Solutions To Problems Of Jackson's Classical Electrodynamics - Kasper van Wyk.pdf

Answers To a Selection of Problems from
Classical Electrodynamics
John David Jackson
by Kasper van Wijk
Center for Wave Phenomena
Department of Geophysics
Colorado School of Mines
Golden, CO 80401
Samizdat
Press
Published by the Samizdat Press
Center for Wave Phenomena
Department of Geophysics
Colorado School of Mines
Golden, Colorado 80401
and
New England Research
76 Olcott Drive
White River Junction, Vermont 05001
c Samizdat Press, 1996

Release , January 1999
Samizdat Press publications are available via FTP or

Permission is given to freely copy these documents.
Contents
1 Introduction to Electrostatics 7
Electric Fields for a Hollow Conductor . . . . . . . . . . . . . . . . . . . . . . . . . 7
Charged Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Charge Density for a Hydrogen Atom . . . . . . . . . . . . . . . . . . . . . . . . . 10
Charged Cylindrical Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Green’s Reciprocity Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Boundary-Value Problems in Electrostatics: 1 15
The Method of Image Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
An Exercise in Green’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Two Halves of a Conducting Spherical Shell . . . . . . . . . . . . . . . . . . . . . . 19
A Conducting Plate with a Boss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Line Charges and the Method of Images . . . . . . . . . . . . . . . . . . . . . . . . 24
Two Cylinder Halves at Constant Potentials . . . . . . . . . . . . . . . . . . . . . . 26
A Hollow Cubical Conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
8 Waveguides, Resonant Cavities and Optical Fibers 31
Time Averaged Forces Per Unit Area on a Condu