# Different forms of electric displacement vector D

In Irodov's Basic Laws of Electromagnetism, D is derived as D=ε°E+P. Later substituting the polarization vector for an isotropic dielectric as P=Χε°E, the result reached is D=ε°εD where ε is dielectric constant of the dielectric.

However later in an example he says that the second result is not valid (in that particular example). See Example 3. Does the invalidity of the second result mean the sphere is not made of a isotropic material? If yes, how do we infer that? Ifnot,then what is the reason behind the invalidity?

He is probably thinking of ferroelectric body, which manifests electric polarization even without external field. Such material media manifest non-linear relation between electric field and polarization, and hysteresis. So there is no general useful relation between $\mathbf D$ and $\mathbf E$. It is like with ferromagnets - there, there is no general useful relation between $\mathbf B$ and $\mathbf H$.