Hw7_p5406_s06 - HW 7 Phys5406 S06 due 1 In class we found the Green's function inside a cylindrical volume using in part the solution to the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HW 7 Phys5406 S06 due 3/23/06 1) In class we found the Green's function inside a cylindrical volume using, in part, the solution to the cylindrical problem of JDJ. This is a cylinder of radius a and length L. All surfaces are grounded except that at z=L and it is kept at potential V(; ). Show r2GD = 4(r r ). 0 2) Find the potential inside when all surfaces of the above cylinder are grounded and there is a line of charge per unit length  along the z axis from d/2 to 3d/2, where 3d/2 < L. 3)JDJ 2.19. Note I prefer to write the solution as = g2a + g2b (1) g2a = 2 ln(> =c) ln(b=< )= ln(b=c) (2) g2b =2 g2 X (1 m=1 =m) cos[m(  )][(>=c)m (c=>)m][(<=b)m (b=<)m]=[(b=c)m (c=b)m] 0 4)Using the result of 3) i) Let c3 I thus obtaining g2 outside an in nitely long cylinder of radius b; ii) Let b3 0 thus obtaining g2 inside an in nitely long cylinder of radius c; and iii Let c3 I and b3 0 thus obtaining the all space and 2.18a,c using previous homework results. 1 g2 . Compare your answers to JDJ 2.17c (3) ...
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.

Ask a homework question - tutors are online