This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: HW 5 Phys5406 S08 due 2/28/08 1)We will use the solution ¨( r ), obtained in class, inside the empty conducting box with ¨( x; y; c ) = ¨ and all other sides grounded, to get the Green function G D for all Dirichlet problems with this geometry. a) Obtain the completeness relation for expansion of any f ( x ) in a sine series for 0 < x < a , by obtaining the coe cients A j below, ( x x ) = X j [ A j sin j x=a sin j x =a ] : (1) b) You should now write the 3d delta function in a sum of the product of sines. Recall for the work below that r 2 G D ( r ; r ) = 4 ( r r ). c) Now expand the sinh function below for z in the range (0,c) in a sine series, sinh jk z sinh jk c = X m [ A m sin m z=c ] ; (2) and obtain the coe cients A m . Note that in the above equation, the LHS doesn't vanish at z =c, but the RHS does vanish there. Thus the representation of a function in a Fourier series allows you to get accuracy arbitrarily close to the boundary, but perhaps not exactly at the boundary.at the boundary....
View
Full
Document
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
 Blecher
 Magnetism

Click to edit the document details