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:
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:-
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.