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Consider the question:

A solid metal sphere of radius a, carrying a charge of +q, is placed inside and concentric with a neutral hollow metal sphere of inner radius b and outer radius c. Determine the electric field for $r<a, a<r<b, b<r<c, r>c$. Also describe the charge distributions. Diagram to illustrate: Image

Now, the solution goes as follows:-

For $r<a$-the electric field is 0 because no field can exist within a conductor.

For $a<r<b$-the inner sphere acts as a point charge so by gauss's law:-E=q/4πε0 r^2

For $b<r<c$-The E is 0 as no E can exist within the body of a conductor

For $r>c$:-The E acts as if the charge is at a point at center:-so E=q/4πε0 r^2

Now, I only agree with the last one($r>c$). I disagree with the others because I have read that the E within a conductor is 0 and and The sphere with radius c is a conductor, so that should mean that E=0 for $r<a,a<r<b, b<r<c$. The charge distribution should be something like:-

enter image description here

This would give E=0 at all points. But the solution just gives -q at radius b and +q at radius c.

This question is really puzzling me and any help in clarifying this doubt will be greatly appreciated.

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closed as off-topic by G. Smith, John Rennie, GiorgioP, Yashas, ZeroTheHero May 12 at 19:54

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    $\begingroup$ “Within a conductor” means “in the material of a conductor”. The solution is correct. If the field were zero between the spheres, Gauss’ Law would be violated. $\endgroup$ – G. Smith May 10 at 6:02
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I disagree with the others because I have read that the E within a conductor is 0

You may have misunderstood what you read. By "within a conductor," we mean inside the body of the conductor. If there are hollow regions within the conductor, then there is no reason that the electric field should be zero in those regions, and in general (as you can see) it is not.

A note on your drawing - I can't quite read what you wrote there, but charges are not permitted to "migrate" from one conductor to another if they are separated by an insulating material like vacuum or air.

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