Got me thinking there. As far as I understand.. the field is zero at all points inside the conductor. I don't know if that means the field does not exist inside the conductor, or whether it does technically exist yet at some variant of null..
I'm still amazed that the EM field requires no medium to propagate.. took me years to find a way to visualise that it does just that.
Almost 25 years ago, I enjoyed this explanation I just searched again in order to submit this post, is still present on the web :
----> http://amasci.com/miscon/whatis.html
Am happy it is still available. There is many branches in the subject, abundant links within the tutorial, each one surprising. Explore those embedded links within the text and be prepared for an overdose !
Many misconceptions that teach things the wrong way since lesson one. And no institution reforms it to a scientific consensus.