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If I have a spherical conductor (perhaps a shell) and "inside", as in the hollow area there is nothing. The electric field is 0. But what happens if there is a charge "inside" (not like inside the conductor, but in the hollow region) or some type of insulator with a nonzero net charge? Would there exist a field?

I drew a picture to illustrate. Not to scale by the wayenter image description here

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"Inside a conductor" usually is taken to mean literally within the medium of the conductor - in the metal. The example @jak is using would normally be phrased as "in a pocket..." or "in a bubble..." or "in a cavity within the conductor". –  Colin Fredericks Jul 2 '12 at 20:01

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For a static situation (i.e. no charges moving or current flowing) the net electric field is always zero inside of a conductor. Where by 'inside' I mean actually inside the material itself, not a region of free space that is simply enclosed by the material. The reason for this is, say there is an electric field $\vec{E}_0$, applied to the conductor- by definition there is an essentially infinite well of free charge that can move. This charge will move in response to the applied electric field and set up its own induced field, $\vec{E}_{ind}$. This field will oppose the orignal field and charge will keeping moving until it reaches equilibrium such that $\vec{E}_0+\vec{E}_{ind}= \vec{E}_{net} = 0 $. In practice this happens almost instantaneously. Above I haven't mentioned anything about shapes or charges outside the conductor so this holds for all static electric field configurations, including the one you describe above.

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So the blue text region will have no electric field because we are still "inside" a conductor? –  sidht Jul 2 '12 at 19:47
    
@jak - I edited to answer your question, let me know if you are still confused. –  DJBunk Jul 2 '12 at 19:52
    
yeah that's what I thought by "inside" –  sidht Jul 2 '12 at 19:56
    
@jak, if there is a charge in the blue text region of your diagram, then there will be a non-zero electric field in that region. However the field inside the conducting shell will still be zero. See section 2.5.2 of Griffiths - Figure 2.45 is exactly what you ask for. –  Vijay Murthy Jul 2 '12 at 20:31
    
@DJBunk: You don't metion Gauss's Law in the answer to the op. Its true that the existence of free charge is important, but the demostration that the electric field is zero inside conductors is based on Gauss's Law. This is taught in Calculus based physics and on every major text on EM theory! –  Ernesto Ulloa Jul 4 '12 at 15:18

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