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,
--The problem with my last post's idea, that the solar wind was this "nonlinear effect", is: Suppose the Earth were just a boring permanent bar magnet (no radioactivity, liquid flow, or anything complicated). Then the same effects on the solar wind would happen, but this Earth's field is not being generated by any kind of power expenditure, so something is silly re the idea this is a power loss & etc. Despite the numerical coincidence that this "loss" and "heat input" were close. Revert to the more-boring idea that the Joule heat from electrical resistance, is emitted in a different place (anyhow different distribution) than the radioactive heat. For example, the solid inner core, presumably has 2 or more times less electrical resistivity than the molten-metal outer core, and has no fluid convection to induce voltages, hence would be expected to be warmed much less by I*I*R ohmic heating, than the liquid outer core. So the dynamo's joule heat is emitted higher up than the radioactive input-heat, so the whole kaboodle serves as another heat-transfer mechanism. Another reason this should be true is increasing pressure decreases resistivity R, so more R at higher altitudes, so more I*I*R joule heating happens there if electrical current densities do not depend much on location. If we crudely approximate the heat-output and heat-input as being in totally disjoint locations, then it is impossible for the I*I*R ohm-joule-heat power to exceed the total radioactive heat input. This sets an upper limit on the Earth's magnetic field. What is that upper bound? And is is relevant? The current I required to generate the observed Earth magnetic dipole moment of 8*10^22 amp*meter^2 is (assuming it flows equatorially at radius=3000 km) is I=2.8*10^9 amps. The resistivity of the molten metal is thought to be about 0.7*10^(-6) ohm-meters. Suggesting R ought to be about 2*10^(-13) ohms. Thus the present joule heat ought to be about I*I*R = 1.6 megawatts. Which is tiny compared to the many terawatt heat source. So, either this effect is irrelevant, or the fluid flow is complicated and turbulent and the electrical current is complicated too, but time-averages to a simple ring current while the fluid flow time-averages to a simple "rise to poles sink at equator" flow. With this postulate, the true complicated current is much larger and yields much greater joule heating. With this explanation, if we postulated that the true fluctuating current densities are perhaps 3000 times larger than the time-averaged current, then the upper bound would yield about the actual magnetic field. Bah. Fluid turbulence. Uncalculatable crud.