FIRST UNDERSTAND WHY FIELD INSIDE CONDUCTORS IS ALWAYS ZERO.

CONDUCTORS BY DEFINITION CAN CARRY CHARGE THROUGH THEM. tHEY ARE HAVING FREE ELECTRONS IN ABUDANCE. THUS CHARGE SETS A CURRENT INSIDE THE CONDUCTOR AND WITHIN A SHORT TRANSITION TIME ALL THE CHARGE GO TO SURFACE, YOU CAN SAY BY REPULSION. SO WHEN THERE IS NO CHARGE INSIDE, THE FIELD IS ZERO. TAKE A GUASSIAN SURFACE JUST BELOW THE SURFACE OF YR CONDUCTOR, NO CHARGE INSIDE SO FIELD IS ZERO AS PER GAUSS LAW ALSO.

NOW WHEN CHARGE IS INSIDE ACAVITY IT INDUCES AN OPPSITE CHARGE AT INNER SURFACE AND SIMILAR CHARGE AT OUTER SURFACE. nOW IF YOU TAKE GUASSIAN SURFACE INSIDE BODY OF CUNDUCTOR NET CHARGE INSIDE GAUSSIAN SURFACE IS ZERO HENCE FIELD IS ZERO. IT IS DUE TO CAPABILITY OF CONDUCTORS TO GET INDUCED CHARGES WHICH IS DUE TO FREE CHARGE CARRIERS.