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Unformatted text preview: HW 6 Phys5406 S10 due 3/18/10
1) Suppose two semi-inﬁnite conducting plates intersect along the entire z axis and form
a right angle. The plates are isolated from each other with a thin layer of insulator. The
potential is desired in the region x, y > 0.
a) Solve an appropriate image problem and obtain the Green function, GD .
b) Solve another appropriate image problem and obtain the reduced Green function,
g2 (x, x′ , y, y ′).
c) Integrate GD over z’ and show that you also get g2 .
d) Instead of integrating g2 over ρ′ , if you want g1 (φ, φ′ ), assume the plate running along
the positive x axis has constant potential V and the plate running along the positive y axis
has constant potential V’. Use the solution of the LaPlace equation to get g1 . 2) Consider a hollow spherical conductor of inner radius a. There is a point charge q
at dez , where d < a.
a) Find the surface charge density induced on the shell’s inner surface. Note, it is not uniform.
b) Using only the point charge and the surface charge density at r=a, explicitly calculate
the potential at any point r > a. You should know the answer as a check. 3) Consider a solid dielectric sphere of radius a and permitivity ǫ. A elementary electric dipole p = pez is at dez , where d > a. Find the potential at all points in space. 4) An inﬁnitely long cylindrical conductor of radius a is kept at potential V. The cylinder axis runs parallel to ez and an inﬁnite grounded conducting plane, x=0. If the cylinder
axis passes through (x,y)=(c,0), ﬁnd the potential at any (x,y), where x > 0. 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.
- Spring '10