Consider the following statement:
In the case of a linear dielectric of arbitrary shape, when no free charges are present, in an external applied electric field $\vec E_0$, then $\vec D=0$.
Is this statement always true (considering that $\nabla \times \vec D= \nabla \times \vec P$) and can it be proved? If it is false can you please provide a counter example.
Can a similar statement be made for the auxiliary field $H$ in terms of the magnetization $M$?