emhw08 - You will have dierent expansion coecients inside...

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Electromagnetic Theory I Problem Set 8 Due: 24 October 2011 29. J, Problem 4.4 30. In class we were able to use the method of images to Fnd the potential for a point charge outside a grounded conducting sphere. We also successfully used the method to Fnd the Felds of a charge above and below the planar interface between two di±erent homogeneous dielectrics. but as we shall see, the method fails for a point charge outside a uniform dielectric sphere. Assume the dielectric constant is ± inside a sphere of radius R and ± 0 outside the sphere. a) Set up and solve for the potential of a point charge q a distance D > R from the center of the dielectric sphere as an expansion in Legendre polynomials (or spherical harmonics).
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Unformatted text preview: You will have dierent expansion coecients inside and outside the sphere, which you are to determine by the matching conditions at the boundary. b) Show that in the limit / , the result reduces to the potential for a point charge outside a conducting sphere, by expanding the latter solution in Legendre polynomials and comparing coecients. c) or Fnite / discuss why the solution cannot be expressed in terms of a single image charge, even though when / it can. 31. J, Problem 4.10 32. J, Problem 4.13 1...
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This note was uploaded on 01/08/2012 for the course PHY 6346 taught by Professor Staff during the Spring '08 term at University of Florida.

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