Problem with understanding polarization

[neworder1]

Suppose we have a ball made of linear dielectric with permittivity \epsilon, with some initial homogenous polarization \vec{P} aligned with z axis. Then we know that inside the ball the polarization generates an electric field \vec{E}=\frac{-1}{3\epsilon_{0}}\vec{P} (standard calculation). But we also know that in a linear dielectric we have the relation \vec{P}=(\epsilon - \epsilon_{0})\vec{E}, and these two equations lead to contradiction since we have \vec{E}=\frac{-1}{3\epsilon_{0}}\vec{P} = \frac{-1}{3\epsilon_{0}}(\epsilon - \epsilon_{0})\vec{E}. Does it mean that a linear dielectric can't be polarized this way without an external field?

 

[Euclid]

Suppose we have a ball made of linear dielectric with permittivity \epsilon, with some initial homogenous polarization \vec{P} aligned with z axis. Then we know that inside the ball the polarization generates an electric field \vec{E}=\frac{-1}{3\epsilon_{0}}\vec{P} (standard calculation). But we also know that in a linear dielectric we have the relation \vec{P}=(\epsilon - \epsilon_{0})\vec{E}, and these two equations lead to contradiction since we have \vec{E}=\frac{-1}{3\epsilon_{0}}\vec{P} = \frac{-1}{3\epsilon_{0}}(\epsilon - \epsilon_{0})\vec{E}. Does it mean that a linear dielectric can't be polarized this way without an external field?

Yeah, of course! If there is no field, and the object is polarized... it's not a linear material.