Why charge induce inside doesnt depend on what the outer potential is, in a conductor? Let's suppose we have a conducting shell which has an outer radius $R$ and inner radius $r$. A charge is kept inside (not at the centre). We know that a charge will be induced in both surfaces. But suppose we ground the outer shell, then why would the charge distribution induced inside remain the same as if not earthed?
 A: In the absence of a power source, there can be no electric field inside the material of a conductor.  Any such field would move fee electrons around until there was no more field. Any charge inside a cavity in a conductor will induce an equal but opposite charge on the inner surface of the conductor. That is required by Gauss's law. The distribution of charge on the inner surface will be such that the resultant field in the conductor will be zero.  If the conductor was neutral and isolated, that leaves an equal and opposite charge in the conductor, which repels itself to the outer surface. If the conductor is grounded, that charge continues on to the ground.  In any case, the field within the conductor remains at zero, and since no two points in or on a surface of the conductor are connected by a field line, the entire conductor must be at the same potential.
A: Its most probably due to the electrostatic shielding which says the what happens inside the shell will not get affected by outside , though i dont have a proof of this fact.
