Analysis of the distribution of currents induced by a changing magnetic field in a volume conductor

Magnetic stimulation of the central or peripheral nervous system is being increasingly used in the clinical evaluation of nervous system lesions. The stimulation is produced by currents induced within the tissue by a changing magnetic field resulting from a current discharged through an externally placed coil. In previous work to elucidate the distribution of such induced current, a computer model produced the surprising result that a coil oriented with its plane perpendicular to the surface of a volume conductor with a plane surface produces no component of current perpendicular to the surface anywhere within the conductor. Experimental measurements of the electric field in a volume of saline confirmed this result. The author provides further confirmation by deriving a theoretical proof for the absence of induced current perpendicular to the surface within a volume conductor having an infinite plane surface, and extends the result to a conductor with a spherical surface.