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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) ...
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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
 Blecher
 Magnetism

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