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F07_hw05

# F07_hw05 - Physics 505 Homework Assignment#5 Due Thursday...

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Physics 505 Fall 2007 Homework Assignment #5 — Due Thursday, October 11 Textbook problems: Ch. 3: 3.13, 3.17, 3.26, 3.27 3.13 Solve for the potential in Problem 3.1, using the appropriate Green function obtained in the text, and verify that the answer obtained in this way agrees with the direct solution from the differential equation. 3.17 The Dirichlet Green function for the unbounded space between the planes at z = 0 and z = L allows discussion of a point charge or a distribution of charge between parallel conducting planes held at zero potential. a ) Using cylindrical coordinates show that one form of the Green function is G ( ~x, ~x 0 ) = 4 L X n =1 X m = -∞ e im ( φ - φ 0 ) sin nπz L sin nπz 0 L I m L ρ < K m L ρ > b ) Show that an alternative form of the Green function is G ( ~x, ~x 0 ) = 2 X m = -∞ Z 0 dk e im ( φ - φ 0 ) J m ( ) J m ( 0 ) sinh( kz < ) sinh[ k ( L - z > )] sinh( kL ) 3.26 Consider the Green function appropriate for Neumann boundary conditions for the volume V between the concentric spherical surfaces defined by r = a and r = b , a < b .

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F07_hw05 - Physics 505 Homework Assignment#5 Due Thursday...

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