Whaddya get when....

[Antigua]

I can't think of a reason why the magnet's permeability should have a significant influence on the spatial distribution of the static magnetic flux. After all the magnet is the source of all flux. Any flux the magnet injects into the screws must re-enter the magnet via its other/outer pole. And according to physics the flux always takes the shortest or most attractive return path.
The signal AC flux is just a modulation of the static flux and can't take a path completely different from the static flux.
So with a single magnet a P-90 will have an asymmetrical aperture, sensing the string only at the side where the magnet is.

The screws form a low reluctance path between the strings and the coil. The reason the reluctance path is low is both because of proximity and permeability. The AlNiCo bar on the other hand, is neither close to the strings, nor especially permeable, and so the reluctance, or resistance, between the string and magnet is high.

One demonstration of this in action is that the voltage output of a Strat pickup with steel pole pieces and a ceramic magnet underneath is higher than the voltage output of an AlNiCo single coil, because even though the flux density of the AlNiCo pole pieces are a lot higher than that of the steel/ceramic single coil, the steel pole pieces generate a much lower reluctance path between the string and the coil, and that pays off in the form of increased voltage output. A P-90 is structurally similar to the steel/ceramic pickup which benefits from the spacial relation between the strings, steel pole pieces and coil. It's worth further testing, though. I might try out the experiment I described above.

[Helmholtz]

The screws form a low reluctance path between the strings and the coil. The reason the reluctance path is low is both because of proximity and permeability. The AlNiCo bar on the other hand, is neither close to the strings, nor especially permeable, and so the reluctance, or resistance, between the string and magnet is high.

Sorry, I don't seem to get your point.
Maybe you are overlooking that all of a magnet's flux flows from its north pole to its south pole, preferably taking the path of least total reluctance.
And that includes the return path from the strings to the other pole of the magnet.

[Antigua]

Sorry, I don't seem to get your point.
Maybe you are overlooking that all of a magnet's flux flows from its north pole to its south pole, preferably taking the path of least total reluctance.
And that includes the return path from the strings to the other pole of the magnet.

Lines of flux also return from the string to the bottom of the screws, though, and it will to a greater degree, because the screws are of a higher permeability than the AlNiCo. The AlNiCo is a permanent magnet, but it's also a path of higher reluctance.

[Helmholtz]

Lines of flux also return from the string to the bottom of the screws, though, and it will to a greater degree, because the screws are of a higher permeability than the AlNiCo.

Sorry, no.
Static flux must always return to the opposite pole of the magnet, just like an electrical current always returns to the opposite pole of its source.

[Antigua]

Sorry, no.
Static flux must always return to the opposite pole of the magnet, just like an electrical current always returns to the opposite pole of its source.

A voltage across the coil is not created by static flux though, it's generated by changing flux, and there is a greater degree of change in the permeable core than their is air or AlNiCo. That's why the inductance increases so much when steel is introduced to the core, and why it changes so little when AlNiCo is removed from underneath.

[max oersted]

I should probably explain why I asked the question in the first place. A friend has an Epiphone Casino. He wants to remove the neck pickup and try using a Telecaster neck pickup in its place, with an adaptor that employs the same screw holes as the P90 cover. I said "Well why don't you just pull one of the magnets on the neck pickup?", thinking that it would yield the thinner sound he is thinking of trying.

Mark, since this thread is about to devolve into a state that doesn't address your question directly or serve you or your friend/customers issue at all, allow me to provide some further insight. Respectfully to all, as one who does "this" for a living, albeit a humble one- some ideas that might help:

First, depending on what year that Epi Casino was made it could have one of 3 different styles of those Dogear P90s stock from the factory. There's a vintage output version that uses 42AWG, a more modern take on that pickup style that uses 43AWG, and also..while I've not come across these personally on my bench for rewinds or repairs, apparently there are some that are over-wound mudmachines with 43AWG or 44 as well. All use Alnico 5. All use brass frames except for perhaps the newest models. Pulling a magnet will clean things up a bit for sure. To take it a step further under the circumstances I might suggest pulling the A5 magnets and swapping to Alnico 4. One A4 magnet at full charge will impart plenty of energy to the screw poles and will also bring a flatter, more linear frequency response across the board thats not so dissimilar to a Tele neck pickup. Obviously a Tele neck and a P90 are two completely different machines but this will most definitely push the pickup closer.

Another inexpensive tweak would be to swap the pole screws for some with a higher carbon content. This will brighten things up as well.

[Mike Sulzer]

I have not done this experiment in a while, but think the output of the pickup decreases significantly as the screws are turned clockwise, lowering them. This shows that the sensing area over the screws is most important.

Why? First consider a simple model of string magnetization. In this model, the magnetized string consists of two long thin uniformly magnetized cylinders, oppositely directed, with the boundary between the two over the screw. There is a strong vertically directed B field only over the area right above the screws. In this place the horizontal components cancel because the two cylinders are oppositely directed, but the vertical fields add. Remember it is the time changing vertical component (that is, through the coil along its axis) that is sensed.

What does the rest of the cylinders contribute? Well, nothing with this model, except for the other end, which is far away and outside of the coil. This is because a correct model of a uniformly magnetized cylinder is opposite magnetic charges (which do not actually exist, but which make a valid model) on the ends of the cylinder. This is because the fields of the tiny dipoles within the cylinders cancel each other out, and only the ends contribute.

As you correctly point out, actually flux is escaping from the string along its length; that is, the magnetization is not uniform along the length of the cylinder as the simple model assumes, but is decreasing gradually. This means that a fraction of it does contribute a component directed through the coil. But how much does it contribute?

Consider again the vertically directed component through the coil coming from right over the screws. The high permeability screw is magnetized by this (vibrating) field and thus this flux is effectively amplified. The weaker field from somewhere along the string is even weaker at the screws because to the 1/(r^3) fall off, and so little is contributed that way. However, this flux still passes directly through the coil, but it is small to start with and receives no amplification from the screw.

Therefore, I think it is correct to think of this as primary and secondary windows. The primary is directly over the screw. It is strong. The secondary is flux resulting from the rest of the string over the coil. It is weak.

A PU's aperture (string sensing length) is essentially the magnetized section/length of the string above the PU. With 2 magnets the aperture will be symmetrical with reference to the screws, with only one magnet it will be single sided.

[Helmholtz]

This discussion seems to be drifting out of focus.

My statement above was that a P-90 with only one magnet should have its aperture shifted to the side of the magnet (probably only a few mm). Reasoning:

The aperture measurements performed by Prof. Zollner show that typical single coil PUs have a single, gaussian shaped aperture with an effective width of around 10mm, essentially independent of size and construction. The aperture of a standard P-90 was only around 25% (or less than 3mm) wider than that of a Strat PU.

In a separate experiment Zollner measured the longitudinal component of the static flux density in a string above the PU. The effective length of the magnetized string section corresponded well with the width of the aperture.

From this it seems reasonable to assume that the aperture mainly depends on the static field distribution in the vicinity of the string above the PU.

As removing one magnet from a P-90 will leave the PU with an asymmetrical field distribution leaning towards the side with the magnet, it can be assumed that also the aperture becomes asymmetrical wrt the center of the screws.

Correction: I re-read the chapter in Zollner's book and found that I had misinterpreted one of his curves. Actually "magnetized string length" is not a useful concept. And Zollner only measured longitudinal flux, while it's actually radial flux which matters for aperture.

[Helmholtz]

Therefore, I think it is correct to think of this as primary and secondary windows. The primary is directly over the screw. It is strong. The secondary is flux resulting from the rest of the string over the coil. It is weak-

Thanks for explaining the terms. Zollner also mentions an ancillary aperture caused by the lower lower magnet pole. But it couldn't be identified in his direct aperture measurements. So I assume it to be rather insignificant.