest thing to do. There are some things to watch out for. You need a meter that works well with low Q coils. Using a low frequency, say 120 Hz, gets you a measurement very close to the coil inductance unaffected by eddy current losses. Using 1 KHz will result in a measurement a bit lower when using steel cores because of these currents.

Originally Posted by alexirae
Hi guys,

I'm trying to understand how the different polepiece materials can affect the coil inductance of a pickup, for example:

I have a singlecoil 43AWG, with ~6950 turns, 6.7K DC Resistance that has:

Inductance of 3.30H with low carbon steel polepieces
Inductance of 1.74H with magnetized Alnico V polepieces
Inductance of 1.40H without any polepiece (air coil)

So my questions are:
1) Is there a way to calculate how a polepiece material will affect the coil inductance starting from the air coil inductance? (In this example, what would be the coil inductance if we put Alnico II polepieces?)
2) Is this related to the relative permeability of the different materials?, if so, where can I find a table with the different relative permeabilities for each material?
3) Does anyone knows if the inductance of a coil can be calculated in FEMM (or any other FEM software) defining the coil dimesions + number of turns + defining the material properties of the coil core?

Thanks a lot!

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3. Hi Mike, thanks for the reply.

Indeed, these numbers I posted are coming from inductance measures @120Hz of this pickup I described.

I understand that steel has a lot more permeability than Alnico but how much?, Do you know a good resource in internet or a book where we can see the relative permeability values for the different kind of materials (1018, 1022, Alnico 2, 3, 4, 5, etc.)?

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4. For a short table, look here: https://en.wikipedia.org/wiki/Permea...ctromagnetism). I would not worry too much about the exact permeability of different steels because they are high enough so that they all act nearly the same. The relevant value for the various grades of Alnico are harder to find. One place tp look is the materials library in the FEMM program, but these values might not be on the correct part of the hysteresis curve for this application. For example, read this note: Re: [femm] Alnico 8 relative permeability

Originally Posted by alexirae
Hi Mike, thanks for the reply.

Indeed, these numbers I posted are coming from inductance measures @120Hz of this pickup I described.

I understand that steel has a lot more permeability than Alnico but how much?, Do you know a good resource in internet or a book where we can see the relative permeability values for the different kind of materials (1018, 1022, Alnico 2, 3, 4, 5, etc.)?

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5. This might help. These are from my notes, taken from a few data sheets (I think it was Arnold Magnetics). Alnico composition varies greatly from one manufacturer to another, so these will likely not be accurate, but they should be a decent general guideline:

Alnico cast 9 1.3
Alnico sint 8 1.8
Alnico cast 8 2
Alnico sint 8hc 2.4
Alnico cast 8hc 2.8
Alnico cast 5 3.7
Alnico cast 3 5.1
Alnico cast 6 5.6
Alnico cast 2 6.2

(I didn't have sintered permeability data in my notes for some of the grades, but I would imagine that they follow the trend of being slightly lower than their cast counterparts.)

There is a list of test data here that plots permeability vs saturation for various metals that might be relevant:

Properties of soft magnetic materials

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6. Thanks AletheianAlex!

These values were the ones I was looking for, by coincidence and nearly at same time I found the datasheets you mentioned from Arnold Magnetics where you can see the recoil permeability values for cast and sintered Alnico:
- Arnold Magnetics: Cast Alnico Datasheet
- Arnold Magnetics: Sintered Alnico Datasheet

Since the Alnico permeability values are found, now I have new question:
- How you calculate the permeability of Low Carbon Steel (1010, 1018, 1022, etc.) knowing their B/H curve?

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7. Originally Posted by alexirae
Since the Alnico permeability values are found, now I have new question:
- How you calculate the permeability of Low Carbon Steel (1010, 1018, 1022, etc.) knowing their B/H curve?
Yup. Those were the data sheets!

The equations you want are in the link I posted above, but I don’t think that is what you need for 2 reasons:

1) steel does not have consistent magnetic characteristics from one brand to another since that is not a parameter that they control for (with the exception of specialty brands like Carpenter, etc) so you have to find test data (like in the link above), make educated guesses, use a program like FEM (as mentioned by Mr. Sulzer above), and test the materials in-circuit (i.e. build the pickup and test it under real world conditions).

(For example: I did this recently across 1010 steel and alnico 5 pole pieces from 4 different sources and found that the results varied pretty significantly — several hundred Hz difference in peak frequency)

2) BUT (and I think this is the point you were ultimately asking about) as Mr. Sulzer alluded to, we are building pickups, not iron-core inductors, so for what you want the math gets complicated since it is ‘permeability in-circuit’ and not an absolute value (i.e. permeability of a material OF a particular shape, and IN a particular coil, with other particular external factors). In other words: core permeability does not equal material permeability, not even close… it is usually substantially lower.

I can post some of the math if you want since you seem to be a tech-minded fellow (I don’t have them handy, but I can look them up in a few textbooks for you), but the non-mathy bottom line is that if we have a high enough MATERIAL permeability then the CORE permeability is mostly dominated by the shape of the core and operating conditions (flux density and externals/core-loss — like eddy currents, opposing fields, etc). You can confirm that yourself by making poles of different shapes with the same material and running resonant peak or LCR tests. Thats not to say that the material permeability doesn’t matter, it is just a smaller contributor when compared to geometry, saturation, and losses.

Hope that helps. I'll look up that math in case you want it.

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8. Yeap, I got what you pointed out and all that makes sense

What in reality I'm looking for (the root of the issue) is to understand why just simply switching from Alnico 5 to Steel polepieces change the inductance of the pickup almost twice! (The case I exposed in the first post). I think this affects a lot the final sound of the pickup since (from I read/learned) the more the inductance the more the resonant frequency gets shifted to the lower part of the frequency spectrum.

This is all about having some sort of estimate of what the final pickup inductance would be using different polepiece materials and assuming that we have some known values from the pickup you want to design (core width, height, depth, wire AWG gauge, number of turns).

And yes definitely, if you have some interesting math to look at regarding this subject please share it!, I think everyone here in this forum will benefit from that!

Thanks again for all the info!

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9. Originally Posted by alexirae
...What in reality I'm looking for (the root of the issue) is to understand why just simply switching from Alnico 5 to Steel polepieces change the inductance of the pickup almost twice! (The case I exposed in the first post). I think this affects a lot the final sound of the pickup since (from I read/learned) the more the inductance the more the resonant frequency gets shifted to the lower part of the frequency spectrum.

This is all about having some sort of estimate of what the final pickup inductance would be using different polepiece materials and assuming that we have some known values from the pickup you want to design (core width, height, depth, wire AWG gauge, number of turns).

And yes definitely, if you have some interesting math to look at regarding this subject please share it!, I think everyone here in this forum will benefit from that!

Thanks again for all the info!
Sure I can post some math. I’m sure some of the smarties here can probably give a more nuanced answer, but I’ll give you what I have.

Let me first say though, that I think you were barking up the right tree by just building and testing. The math will help you understand the trends, but testing will make the specifics more meaningful in terms of building. That aside though, just for the sake of knowledge: for core permeability you adjust for 2 major things: demagnetization factor with respect geometry, and level of magnetic core saturation (as well as smaller contributors like eddy current/hysteresis losses, frequency, and temperature, but we’ll ignore that for now).

1) Core permeability adjusted for demagnetizing factor
μc = μr / (1 + M * (μr - 1))

Where:
M = demagnetizing factor = (dc^2/lc^2)*(ln(2lc/Dc)-1)
μc = effective core permeability
μr = relative material permeability
dc = core diameter
lc = core length

Formula M is simplified for a reasonable range of aspect ratios that I grabbed from magnetic measurement handbook, so there are more complex version floating around that would handle more extreme aspect ratios and different pole shapes, but generally we are talking about ratios of 2:1 to 4:1 for pickup pole pieces, so we should be ‘close enough for jazz’. There is a ton of info out there on demagnetizing factor going back decades, so I’m sure you can find a formula that like better.

When I get the time, I’d like to make small program to calculate that, but I need more complete data that is backed up by testing, and I am up to my earballs in wire and magnets at the moment…

As far as the μr variable of mild steel grades goes, there is a decent amount of data online — which of course varies from brand to brand or even batch to batch - but here is a list that I had on my desktop which (like the alnico list) might give you a general idea (I took these from FEMM data if I recall):

grade / saturation density(Bsat) / H(μmax) / μr
1008 / 2.15T / 120 / 1400
1010 / 2.75T / 320 / 900
1018 / 2.45T / 800 / 550

Also remember that this is the permeability of the core, not the pickup: since you started the post by listing inductance measurements of the system (with air, steel, and alnico cores) I assume that you are interested in overall inductance, so you have to figure in the coil’s self-inductance to the system. That is easy enough, and there are a zillion coil inductance calculators online that you can use to estimate it once you have your core permeability and then adjust it to suit your particular coil and pole arrangement.

The relationship of the size and shape of the coil relates to the system as well. There are too many variables in pickup shape to get into, and I'm sure there is plenty of info on this board already, but it is worth remembering that it is possible to fall outside of what is useful in the case of a really shallow coil depth, or on the opposite end of the spectrum where piling on more wire is just increasing turns count, resistance and capacitance, which effects the tone, but falls outside of optimal range for efficiency. (I hesitate to mention it since I have only tested this in terms of single-pole coils, but you mentioned coil shape and size in your last post: the consensus seems to be that in terms of just efficiency for an iron-core system, the coil diameter should be about 2x the core diameter, and the coil length should be about 75 to 90% of the core length — which it tends to be in guitar pickups anyway).

2) Core permeability adjusted for magnetic saturation

Basically this is what I linked to in the last post. I don’t have any math around for calculating that for a particular geometry, so I have been using a combination of data found online, femm, and real world testing (basically starting with no magnets and adding more while plotting the points in a notebook until I find the linear region, knee, and saturation point).

Again, as Mr. Sulzer mentioned, these curves are included with FEMM, and you can even use it to print out curves, so that is very helpful. But we are basically running the pole pieces in the linear region, so we can guesstimate the percentage of core permeability that we are losing due to the magnetic field since the curves are fairly parallel until the knee, and then drop like a stone at saturation.

Another issue is that the pole material is more saturated in the area in contact with the magnet, and less saturated at the furthest point, so since that is not consistent. When I tried to find info on magnet manufacturer sites a while back, the consensus seemed to be “don’t calculate it: FEA simulate it, then test it”. I have partial info from holding magnet articles and speed/position sensor data, but not complete enough to bother posting here.

So maybe someone can jump in with a link to the math, but sometimes you just have to bust out the magnet wire and alligator clips…

(Those other factors that we ignored come into play as well… i.e. if you have a thick copper grounding plate under your pickup, you will effect the inductance and end up shifting your resonant peak upward, and that will be different for alnico vs steel poles, etc, etc)

Sorry that post went so long... I didn't intend that. And take this all with a grain of salt: I am not an engineer by trade, just a nerd by choice. Hopefully someone will jump in here with whatever I am missing or some better information on coil geometry (other than just the obvious increase in L R and C) since my interests are mainly in terms of efficiency.

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10. Originally Posted by AletheianAlex

1) Core permeability adjusted for demagnetizing factor
μc = μr / (1 + M * (μr - 1))

Where:
M = demagnetizing factor = (dc^2/lc^2)*(ln(2lc/Dc)-1)
μc = effective core permeability
μr = relative material permeability
dc = core diameter
lc = core length

Formula M is simplified for a reasonable range of aspect ratios that I grabbed from magnetic measurement handbook, so there are more complex version floating around that would handle more extreme aspect ratios and different pole shapes, but generally we are talking about ratios of 2:1 to 4:1 for pickup pole pieces, so we should be ‘close enough for jazz’. There is a ton of info out there on demagnetizing factor going back decades, so I’m sure you can find a formula that like better.
With pickup coils, I suspect that equation is valid for only much larger length to diameter ratios. I get much too large for 4:1.

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11. Oh, I’m sure. That equation is actually for an ellipsoid at smallish aspect ratios, so it has to be approximated for a cylinder. I thought I mentioned that before “simplified for a reasonable range”, but apparently I didn’t, so thanks for the catch. That math got ugly fast, so I didn’t post any of it. I tried to boil the adjustment down to general adjustment coefficient to get closer to reality, but that didn't work out.

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12. Originally Posted by alexirae
Hi guys,

I'm trying to understand how the different polepiece materials can affect the coil inductance of a pickup, for example:

I have a singlecoil 43AWG, with ~6950 turns, 6.7K DC Resistance that has:

Inductance of 3.30H with low carbon steel polepieces
Inductance of 1.74H with magnetized Alnico V polepieces
Inductance of 1.40H without any polepiece (air coil)

So my questions are:
1) Is there a way to calculate how a polepiece material will affect the coil inductance starting from the air coil inductance? (In this example, what would be the coil inductance if we put Alnico II polepieces?)
2) Is this related to the relative permeability of the different materials?, if so, where can I find a table with the different relative permeabilities for each material?
3) Does anyone knows if the inductance of a coil can be calculated in FEMM (or any other FEM software) defining the coil dimesions + number of turns + defining the material properties of the coil core?

Thanks a lot!
Some good info in this thread. In ball park terms anyway, the numbers quoted above are reasonable.

In a guitar pickup, the effect of permeability on inductance falls off as the permeability increases. You don't get anything close to a 1:1 increase of inductance with permeability because the pole piece is basically a short, open magnetic circuit with a massive air gap. The relationship approaches 1:1 at very low relative permeability (close to 1), but falls off rapidly as the permeability increases.

The other thing about most conventional pickups is that a lot of the core of the coil is still filled with air, even with the pole pieces installed, such that the effective permeability of the core is much less than the actual permeability of the pole piece material itself.

In my experience, AlNiCo 5 is the lowest, and 2 is the highest in terms of permeability, but I've only gotten the odd samples of the other alloys. I've worked with 2 and 5 far more than the others. 3 tends to be intermediate between 2 and 5.

Your numbers are not inconsistent with what I've seen. In a Zexcoil coil (which you can think of as a "mini rail") the pole piece fills most of the core. If you compare the coil inductance with the pole piece installed to the air coil inductance you get numbers like:

A5 = 1.4
A3 = 1.7
A2 = 2.8
Steel = 6.5

I measure A4 and A8 being pretty close to A3.

Whereas you see A5 = 1.2 and steel = 2.4.

So, you can say that the A5 permeability is at least 1.4. The stuff I was using I think had a permeability of about 1.8, based on my estimation.

I don't actually use AlNiCo in any of the commercial Zexcoils, but I get AlNiCo-like tones using other materials.

Also, there is no upper limit to when the absolute value of permeability matters in the tone and response of a pickup. It's true that it saturates, but it still matters.

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13. I might be able to make what Mike and Scott have said more intuitive. The inductance of a coil - or even a straight piece of wire - is related to both the electric circuit and the magnetic circuit. The electric circuit is easy to identify because it's composed almost entirely of tangible conductors like copper wire. The magnetic circuit includes iron pole pieces, alnico rods, and also a lot of air. Here's a random Google image:

The red arrows represent the electric current in the copper wire and the blue arrows represent the magnetic flux in the magnetic circuit. The total resistance around the electric circuit consists of all the individual resistances in series. The magnetic reluctance around the magnetic circuit consists of the reluctances of all the individual parts of the magnetic circuit in series. In the image above, the electric circuit is just a loop of wire, but we know that in general there might be any number of components and we just add all the individual resistances to get the total loop resistance. In the image above the entire magnetic circuit consists entirely of air, but we could put other things in there like iron slugs or alnico rods. The total reluctance would then be the sum of the reluctance through the iron or alnico in series with the reluctance of what ever part of the circuit remained air. We could completely replace all of the air with something with low reluctance (high permeability) if we wanted to, then we'd have an iron cored inductor.

If you didn't already know, reluctance is analogous to electrical resistance while magnetic permeability is analogous to electric conductivity. And, just as resistance = 1/conductance, reluctance = 1/permeability. Well, at least they're inversely proportional. You get the idea. Most of us are more comfortable thinking about resistance than conductance, so I'm looking at the magnetic circuit in terms of reluctance rather than permeability.

Anyway, consider an electric circuit with multiple components where one of those components has a large resistance. You can reduce the resistance of all the other components as much as you want, even make them zero, but the total resistance of the circuit will never be less than that one component with large resistance. Fixing everything else will get you only so far.

Likewise with the magnetic circuit. No matter what you put inside the coil, no matter how high the permeability, the total circuit will always be limited by the reluctance of all that air that the flux goes through on the rest of its trip around the circuit. The part of the circuit that we're replacing with iron is less than half of the total circuit. Even if we reduce that part to zero, we'll never reduce the circuit reluctance more than that. And so goes the self inductance...

I hope that makes some sense.

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14. Originally Posted by Tony Bones
The magnetic reluctance around the magnetic circuit consists of the reluctances of all the individual parts of the magnetic circuit in series.
When I look at that figure, I see an infinite number of magnetic circuit paths, each with its own reluctance, each driven by its own magnetomotive force (like voltage). I think they all must be connected in parallel, and the result is anything but intuitive or easy to understand.

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15. Originally Posted by Mike Sulzer
When I look at that figure, I see an infinite number of magnetic circuit paths, each with its own reluctance, each driven by its own magnetomotive force (like voltage). I think they all must be connected in parallel, and the result is anything but intuitive or easy to understand.
LOL Tell me about it! But the same is true of electrical conduction, isn't it? It's true that the electrons are confined to a wire, but there are an infinite number of paths through the wire. Somehow, we manage to lump them all together and it works out. The analogy works better with iron core inductors where there's a long path through high perm iron and then a short path through an air gap. The flux path is well defined and you don't have to make the air gap very big before its reluctance is bigger than that of the iron.

Anyway, I don't need to tell you that the analogy is deeply flawed, but it has helped me make some sense of things like this, so I thought I'd share.

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16. Yes, the circuit approximation to the more general problem is extremely accurate for the usual electrical circuits. As you said, it is also valid in its magnetic form for magnetic circuits involving high permeability material in most of the path and one or more regions of lower permeability, regions simple in form such as small air gaps. No problem there. The circuit approximation is not at all valid for the short open cores of a pickup, for example. It is a very approximate concept only, and if used to make deductions about how pickups work, it leads to errors in some cases. That is the problem: not having a simple intuitive concept, but rather knowing when not to use it. The reluctance concept is a valuable simplifying tool, but knowing when not to use it requires a greater understanding. Therefore it alone is not a good stepping stone to better understanding.

Originally Posted by Tony Bones
LOL Tell me about it! But the same is true of electrical conduction, isn't it? It's true that the electrons are confined to a wire, but there are an infinite number of paths through the wire. Somehow, we manage to lump them all together and it works out. The analogy works better with iron core inductors where there's a long path through high perm iron and then a short path through an air gap. The flux path is well defined and you don't have to make the air gap very big before its reluctance is bigger than that of the iron.

Anyway, I don't need to tell you that the analogy is deeply flawed, but it has helped me make some sense of things like this, so I thought I'd share.

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17. Originally Posted by Mike Sulzer
Yes, the circuit approximation to the more general problem is extremely accurate for the usual electrical circuits. As you said, it is also valid in its magnetic form for magnetic circuits involving high permeability material in most of the path and one or more regions of lower permeability, regions simple in form such as small air gaps. No problem there. The circuit approximation is not at all valid for the short open cores of a pickup, for example. It is a very approximate concept only, and if used to make deductions about how pickups work, it leads to errors in some cases. That is the problem: not having a simple intuitive concept, but rather knowing when not to use it. The reluctance concept is a valuable simplifying tool, but knowing when not to use it requires a greater understanding. Therefore it alone is not a good stepping stone to better understanding.
So it doesn't help anyone understand why high perm pole pieces will increase the inductance only so much? Bummer.

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18. Originally Posted by Tony Bones
So it doesn't help anyone understand why high perm pole pieces will increase the inductance only so much? Bummer.
Oh it does; it just helps most those who already understand more. That is why I think for both pickups and inductors in general it is best to emphasize the law of magnetic induction first, and only then, the details of the magnetic field when a permeable material is used in the core.

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19. Originally Posted by Tony Bones
So it doesn't help anyone understand why high perm pole pieces will increase the inductance only so much? Bummer.
I did find the analogy helpful. The diagram not so much.

But since you noted that the image was randomly pulled from the web, I gave it little credence. It seems to depict the magnetic field produced by a single current-carrying loop (driven by an internal Escher battery?) rather than the voltage induced in a coil by a changing magnetic field.

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20. I can see where that would be confusing. My real desire for the image was that it make clear that there is both an electric circuit and a close magnetic circuit. Those flux lines are all closed loops. I know some of them appear to go off somewhere, but really they just make bigger loops and come back around. They have to; there are no magnetic monopoles.

Ultimately, all of this comes around to the question of the inductance of a pickup. Inductance is essentially the flux in the magnetic circuit reacting and "pushing back" when a changing current is driven through the coil (back emf.) The degree to which the magnetic flux can produce back emf depends on the reluctance around the magnetic circuit. You can make the reluctance very low by putting the coil inside an iron core. Then the entire magnetic circuit (or enough of it) is travelling through hi perm (low reluctance) material and the inductance will be very high.

Here's another image pulled from the cloud. It suggests a humbucker, but you can imagine removing one of the coils...

You can reduce the reluctance a little by replacing just the part inside the coil with iron or alnico, but the total reluctance remains dominated by the rest of the circuit which is through air.

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21. Originally Posted by Tony Bones
Here's another image pulled from the cloud. It suggests a humbucker...

You can reduce the reluctance a little by replacing just the part inside the coil with iron or alnico, but the total reluctance remains dominated by the rest of the circuit which is through air.
The transformer image suggests a humbucker, if you chop off the top of the core and replace it with a floating ferrous string. Then some of the magnetic circuit travels thru just air, while some travels thru air to string to air. At any rate, the total "series reluctance" remains dominated by the high thru-air reluctance. I think that's more-or-less what you're saying.

I think the "problem" here is that stock images just don't depict the magnetic circuit configurations unique to guitar pickups.

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22. Originally Posted by rjb
The transformer image suggests a humbucker, if you chop off the top of the core and replace it with a floating ferrous string. Then some of the magnetic circuit travels thru just air, while some travels thru air to string to air. At any rate, the total "series reluctance" remains dominated by the high thru-air reluctance. I think that's more-or-less what you're saying.

I think the "problem" here is that stock images just don't depict the magnetic circuit configurations unique to guitar pickups.
I think the image does an adequate job showing the iron core that would be necessary to significantly increase inductance. If I cut the top off then it wouldn't show that any more.

In any case, understanding what is unique about guitar pickups requires understanding the more general case, doesn't it? a side effect of travelling and learning about other cultures is that we end up with a deeper understanding of our own.

Perhaps the only thing we've learned is that inductance measurements of guitar pickups are of limited value.

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23. Originally Posted by Tony Bones
I think the image does an adequate job showing the iron core that would be necessary to significantly increase inductance. If I cut the top off then it wouldn't show that any more.
OK, I've re-read your previous post and think I see what you're driving at.
If you were to remove one of the coils from the transformer image, that configuration would have higher inductance than a coil around a cylindrical iron core. I concur. Let's quit while we're ahead.

V(t)=L di/dt,
-rb

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