I have concluded that in a uniform dielectric, volume free charge density $\rho_0$ and volume polarization charge density $\rho'$ satisfy $$ \rho' = \frac{-(\epsilon - \epsilon_0)}{\epsilon}\rho_0 $$ which can be derived from the differential form of Gauss's law.

It seems to show an interesting fact that $\rho'$ is always less than $\rho_0$. How do you explain this? Thanks!


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