[amelius]

Question: assume you have a closed hull around some domain D, and record the electric and magnetic fields E and H at the entire hull; at a later moment you prescribe E and H at the hull; will this setup regenerate the original values of E and H inside the domain D?

[ckemere]

To maybe short-circuit your idea, magneto-encephalography (MEG) uses magnetic field sensors to sense brain activity. Coherent currents from ~100K neurons produce femto-tesla signals (about 1 billionth of the earth's magnetic field). This currently requires liquid helium cooled superconductors (though there is some work trying on nanofabricated room-temperature ultraprecise field sensors). To induce effects, the TMS magnets produce reasonable fractions of a Tesla.