1. 1/24/2014PHY 712 Spring 2014 -- Lecture 61 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 6: Continue reading Chapter 2 1.Methods of images -- planes, spheres 2.Solution of Poisson equation in for other geometries -- cylindrical

2. 1/24/2014PHY 712 Spring 2014 -- Lecture 62

3. 1/24/2014PHY 712 Spring 2014 -- Lecture 63 Survey of mathematical techniques for analyzing electrostatics – the Poisson equation 1.Direct integration of differential equation 2.Green’s function techniques 3.Orthogonal function expansions 4.Method of images

4. 1/24/2014PHY 712 Spring 2014 -- Lecture 64 Method of images Clever trick for specialized geometries:  Flat plane (surface)  Sphere Planar case: Consider a grounded metal sheet, a distance d from a point charge q. d q

5. 1/24/2014PHY 712 Spring 2014 -- Lecture 65 A grounded metal sheet, a distance d from a point charge q. d q Mobile charges from the “ground” respond to the force from the charge q. x z y

6. 1/24/2014PHY 712 Spring 2014 -- Lecture 66 A grounded metal sheet, a distance d from a point charge q.

7. 1/24/2014PHY 712 Spring 2014 -- Lecture 67 A grounded metal sheet, a distance d from a point charge q. d q

8. 1/24/2014PHY 712 Spring 2014 -- Lecture 68 A grounded metal sheet, a distance d from a point charge q. d q

9. 1/24/2014PHY 712 Spring 2014 -- Lecture 69 A grounded metal sphere of radius a, in the presence of a point charge q at a distance d from its center. r d q a

10. 1/24/2014PHY 712 Spring 2014 -- Lecture 610 A grounded metal sphere of radius a, in the presence of a point charge q at a distance d from its center. r d q a

11. 1/24/2014PHY 712 Spring 2014 -- Lecture 611 A grounded metal sphere of radius a, in the presence of a point charge q at a distance d from its center. r d q a

12. 1/24/2014PHY 712 Spring 2014 -- Lecture 612 Use of image charge formalism to construct Green’s function

13. 1/24/2014PHY 712 Spring 2014 -- Lecture 613 Solution of the Poisson/Laplace equation in various geometries -- cylindrical geometry with no z-dependence (infinitely long wire, for example):  

14. 1/24/2014PHY 712 Spring 2014 -- Lecture 614 Solution of the Poisson/Laplace equation in various geometries -- cylindrical geometry with no z-dependence (infinitely long wire, for example):  

15. 1/24/2014PHY 712 Spring 2014 -- Lecture 615 Solution of the Poisson/Laplace equation in various geometries -- cylindrical geometry with z-dependence   z

16. 1/24/2014PHY 712 Spring 2014 -- Lecture 616 Cylindrical geometry continued:

17. 1/24/2014PHY 712 Spring 2014 -- Lecture 617 Cylindrical geometry example:

18. 1/24/2014PHY 712 Spring 2014 -- Lecture 618 Cylindrical geometry example:

19. 1/24/2014PHY 712 Spring 2014 -- Lecture 619 Comments on cylindrical Bessel functions m=0 J0J0 K0K0 I 0 /50 N0N0

20. 1/24/2014PHY 712 Spring 2014 -- Lecture 620 m=1 J1J1 N1N1 K1K1 I 1 /50