Actually you don't need to split charges to have a movement of the fluid. To give you an idea, when you have a magnet and bring an iron thing next to it, it "forces" some items of the iron thing to become oriented in the same direction as the magnetic field. Then, it becomes itself a non-permanent magnet (it creates its own magnetic field; depending on the matter, the magnetic field will destroy the magnetic field inside of the thing or be oriented in the same direction). Both the magnet and the iron item remain (even locally) electrically neutral in this process.
Now in the center of the earth the situation is a bit different, since it is liquid. Electrons are free to move in the fluid (because Ni-Fe are not very careful of their outer electrons), but they remain anyway electrically neutral at any time (when an electron leaves his Iron atom, another one takes its place and so on). Thus we have a global mouvement of charges whithout need to split them.
This generates an electrical current that in return creates a magnetic field.
So am I right in thinking that the charge separation is the result of positive feedback, in that an intial deviation from neutrality would generate a field, and this would (somehow) cause a greater separation of charges, resulting in a kind of self-maintaining charge separation? Or is there another explanation?
The correct image would be that a small current creates a small magnetic field, which will have positive feedback on the movement of particles, and so on! But it's not so simple. Actually, that's an open question that interest both mathematicians and physicists (including myself ;) ), and the answer is not so simple to answer theoretically and most of the situations we can imagine lead to an exponentially decreasing magnetic field (but it's not what we observe in the earth, the sun and many other stellar object, so there exists other possibilities!).
Why is that not so simple? Because when an electron moves, it radiates some electromagnetic field, and part of it is "lost" (you can imagine that as the fact that some part of the electromagnetic field of the earth gets out of it, thus by conservation of energy the kernel loses some energy!). Thus we have positive feedback between the magnetic field and the mouvement of the fluid on the one hand, and "lost" due to radiations.
Now how did it begin? The kernel had initially his own mouvement, and we only needed a small pitch (which statistically happens for sure) to launch the full system gradually, and that's it, we're now in that!
If you want to know more on that subject, the keyword is Magnetohydrodynamics. The situation has been put in equations long ago, and there are some very good explanations (far better than my little blabla) on how it works on the internet.
To answer to Luboš Motl question
I would also like to know what is the natural variability in the magnitude of the magnetic field in 100 years etc. Is it common that it decreases by 10% in 150 years, like in the recent 150 years? –
It's even worse than that, actually we have "very often" a phenomena called geomagnetic reversal, that is that the north becomes south and south becomes north. Actually it didn't happen since we invented the compass, but we spotted this phenomena by the fact that some volcanic rock didn't have the same magnetic orientation (cf my first paragraph) when they formed along the ages. This phenomena is also very hard to predict theoretically, although we managed to see it in experiments in the last decade. Watch out, it may happen for real in the next centuries :)
(By the way, it happens faaar more often in the sun - about every ten years -, and this was already observed for long)
