In a conductor, there are equal number of electrons and protons (Free electrons are those electrons which are loosely bounded to an atom). Therefore, the conductor as a whole is neutral since there is no excess charge on the conductor. Hence there is no electric field outside the conductor.

At the angstrom level inside the conductor, there is a large electric field between a proton and an electron inside a single atom. There are large numbers of such atoms closely packed with each other and if we take the average electric field of these atoms, it will be nearly equal to zero. This is due to the fact that opposite electric fields cancels each other and such large numbers of atoms cancels each other’s electric field.

Therefore, the electrostatic field inside the conductor is zero.