hw7_p5406_s07 - is cut out of the plane A conducting...

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HW 7 Phys5406 S07 due 3/22/07 1)JDJ 2.7 parts a, b, and c 2)A point charge q is at position D e z relative to the center of a dielectric sphere of radius a and permitivity ± . What is the polarization of the sphere? Make this calculation for D > a and D < a. I would not try to use the method of images to obtain the solution. However, show that the solution once obtained, is equivalent to an infinite number of images. 3)Let the plane z=0 be a grounded conductor. A hole of radius infinitesimbly larger than a
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Unformatted text preview: is cut out of the plane. A conducting hemisphere of radius a is inserted so that the center of the hole and sphere, if it was whole, coincide and the hemisphere lies in the region z > 0. If the hemisphere is kept at constant potential V, what is the potential for in the region z > 0 outside of the hemisphere? You should write the potential in spherical coordinates and explicitly write out the first two leading terms. What is the Green function for this geometry? 4) JDJ 6.8 1...
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