Relative permeability of different magnets

[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.

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.

[Tony Bones]

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.

[Mike Sulzer]

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.

[rjb]

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.

[Tony Bones]

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.

[rjb]

Here's another image pulled from the cloud. It suggests a humbucker...

[ATTACH=CONFIG]36583[/ATTACH]

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.

[Tony Bones]

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.

[rjb]

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