Yes a magnetic field comes from kinks in the electric field. Watch Walter Lewin on Academic Earth he explains this quite well.
Meanwhile the electric induction from a time varying current is in my understanding due to bending of electric field lines due to acceleration similar to the effect from moving a hose side to side as water comes out, the induction created by such agrees with the expected induction along a wire. Tracks at: http://www.ias-spes.org/SPSISW2013/PDFs/SPSIS_Tracks.pdf Subject Areas at: http://www.ias-spes.org/SPSISW2013/PDFs/SPSIS_Subject_Areas.pdf
