Problemas de Jackson sobre Função de Green

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Ph196c Homework1 Due: Friday, Apr 9, 5pm, 337 
Lau.
In spherical polar coordinates we found that the Coulomb potential of a point charge q on the z axis a distance r£ 
from the origin could be expressed using the Legendre polynomial generating function
 1ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅè!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!r2+r£ 2-2 r r£ cos q = ‚ =0¶ r<ÅÅÅÅÅÅÅÅÅÅr>+1 P Hcos qL.
Of course, this just arises by expressing the Green function in 3D free space in two different ways. 
In general, you can express the Green function in 2D (potential of an infinitely long 3D line charge with unit 
charge per unit length) and 3D in various ways, analogous to the above formula. In particular, the 2D Green 
function expressed as a series in the functions that arise from Laplace's equation in 2D polar coordinates is 
especially useful in the study of magnetism and I urge you to remember its existence later in the course. It is 
developed in the first problem below.
1. Jackson, problem 2.17. 
2. Jackson, problem 3.1.
3. Jackson, problem 3.13.
4. Jackson, problem 3.2.
5. Jackson, problem 3.3.
6. Jackson, problem 3.7.