This sounds like the sort of thing that is used to charge electric toothbrushes, although they typically use concentric coils for maximum transfer - I think they still don't transfer much current. I suppose if you could get produce a field of magnets with adjacent magnets having opposite polarity and with each magnet alternating, you'd get a continually changing field which would induce a current into any coil in the area. No idea how effective it would be, but I wonder what that would do to the electrics and electronics of the Arduino itself?