In 4 Chem-Phys we are trying to understand the differences between conducting objects that have a net charge and NON-conducting objects that have a net charge. Remember, what we are discussing is only for STATIC electricity.
Conductors/metals have those metallic bonds, where the delocalized electrons can move. If an E-field interacts with a conducting material, such as one of the shells we were talking about in class, then that shell can polarize. The consequence of the polarization and the behavior of conductors with static charge is that the net charge ends up on the outer surface. This also means that the E-field inside the conducting material is E = 0. Note that if the E-field is not 0 inside a conductor, then there would be an electric current, and not static electricity. The video for conductors is here.
NON-conductors/insulators do not have metallic bonds or a 'sea of free electrons,' which is why they do not conduct currents. But this means it is OK for any net charge to be spread throughout the volume of the material - it can't move, so it would still be static charge. According to Gauss's law, there will be an E-field inside the material. This is where we need to work with charge density, which is charge/volume. Our job using Gauss's law is the same as always: try to figure out what to put in for the charge inside any particular region of the system. The video for NON-conductors is here.