Q:

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.  

