1. 01/31/2014PHY 712 Spring 2014 -- Lecture 71 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 7: Start reading Chapter 3 Solution of Poisson equation in for special geometries – A.Cylindrical B.Spherical

2. 01/31/2014PHY 712 Spring 2014 -- Lecture 72

3. 01/31/2014PHY 712 Spring 2014 -- Lecture 73 Solution of the Poisson/Laplace equation in various geometries -- cylindrical geometry with z-dependence   z

4. 01/31/2014PHY 712 Spring 2014 -- Lecture 74 Cylindrical geometry continued:   z

5. 01/31/2014PHY 712 Spring 2014 -- Lecture 75 Cylindrical geometry continued:   z

6. 01/31/2014PHY 712 Spring 2014 -- Lecture 76 Solutions of Laplace equation inside cylindrical shape Example with non-trivial boundary value at z=L kk m=0 m=1 m=2

7. 01/31/2014PHY 712 Spring 2014 -- Lecture 77 Solutions of Laplace equation inside cylindrical shape Example with non-trivial boundary value at z=L

8. 01/31/2014PHY 712 Spring 2014 -- Lecture 78 Solutions of Laplace equation inside cylindrical shape Example with non-trivial boundary value at  =a kk m=0 m=1 m=2

9. 01/31/2014PHY 712 Spring 2014 -- Lecture 79 Solutions of Laplace equation inside cylindrical shape Example with non-trivial boundary value at  =a

10. 01/31/2014PHY 712 Spring 2014 -- Lecture 710 Green’s function for Dirchelet boundary value inside cylindar:

11. 01/31/2014PHY 712 Spring 2014 -- Lecture 711 Comments on cylindrical Bessel functions m=0 J0J0 K0K0 I 0 /50 N0N0

12. 01/31/2014PHY 712 Spring 2014 -- Lecture 712 m=1 J1J1 N1N1 K1K1 I 1 /50

13. 01/31/2014PHY 712 Spring 2014 -- Lecture 713 Some useful identities involving cylindrical Bessel functions

14. 01/31/2014PHY 712 Spring 2014 -- Lecture 714 Poisson and Laplace equation in spherical polar coordinates http://www.uic.edu/classes/eecs/eecs520/textbook/node32.html

15. 01/31/2014PHY 712 Spring 2014 -- Lecture 715 Poisson and Laplace equation in spherical polar coordinates -- continued

16. 01/31/2014PHY 712 Spring 2014 -- Lecture 716 Properties of spherical harmonic functions

17. 01/31/2014PHY 712 Spring 2014 -- Lecture 717 Useful identity:

18. 01/31/2014PHY 712 Spring 2014 -- Lecture 718 Example -- continued

19. 01/31/2014PHY 712 Spring 2014 -- Lecture 719 Useful identity:

20. 01/31/2014PHY 712 Spring 2014 -- Lecture 720 Useful identity:

21. 01/31/2014PHY 712 Spring 2014 -- Lecture 721 Some spherical harmonic functions: