Maxwell's equations & Conductors

If there is an E field in a region with mobile charge carriers then there will be a current. So after all currents have died away, either the E field must be cancelled or the medium will have run out of charge carriers. Does that help?

 

http://en.wikipedia.org/wiki/Faraday_cage

marlon

 

Zero E field is an idealization that holds for perfect conductivity where exactly enough charges can move to the surface to screen out an ambient field. This is actually seen in superconductors, although related phenomena like the Meissner effect require quantum mechanics to explain. For ordinary metals of finite conductivity, a small DC field can exist inside according to Ohm's Law
[tex]\vec{J}=\sigma\vec{E}[/tex]

Time varying fields, on the other hand, are screened by circulating eddy currents, and penetrate a small distance characterized by the skin depth. This is covered under discussions of wave propagation in conducting media, in upper class E&M books like Schwartz or Reitz and Milford. Here's a link that contains the derivations in sections 6.19-6.20
"www.sp.phy.cam.ac.uk/teaching/em/waves.pdf"[/URL]

 

If you mean inside a void in a conductor - sure, E can be non-zero in there.

 

I would call 'inside the conductor' inside of the conducting shell.

 

The solid region - where the mobile charges are.

 

Yes, it would always be zero. Just keep in mind that this, like much of classical physics, is an idealization.