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ECE309-2008-hw5

# ECE309-2008-hw5 - ECE 309 Electromagnetic Fields University...

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ECE 309 — Electromagnetic Fields University of Virginia Fall 2008 Homework # 5 — Dielectrics and Capacitors Due: Wednesday, October 1 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. Consider a uniformly polarized sphere of radius R with polarization parallel to the z -axis (figure (a) below): (a) (b) (a) Find the bound surface charge density and bound volume charge density of the sphere. (b) Find the electric field both inside and outside the sphere. ( Hint: To work this problem, consider the polarized sphere to consist of two uniformly charged spheres that are slightly displaced from each other as shown in figure (b) above. When there is no polarization, the charged spheres overlap

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ECE309-2008-hw5 - ECE 309 Electromagnetic Fields University...

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