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emhw08 - You will have di±erent expansion coe²cients...

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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 find the potential for a point charge outside a grounded conducting sphere. We also successfully used the method to find the fields of a charge above and below the planar interface between two different 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 di±erent expansion coe²cients 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 coe²cients. c) ³or 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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