I believe, Earth could be approximated by a molten, metallic, non-magnetic sphere, with a molten stony sphere around it. However,
- As far I know, the magnetic properties of the lava in the crust, in its temperature and pressure, is not very well known.
- The case is the same, for a greater extent, to the core. As far I know, the core is mostly a mix of different elements, with a large part of iron, so the amount and ratio of the non-ironic part might affect significantly the permeability.
I believe, getting the answer to this question could be better answered experimentally. However, in its naive form (getting a current around the equator) it seems unfeasible.
Corresponding this, I found nothing by google. Maybe lesser direct measurements are possible (like the interaction of the Earth's magnetic field to some external one?)
Is it known? How was it calculated?