Classical Electrodynamics
Part II
by
Robert G. Brown
Duke University Physics Department Durham, NC 27708-0305 rgb@phy.duke.edu
Acknowledgements
I'd like to dedicate these notes to the memory of Larry C. Biedenharn. Larry was my Ph.D. advisor at Duke and h
Electrostatic Field Problems:
Spherical Symmetry
EE 141 Lecture Notes
Topic 7
Professor K. E. Oughstun
School of Engineering
College of Engineering & Mathematical Sciences
University of Vermont
2014
Motivation
Spherical Coordinates
Coordinate transformati
A Companion to Classical Electrodynamics
3rd Edition by J.D. Jackson
Rudolph J. Magyar
September 30, 2008
c Rudolph J. Magyar. No portion of this may be reproduced for prot
without the expressed prior written consent of Rudolph J. Magyar.
1
A lot of thing
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
5
Boundary value problems and Greens functions
Many of the lectures so far have been concerned with the initial value problem
L[y] = f (x),
y(x0 ) = , y (x0 ) = ,
(5.1)
where L is the dierential operator
L[y] =
d2 y
dy
+ a1 (x) + a0 (x)y.
2
dx
dx
(5.2)
Fr
4
Greens Functions
In this section, we are interested in solving the following problem. Let be an open, bounded subset of Rn . Consider u = f x Rn (4.1) u=g x .
4.1
Motivation for Greens Functions
y G(x, y) = x G(x, y) = 0 y y
Suppose we can solve the pr
Problem 2.7
gonsider potentil prolem in the hlfEspe dened y z ! HD with hirihlet oundry
onditions on the plne z a H @nd t innityAF
2.7.a. Write down the appropriate Green function
GD @~ ; ~ H A
xx
ap
I
@x xH A C @x xH A C @x xH A
1
1
2
2
2
2
3
2
3
G@~ ; ~
Boundary-value Problems in Electrostatics I
Karl Friedrich Gauss (1777 - 1855) December 23, 2000
Contents
1 Method of Images 1.1 1.2 1.3 1.4 Point Charge Above a Conducting Plane . . . . . . . . . Point Charge Between Multiple Conducting Planes . . . Poin
Chapter 12
Greens Functions
12.1
One-dimensional Helmholtz Equation
Suppose we have a string driven by an external force, periodic with frequency
. The dierential equation (here f is some prescribed function)
1 2
2
2 2
2
x
c t
U (x, t) = f (x) cos t
(12.
18.303: Notes on the
1d-Laplacian Greens function
Steven G. Johnson
October 12, 2011
In class, we solved for the Greens function G(x, x ) of the 1d Poisson equation
f where u(x) is a function on [0, L] with Dirichlet boundaries u(0) = u(L) = 0.
We obtaine
3.2 The Method of Images
Please refer to D. K. Chengs Field and Wave Electromagnetics, Chapt. 4-4.
more complete section for the introduction to the method of images.
Its a
z
q
3.2.1 The Classic Image Problem
Suppose a point charge q is held a distance d
MATH34032: Greens Functions, Integral Equations and the Calculus of Variations
1
Section 2
Greens Functions
In this section we show how the Greens function may be used to derive a general solution
to an inhomogeneous Boundary Value Problem.
Boundary Value
Problem Set 08
Note: The problem set is due November 05 by midnight. Please return directly to me in
my ofce Rutherford 82]. If Im not there slip your assignment below my door.
1. A conducting cone of angle (91 is inside another conducting cone of angle 9
Greens Functions
Greens Function of the Sturm-Liouville Equation
Consider the problem of nding a function u = u(x), x [a, b], satisfying
canonical boundary conditions at the points a and b, and the equation
Lu(x) = f (x) ,
where
L =
1
w(x)
d
d
p(x)
q(x)
Physics 506 Practice Midterm
Winter 2006
The midterm will be a 120 minute open book, open notes exam. Do all three problems. 1. A resonant cavity is in the shape of a rectangular box with sides of lengths a, b and c. a) Assuming innite conductivity for th
Physics 506 Practice Final
Winter 2006
The nal will be a 3 hour open book, open notes exam. Do all four problems. 1. Two parallel innitely long straight wires of negligible cross-sectional area are separated by a distance a and are at rest in an inertial
Physics 506 Practice Final
Winter 2006
The nal will be a 3 hour open book, open notes exam. Do all four problems. 1. Two parallel innitely long straight wires of negligible cross-sectional area are separated by a distance a and are at rest in an inertial
Electrodynamics 513 Midterm Exam
October 13, 2013
You are only allowed to use your own unmarked copy of the textbook J.D. Jackson Classical
Electrodynamics. No other notes, printed materials, or calculators are allowed. Please make
sure to do various chec