Axisymmetric solid of revolution derivable from section at FIG. 5 is generally toroidal with electric current(s) in windings 110, 160 preferably flowing circumferentially along major circle(s) during power coupling device operation. Current(s) in windings 110, 160; current(s) in half-shields 120, 170; and the volume of space swept out by shield airgap(s) 101 emerge from plane of paper perpendicularly at FIG. 5 but as these emerge therefrom they curve to follow toroidal major circle(s). Cores 115, 165 preferably shunt and align magnetic flux such that magnetic field lines escape therefrom primarily only in region(s) of core airgap(s) and such that magnetic flux loops lie in planes of toroidal minor circle(s). Half-shield(s) 120, 170 preferably have electrically conductive material(s) distributed therein as is sufficient to substantially cancel magnetic flux lines impinging thereon before effects of such impinging magnetic flux lines would reach shield airgap(s) 101 and/or outer surface(s) of half-shields 120, 170.