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:

Problem:

The space between the plates of a parallel-plate capacitor is filled with two slabs of linear dielectric material.  Each slab has thickness s, so the total distance between the plates is 2s.  Slab 1 has a dielectric constant of 2, and slab 2 has a dielectric constant of 1.5.  The free charge density on the top plate is σ and on the bottom plate −σ.  (The top plate is touching slab 1.)
(a)  Find the electric displacement D in each slab.
(b)  Find the electric field E in each slab.
(c)  Find the polarization P in each slab.
(d)  Find the potential difference between the plates.
(e)  Find the location and amount of all the bound charge.
(f)  Now that you know all the charge (free and bound), recalculate the field in each slab, and compare with your answer to (b).

Solution: