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.

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Presentation transcript:

02/03/2014PHY 712 Spring 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

02/03/2014PHY 712 Spring Lecture 82

02/03/2014PHY 712 Spring Lecture 83 Poisson and Laplace equation in spherical polar coordinates

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

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

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

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

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

02/03/2014PHY 712 Spring Lecture 89 Example:

02/03/2014PHY 712 Spring Lecture 810 Example:

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

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

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

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

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

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

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

02/03/2014PHY 712 Spring 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).

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

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

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

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

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