Fukushima's Theorem

In physics, Fukushima's Theorem holds that for all points beneath the ionosphere the magnetic fields from field-aligned currents and their corresponding Pedersen currents exactly cancel. By superposition the total magnetic field at the ground is then equal to the magnetic field from just the ionospheric Hall currents.

Fukushima's Theorem holds in any planar or spherical geometry, provided that the field-aligned currents are perpendicular to the ground, and that the ionospheric conductance is spatially constant. Neither of these conditions holds strongly in the auroral region of the Earth's ionosphere.