ECE3209-2009-hw5

# ECE3209-2009-hw5 - ECE 3209 Electromagnetic Fields...

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ECE 3209 — Electromagnetic Fields University of Virginia Fall 2009 Homework # 5 — Dielectrics, Capacitance, and Energy Due: Friday, October 9 1. A thick spherical shell (inner radius a , outer radius b ) is ﬁlled with dielectric material with a “frozen in” polarization, ~ P = kr ˆ r , where k is a constant and r is the distance from the center (there is no free charge in this problem). Find the electric ﬁeld in all three regions ( r < a, a < r < b , and r > b ) by two diﬀerent methods: (a) Locate all the bound charge and calculate the ﬁeld it produces. (b) Use Gauss’s Law to ﬁnd ~ D and then obtain ~ E . 2. The MOS (Metal-Oxide-Semiconductor) capacitor is an important electronic component in modern integrated circuits. The charge conﬁguration is similar to that for a Schottky diode except that there is a thin layer of non-conducting oxide (dielectric) between the metal and semiconductor, as shown below. Assume that the metal carries a uniform negative surface charge density of

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## This note was uploaded on 10/16/2010 for the course ECE 309 taught by Professor Weikle during the Fall '08 term at UVA.

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ECE3209-2009-hw5 - ECE 3209 Electromagnetic Fields...

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