Polarization and the electric displacement

Problem:

If one presumes that there exists a true charge density ρtrue, a polarization or bound charge density ρbound, and a total charge density ρtotal, such that ρtrue + ρbound = ρtotal, write the source equations for D, E, and P.  Explain the meaning of these equations.  Briefly address the question:  Which of the fields D or E might be considered the more fundamental field?  Why?  Write the equation(s) describing the relationships between the three field quantities.

Solution:

Problem:

A thin electrically insulating sheet of material has thickness d and lateral extent L × L, where d <<  L.  It is in a vacuum and isolated from external electric fields.  It has frozen-in polarization per unit volume P oriented in the (x,z) plane at an angle θ to the normal to the surfaces, which is in the z-direction.
Find the magnitudes and directions of the electric displacement D and the electric field E both inside and outside the material, stating clearly your reasoning.

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Solution: