show that net field in the interior of a conductor is zero?
Answers
Not always.
Net Electric field inside the conductor is zero only under electrostatic conditions, i.e., charges are stationary. In a conductor free charges are present and they will always be moving inside if an Electric field exists inside. So for the charges to remain stationary there should be no electric field inside a conductor. Not only that no net charges reside inside the conductor either.
So what happens is this: Keep a conductor in an external electric field which is stationary. Instantaneously this field will also be present inside this conductor and the random charges because of this field will move and rearrange in a matter of micro seconds such that the rearranged charges produce an electric field exactly equal and opposite to the external field, thus making the net electric field inside the conductor zero. These charges reside on the outer surface of the conductor and are stationary.
On the other hand if you have time varying electric field an Electric field does exist / penetrate a small depth in the conductor. This is known as skin depth.