Someone argues: 'The relation is a law of electrostatics

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric fields in matter · Electric fields in matter

The Boundary-Value Problem, Ch Linear dielectrics and the boundary-value problem with matter in it

Problem

Someone argues: 'The relation

\mathbf{P} = \varepsilon_0\chi_e\mathbf{E}

is a law of electrostatics, on the same footing as

\nabla\cdot\mathbf{D}=\rho_f

. It must therefore hold for every dielectric, at every field strength, frequency and field direction; in particular, doubling

\mathbf{E}

always doubles

\mathbf{P}

in any material.' ((a)) Name the four separate assumptions bundled into

\mathbf{P}=\varepsilon_0\chi_e\mathbf{E}

. ((b)) Give one named material or situation for which the claim fails, and say which of the four assumptions breaks down there.