hw7_p5406_s08 - HW 7 Phys5406 S08 due 3/20,08 1) JDJ 3-1,...

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Unformatted text preview: HW 7 Phys5406 S08 due 3/20,08 1) JDJ 3-1, solve this using the Green's function in spherical coordinates. Choose your axes so that you have azimuthal symmetry, and rst obtain the 2D Green function. 2) There are two grounded spherical surfaces of radii a and b with a < b. At a  d  b, there is a point charge q. r = dez , Using the Green's function in spherical coordinates nd the potential in the region between the two spheres for r < d and r > d. How many image charges are required. Specialize to the cases i) a ! 0 and ii) b ! 1 and solve the problems of the potential i) inside b when there is a point charge inside b and ii) outside a when there is a point charge outside a. 3)Two grounded, conducting half planes touch all along the z axis. One plane coincides with  = 0 while the other coincides with  = =4. Put a point charge q somewhere in the space between the planes, at r', with coordinates x',y',z'. a)Solve for the potential in that space at r, coordinates x,y,z. b)From this result obtain the Green function for this geometry. c)Now remove q from the problem. Using the Green Function found above, nd the potential in the space between the two half planes of problem 1 if the half plane along  = 0 is kept at constant potential V and the other half plane is grounded. 4)JDJ 2.10. In part c do not assume that q is placed directly above the hemispherical boss. It is placed at diatance d from the boss center (d>a) and to the right of the plane. Inaddition to solving for the charge induced on the boss, obtain the Green function for this geometry. 1 ...
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This note was uploaded on 12/24/2011 for the course PHYS 5406 taught by Professor Blecher during the Spring '10 term at Virginia Tech.

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