1. 02/03/2014PHY 712 Spring 2014 -- Lecture 81 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 8: Start reading Chapter 4 Multipole moment expansion of electrostatic potential – A.Spherical coordinates B.Cartesian coordinates

2. 02/03/2014PHY 712 Spring 2014 -- Lecture 82

3. 02/03/2014PHY 712 Spring 2014 -- Lecture 83 Poisson and Laplace equation in spherical polar coordinates http://www.uic.edu/classes/eecs/eecs520/textbook/node32.html

4. 02/03/2014PHY 712 Spring 2014 -- Lecture 84 Poisson and Laplace equation in spherical polar coordinates -- continued

5. 02/03/2014PHY 712 Spring 2014 -- Lecture 85 Properties of spherical harmonic functions

6. 02/03/2014PHY 712 Spring 2014 -- Lecture 86 Legendre and Associated Legendre functions

7. 02/03/2014PHY 712 Spring 2014 -- Lecture 87 Useful identity:

8. 02/03/2014PHY 712 Spring 2014 -- Lecture 88 Some spherical harmonic functions:

9. 02/03/2014PHY 712 Spring 2014 -- Lecture 89 Example:

10. 02/03/2014PHY 712 Spring 2014 -- Lecture 810 Example:

11. 02/03/2014PHY 712 Spring 2014 -- Lecture 811 Example -- continued:

12. 02/03/2014PHY 712 Spring 2014 -- Lecture 812 Example -- continued:

13. 02/03/2014PHY 712 Spring 2014 -- Lecture 813 Notion of multipole moment:

14. 02/03/2014PHY 712 Spring 2014 -- Lecture 814 Significance of multipole moments

15. 02/03/2014PHY 712 Spring 2014 -- Lecture 815 Relationship between spherical harmonic and Cartesian forms of multipole moments:

16. 02/03/2014PHY 712 Spring 2014 -- Lecture 816 Consider previous example:

17. 02/03/2014PHY 712 Spring 2014 -- Lecture 817 General form of electrostatic potential in terms of multipole moments:

18. 02/03/2014PHY 712 Spring 2014 -- Lecture 818 Example of multipole expansion in evaluating energy of a very localized charge density  (r) in a electrostatic field  (r) (such as an nucleus in the field due to the electrons in an atom).

19. 02/03/2014PHY 712 Spring 2014 -- Lecture 819 Simple examples of multipole distributions x y z x y z

20. 02/03/2014PHY 712 Spring 2014 -- Lecture 820 Another example of multipole distribution

21. 02/03/2014PHY 712 Spring 2014 -- Lecture 821 Another example of multipole distribution -- continued

22. 02/03/2014PHY 712 Spring 2014 -- Lecture 822 Another example of multipole distribution -- continued

23. 02/03/2014PHY 712 Spring 2014 -- Lecture 823 Another example of multipole distribution -- continued