Problem Set 6 The charge density for a hydrogenic p state can be written as r 2 exp r [P 0 (cos ) P 2 (cos )] (r, ) = 2 3 e a0 a0 3 a 0 64 e = 4. 8 10 10 statCoulomb, a 0 = 0. 529 10 8 cm. (a) Determi
411 Problem Set 5 2009 1. Using the solution to Laplaces equation in cylindrical coordinates, 2 (, , z) = 0,
where (, , z) = ,m [a m J m () + b m N m ()]e im e z write a general form for the Greens fu
411 Problem Set 4 2009 1.
Find a solution for the elecrostatic potential inside the following volume, V: -a/2 x a/2, -b/2 y b/2; z 0. Assume that there are no charges in the volume and (a/2, y, z) = (
411 Problem Set 3 Spring 09
of the charge stored and V is the magnitude of the electrostatic potential difference between the two surfaces which form the capacitor. (a) In each of the following find (
Phys 411 Set 2
Jackson problem 1.3
Using the Dirac delta function in the appropriate coordinates express the following charge distributions as three dimensional charge densities (r ). 1. In spherical
Phys 411 Set 1 Special problems
1. (a) By using Gauss law (Eq. ref: Gauss ) and the definition of the Dirac delta function show that if q Er = k 1 3 r r then the charge density is _r = q N 3 r . (b) S
Physics 411 Exam I
March 2, 2004
Name_ 1._(50 points) 2._(25 points) 3._(25 points) total ._(/100 points)
Dr, t 4k 1 o 0 r, t Br, t 0 Er, t k 3
Dr Er
D 1 r, t D 2 r, t n r, t B 1 r, t B 2 r, t n 0 n
*Physics
411 EXAM COVER SHEET.*
You can write any formulas you like on the printed side of these sheets and bring them to the exam. _ Dr = PEr 4 6 Dr, t = 4^k 1 O o _ 0 r, t D 1 r, t ? D 2 r, t 6 n =
Chapter 4
Boundary Value Problems in Spherical and Cylindrical Coordinates
4.1
Laplaces Equation in spherical coordinates
Laplaces equation in spherical coordinates, (r, , ) , has the form 1 1 r2 (r,
Section 4.9
Laplaces equation in cylindrical coordinates
As in the case of spherical coordinates, this equation is solved by a series expansion in terms of products of functions of the individual cyli
Page 61 Solutions to Laplaces equation: (x,y,z), (r,S, j, _, j, z; Helmholtz equation in (r,S, j
Equation
4 2 x, y, z = 0
separation. const.
! ! k=k 1 x +k 2 +k 3 z
General solution: sum over all sep.
Chapter 3
Boundary Value Problems, Introduction
3.1 The method of images There are some problems in electrostatics for which a solution can be obtained by adding image charges outside the region of in
Chapter 2 Introduction to electrostatics
2.1 Coulomb and Gauss Laws
We will restrict our discussion to the case of static electric and magnetic elds in a homogeneous, isotropic medium. In this case th
Fields and potential due to a surface electric dipole layer
A surface electric dipole layer is a neutral charge layer with an electric dipole moment per unit area directed perpendicular to the surface
Chapter 1
Introduction and Survey
1.1 Maxwells equations in a vacuum
1.1.1 Electrostatics The results of the numerous investigations of electromagnetic phenomena carried out during the 18th and 19th c
IV-30
The Dirac Delta Function, (x-xo)
Dirac Delta Function In one dimension, (x-xo) is defined to be such that: ma to b f(x) (x-xo)dx /
+ *0 if xo is not in [a,b]. *f(xo) if xo = a or b; *f(xo) if xo
Physics 411 Final
May 2002
SAMPLE
Name_ 1._(80 points) 2._(35 points) 3._(35 points) total ._(/150 points)
_ Dr = PEr 4 6 Dr, t = 4^k 1 O o _ 0 r, t D 1 r, t ? D 2 r, t 6 n = ar, t 4 6 Br, t = 0 /Br,
Physics 411 Final
Name_
cover p_1
1._(80 points) course ave _ 2._(35 points) course grade _ 3._(35 points) total ._(/150 points) _ 4 6 Dr, t = 4^k 1 O o _ 0 r, t Dr = PEr D 1 r, t ? D 2 r, t 6 n = ar,
Physics 411 Final
May 2001
SAMPLE
Name_ 1._(80 points) 2._(35 points) 3._(35 points) total ._(/150 points)
_ Dr = PEr 4 6 Dr, t = 4^k 1 O o _ 0 r, t D 1 r, t ? D 2 r, t 6 n = ar, t 4 6 Br, t = 0 /Br,
*Physics
411 EXAM COVER SHEET.*
You can write any formulas you like on the printed side of these sheets and bring them to the exam. _ Dr = PEr 4 6 Dr, t = 4^k 1 O o _ 0 r, t D 1 r, t ? D 2 r, t 6 n =
Syllabus for Physics 411: Electrodynamics I Text: Classical Electrodynamics, Third Edition, by J. D. Jackson, John Wiley & Sons, NY 1999 Electrostatics and Maxwells Equations: Coulombs law, Gauss law,