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.

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01/31/2014PHY 712 Spring 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

01/31/2014PHY 712 Spring Lecture 72

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

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

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

01/31/2014PHY 712 Spring 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

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

01/31/2014PHY 712 Spring 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

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

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

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

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

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

01/31/2014PHY 712 Spring Lecture 714 Poisson and Laplace equation in spherical polar coordinates

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

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

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

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

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

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

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