Bound charge
Charge that cannot move freely through a material because it is stuck inside individual atoms or molecules — yet still rearranges locally when the medium is polarized.
Definition
Bound charge is the central distinction §02 makes: the electrons and nuclei inside a dielectric are not free to wander like the conduction electrons in a metal. They are bound — locked into atomic orbitals and chemical bonds — but they can still shift slightly within their atoms when an external field arrives. That tiny intramolecular shift is what makes a dielectric a dielectric, and the displaced charges are bound charges.
The accounting is clean. Inside a polarized dielectric, the bound charge density is ρ_b = −∇·P: wherever the polarization vector field has a positive divergence (dipoles spreading apart), positive bound charge has effectively been carried away and a negative bound charge density appears. At the boundary between dielectric and vacuum, the bound surface charge density is σ_b = P·n̂, where n̂ is the outward unit normal — the discontinuity in the dipole arrangement leaves an exposed layer of charge on the surface. These two formulas, combined, account for every microscopic charge inside the polarized dielectric in two clean macroscopic numbers.
The complementary concept is free charge: the conduction electrons in a metal, the ions deliberately doped into a semiconductor, the explicit charges you place on a capacitor plate — anything you can move around with a wire. The two together (ρ = ρ_f + ρ_b) source the total electric field via Gauss's law in vacuum form ∇·E = ρ/ε₀, but in matter we usually want to talk about the free charge alone, which is exactly what the displacement field D is engineered to do.