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Unformatted text preview: HW 5 Phys5406 S05 due 3/3/05 1)Two grounded, conducting half planes abut along the z axis. One plane is φ = 0 while the other is φ = π/ 4. Put a point charge somewhere in the space between the planes, at r’ , with coordinates x’,y’,z’. Then solve for the potential in that space at r , coordinates x,y,z. From this result obtain the Green’s function. 2)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. 3)Let the plane z=0 be a grounded conductor. A hole of radius infinitesimbly larger than a 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 z > 0 outside of the hemisphere? You should write the potential in spherical coordinates. Explicitly writethe hemisphere?...
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