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.

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1/24/2014PHY 712 Spring 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

1/24/2014PHY 712 Spring Lecture 62

1/24/2014PHY 712 Spring 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

1/24/2014PHY 712 Spring 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

1/24/2014PHY 712 Spring 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

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

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

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

1/24/2014PHY 712 Spring 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

1/24/2014PHY 712 Spring 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

1/24/2014PHY 712 Spring 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

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

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

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

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

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

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

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

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

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