Another problem: What sets the magnetic field value? If there is a fixed velocity field, then induced voltage V is proportional to magnetic field, which via Ohm's law and the law of inductance, means we should approach a current I set by V=I*R where R=resistance, which in turn generates the magnetic field. These equations are linear, so if multiply input magnetic field by X... we multiply output magnetic field by X. There is nothing to set any particular level. And if the output exceeds the input, we would get growth, and what would stop that growth? So something else needs to be put into this picture, some nonlinear effect, which stops the growth and holds the magnetic field at some level. The answer to that is presumably that the input heat-power from radioactive decay, must exceed the Joule power loss I*I*R. But this Joule heat "loss" actually just generates heat which further powers the convection which powers the whole dynamo, so it isn't "loss." So then you realize that the Joule heat is differently distributed than the radioactive heat. So really, this whole thing is a heat-transfer mechanism which allows heat to move out of the Earth's core at a greater rate than convection and conduction alone, sans dynamo, could have done. Plus there is additional "loss" beyond Joule, for example the Earth's magnetic field diverts the solar wind, which effect (exercising your hand to perform "right hand rule" again...) is to diminish the Earth's field and transfer earth-core heat into the solar-wind plasma. This solar-wind loss mechanism must be nonlinear in the magnetic field because there is a volume, the "magnetosphere" which grows the stringer the field is, and outside that volume the Earth;s field is basically canceled out by solar wind effects. The loss is proportional to the field strength times the magnetosphere volume (or surface); and this is clearly growing like a power >1 of the magnetic field. So, CONCLUSION: there is at least one nonlinear loss mechanism preventing huge field growth and which causes the correct qualitative behavior -- self-amplification of small fields, but imposing a ceiling on field strength. So now let us do a numerical estimation to hopefully verify all this. We will compute (a) the earth's heat-generation rate, and compare it with (b) the power loss/transfer from the earth field into the solar wind plasma. (a): wikipedia says Earth internal heat generation rate is 44 to 47 terawatts, although perhaps only 10-20 comes from the core. So say 10^13 watts. (b): view the magnetosphere as bending the solar wind an angle of order 90 degrees. Solar wind properties at 1 AU: speed: 200 to 900 km/sec proton particle energies: 0.2 to 4.2 keV (consequently) proton particle densities: 0.2 to 50 per cm^3 (plus same for electrons) current density of protons (consequently): 6.4*10^(-9) to 3.3*10^(-5) amp/meter^2 The effect then is essentially that the earth is a battery generating order 200-4200 volts at a current of order C*J where J=0.1 nanoamps to 33 microamps/meter^2 is the proton wind proton current (also electron current is same) and C is the cross-sectional area of the Earth magnetosphere which is about pi*r^2 where r=15 to 30 earthradii. proportional to the solar wind. So the current is about 1.8*10^8 to 3.9*10^12 amps. So V*I=power loss to solar wind, is about 3.7*10^11 to 7.7*10^15 watts. This answer (b) is a factor-20000 wide interval (sorry about the crudity) but it does enclose the answer (a) right in the middle (on a log scale), so our picture is not refuted. If this is correct and is really the main thing placing a ceiling on the Earth's magnetic field, then this would predict that if the solar wind were magically turned off, the Earth's field would grow quite a lot larger. And as far as I know from rumors, solar wind variations do indeed cause substantial fluctuations in the Earth's field, suggesting this is indeed the main loss/ceiling-causing mechanism. So back of envelope estimates and simple thinking appear to be successfully getting us quite far.