When you polarize a neutral dielectric, the charge moves a bit, but the total remains ze...

When you polarize a neutral dielectric, the charge moves a bit, but the total remains zero. This fact should be reflected in the bound charges σ_b and ρ_b. Prove from Eqs. 4.11 and 4.12 that the total bound charge vanishes.

Reference equation 4.11

Reference equation 4.12