Pam, thank you. Your answer may explain why the transformers are made of laminated iron cores. I just assumed the lamination was to reduce eddy currents but I guess it also is a way to get around skin effect of single core to carry more flux. One more thing, within the skin depth, the time...
I understand that according to Maxwell's equations time-varying EM fields cannot exist in a perfect conductor (but static magnetic fields can). Also if you have a time-varying magnetic field you also have time-varying electric field and vice versa. And this knowledge is used to solve EM wave...