Imagine you have hollow concentric spheres A and B with radius a and b (b>a), respectively. If A is a conductor and B has a certain density charge, I´ve been taught that B will induce some net charge over A (appart from what it could have yet). But, if, according to Gauss law, the contribution to electric field inside sphere B from its surface charge distribution is zero, How can this interaccion ocurr? How can be any charge displacement inside B?
I assume that A is neutral to begin with. Then inside of A cannot be any charge by Gauss law. This means that the inside of A must neutral.
Then you can take the volume between B and A. The boundary of that are the metal spheres A and B. On the whole boundary surface, there cannot be any electric field as that surface lies inside the metal. If there was any electric field, the electrons would move to counteract it. Therefore there is no total charge between the two spheres. There could be charge on the inside of B and outside of A. The two spheres form a spherical capacitor.