electrostatic shielding When we have an uncharged conductor with a cavity and apply an external electric field, the charges rearrange to keep the electric field inside the metal zero. The driving force is the need to keep electric field inside the metallic layer, zero. Then why is the field inside the cavity also zero? I think this is because the charges would arrange in the same way as in the case of a cavity free conductor but why can't they arrange in a different way?
Why is this arrangement not possible which clearly has a field inside the cavity but not inside the metal?
 A: The cavity has no field inside because the metal boundary enclosing it is an equipotential. And the solution of Laplace equation for the potential inside is a constant corresponding to this potential due to the boundary condition. Therefore there is no electric field inside.  
A: If there is an electric field inside the conducting shell then there must be electric charges on the inner surface of the conducting shell because electric field lines start on positive charges and finish on negative charges.
Start near one of the negative charges on the inside surface of the conducting shell and walk along an electric field line carrying a positive charge until you reach a region near a positive charge on the inside surface of the conducting shell.
The region near the positive charge is at the same potential as the inside surface of the conducting shell near where the negative charge resided because the metallic shell is an equipotential volume.
But you must have done work to move the positive change along the electric field line and hence moved from a region of low potential to a region of higher potential which contradicts the statement that the conductor is an equipotential volume.  
Thus there can be no electric field inside the inside surface of the conducting shell.
A: There must not be any electric field within a conductor. This is why the (blue) charges will arrange against the external (red) field. Those blue charges generate an electric field on their own, the blue field. The strength of the blue field is exactly such that it cancels the red one. Until that is the case, the unmatched part of the red field will move electrons within the conductor.
Because the field cancels in the inside, there is no shifting of charges (polarization) and no surface charge in the cavity.

