Paleomagnetism can be measured as the magnetic field at the time of rock forming is preserved in some minerals.
Could the paleomagnetism and the present magnetic field somehow influence the movements of tectonic plates?
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The electromagnetic force and related field is a strong force at very small distances (governs the way the proton and electron are held to an atom) but is relatively weak over large distances. I don't see how that small force could act on processes involved in the convection of the mantle. If memory serves, the iron in magmas preserves the force of the electromagnetic field on earth at the time the magma cools to form rock. It leaves its imprint but has no affect on the process or origin of magmatism much less the convection that drives plate tectonics