Question

Problem 1. Electrostatics (1) As shown in the Figure below, a parallel-plate capacitor of plate area A is filled with two layers of dielectrics, ch and d2 thick, with permittivities fringe effect at the four edges (assuming rectangular plates), find the fields Ei and Es in the two dielectrics if a voltage V (assumed positive) is applied to the top plate with regard to the bottom plate. (Note: both magnitudes and directions needed.) and a, respectively. Ignoring the (2) Find the surface charge densities of the two plates when the voltage V is applied. (3) Derive an expression for the capacitance per plate area. (Note: simply writing down the result or claiming equivalence to two capacitors in series without proof does not earn points.) 2-2 (4) Is there any discontinuity in electric field at the interface between the two dielectrics? Explain the discontinuity or the absence thereof. (5) The permittivities can be expressed as a-&ia and e-ean, where a is the permittivity of free space, and ei and &2 are the dielectric constants of the two dielectrics, respectively. The breakdown fields are Esi and Es for the two dielectrics, respectively. Given &1-4, s2-28, Esi 1 V/nm, and Es -0.5 V/nm, which dielectric limits the voltage V' tha: can be applied to this capacitor? (6) In a particular engineering context, both large total dielectric thickness and large capacitance per area are desired, therefore the optimal configuration is to use only the dielectric of &2 28 (i.e, di - 0). Due to material properties, however, a layer of the dielectric of &1-4, at least 1.5 nm thick, always covers the bottom electrode. A figure of merit, the equivalent thickness de, is define as the thickness of a capacitor filled only with the dielectric of a1-4 that has the same capacitance as a capacitor with a di thick layer of the dielectric of &1 -4 and a da thick layer of the dielectric of &2- 28. Find an expression of de. (7) (Optional, for bonus) Based on the expression, discuss the engineering significance of this figure of merit, the advantage of using the dielectric of a larger dielectric constant, and the limitation to the advantage.

Answer 1

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