hw6_p5406_s06 - HW 5 Phys5406 S06 due 3/16/05 (after break)...

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Unformatted text preview: HW 5 Phys5406 S06 due 3/16/05 (after break) 1)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 , with coordinates x',y',z'. Then solve for the potential in that r' space at r, coordinates x,y,z. From this result obtain the Green function for this geometry. 2)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. Also solve for the potential if the plane  = 0 is grounded except for xa where it is at potential V. 3)A point charge q lies a distance D from a dielectric sphere of radius a and permitivity . What is the polarization of the sphere? Make this calculation for D>a and D<a. 4)JDJ 2.7 parts b and c 5)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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