The Displacement Field, <b>D</b>

The Displacement Field, D

A parallel plate capacitor of area A is filled with a linear, isotropic, homogeneous delectric of given dielectric constant to create a capacitance C. A voltage V is applied. Demonstrate that you understand the differing concepts of D, E, and P by finding each in the dielectric and the surface bound charge density.

QUESTIONS
(Score is number right minus number wrong.)

In electrostatics, the field E and the fields P and D are fundamentally different because the curl of E always vanishes but the curls of P and D do not necessarily vanish.

: True; False

In Equation (6) we define a new fictitious field E(vac), but the change is purely cosmetic to create a divergence equation that looks just like the one Maxwell says an electric field should satisfy. Still, the curl of D and hence of the new field do not necessarily vanish.

Refer to the diagram. Where in the capacitor is it NECESSARILY so that the curls of P and hence of D do not vanish. (See Equation (7)).

: At the center of the dielectric.; Between the dielectric and the plates.; At the x-edge of the dielectric.; At the y and z-edges of the dielectric.

Assuming that the dimensions of the plates are large compared to their separation, where is it likely that the curl of D vanishes?

: Where the x-component of P vanishes but the other components do not.; Where the x-component of P is constant as a function of y and z.; Where the x-component of P is constant with respect to x, but not with respect to y and z.

If we stay away from the places in the capacitor where curl D does not vanish, then Equation (6b) describes a regular electrostatics field with vanishing curl. We should know the answer for the field inside a parallel plate capacitor that satisfies this equation.

For the capacitor shown in the figure with a free surface charge density, the field inside (but away from the edges) is