Well, if you have seen Ohm's Law in form j=(sigma) E, where sigma is conductivity, try setting it infinite (for an ideal inductor). You will see that for finite j, E=0. Why doesn't j go to infinity? Well, j is proportional to drift velocity. That can't really go to infinity now, can it? There's a theoretical to limit even if you get into deep waters of real superconductors. You may think it may become still fairly large because lower resistance actually should strike as less number of collisions. It turns out that even then the velocities are much smaller than c.


Answer by Manish K. as a reply to a comment on https://www.youtube.com/watch?v=PMTOVRyPLOI