hw6_p5406_s05

# hw6_p5406_s05 - homework of this semester to write the...

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HW 6 Phys5406 S05 due 3/17/05 1)Derive the 2D Green’s function for the space between two inﬁnitely long right circular cylinders. The inner cylinder has outer radius a and is kept at potential V(a, φ ). The outer cylinder has inner radius b and is kept at potential V(b, φ ). Find the 2D Green’s function in the space between the cylinders. Let a 0 and obtain the 2D Green’s function interior to b. Let b → ∞ and obtain the 2D Green’s function exterior to a. Finally let a 0 and b → ∞ and ﬁnd the all space 2D Green’s function. You can use the results from the ﬁrst
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Unformatted text preview: homework of this semester to write the answers in terms of natural logs. You can also use them to check your answer for the all space part of the problem and you can check your other answers by examining JDJ 2-18 and 2-19 2)Use the Green’s function you found in problem 1 to solve JDJ 2.13. Instead of JDJ’s tan-1 term, you may ﬁnd it easier to use, with x = ρ /b, 2[ x cos( φ )-x 3 cos(3 φ ) / 3 + x 5 cos(5 φ ) / 5-x 7 cos(7 φ ) / 7 ... ] (1) 1...
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