PHY 712 Electrodynamics

MWF 9-9:50 AM OPL 103 http://www.wfu.edu/~natalie/s17phy712/

Instructor: Natalie Holzwarth Phone:758-5510Office:300 OPL e-mail:natalie@wfu.edu

Course schedule for Spring 2017

(Preliminary schedule -- subject to frequent adjustment.)
Lecture date
JDJ Reading
Topic
HW
Due date
1 Wed: 01/11/2017 Chap. 1 Introduction, units and Poisson equation #1 01/18/2017
2 Fri: 01/13/2017 Chap. 1 Electrostatic energy calculations #2 01/18/2017
Mon: 01/16/2017 MLK Holiday - no class
3 Wed: 01/18/2017 Chap. 1 Poisson equation and Green's theorem #3 01/20/2017
4 Fri: 01/20/2017 Chap. 1 and 2 Poisson equation in 2 and 3 dimensions #4 01/23/2017
5 Mon: 01/23/2017 Chap. 1 and 2 Brief introduction to grid solution methods #5 01/25/2017
6 Wed: 01/25/2017 Chap. 2 Method of images #6 01/27/2017
7 Fri: 01/27/2017 Chap. 3 Cylindrical and spherical geometries #7 01/30/2017
8 Mon: 01/30/2017 Chap. 3 & 4 Multipole analysis #8 02/01/2017
9 Wed: 02/01/2017 Chap. 4 Dipoles and dielectrics #9 02/03/2017
10 Fri: 02/03/2017 Chap. 4 Dipoles and dielectrics #10 02/06/2017
11 Mon: 02/06/2017 Chap. 5 Magnetostatics #11 02/08/2017
12 Wed: 02/08/2017 Chap. 5 Magnetostatics and the Hyperfine Interaction #12 02/10/2017
13 Fri: 02/10/2017 Chap. 5 Magnetic dipoles and dipolar fields #13 02/13/2017
14 Mon: 02/13/2017 Chap. 6 Maxwell's Equations #14 02/15/2017
15 Wed: 02/15/2017 Chap. 6 Electromagnetic energy and forces #15 02/17/2017
16 Fri: 02/17/2017 Chap. 7 Electromagnetic plane waves #16 02/20/2017
17 Mon: 02/20/2017 Chap. 7 Dielectric media
18 Wed: 02/22/2017 Chap. 7 Complex dielectrics
19 Fri: 02/24/2017 Chap. 1-7 Review -- Take home exam distributed
20 Mon: 02/27/2017 Chap. 8 Wave guides Exam
21 Wed: 03/01/2017 Chap. 8 Wave guides Exam
22 Fri: 03/03/2017 Chap. 8 Wave guides Exam Due
Mon: 03/06/2017 Spring break - no class
Wed: 03/08/2017 Spring break - no class
Fri: 03/10/2017 Spring break - no class
Mon: 03/13/2017 APS Meeting - no class
Wed: 03/15/2017 APS Meeting - no class
Fri: 03/17/2017 APS Meeting - no class
23 Mon: 03/20/2017 Chap. 9 Sources of Radiation #17 03/24/2017
24 Wed: 03/22/2017 Chap. 9 & 10 Radiation and Scattering
25 Fri: 03/24/2017 Chap. 9 & 10 Radiation and Scattering #18 03/27/2017
26 Mon: 03/27/2017 Chap. 11 Special relativity #19 03/31/2017
27 Wed: 03/29/2017 Chap. 11 Special relativity
28 Fri: 03/31/2017 Chap. 11 Special relativity #20 04/3/2017
29 Mon: 04/03/2017 Chap. 14 Radiation from moving charges #21 04/5/2017
30 Wed: 04/05/2017 Chap. 14 Radiation from moving charges #22 04/7/2017
31 Fri: 04/07/2017 Chap. 14 Radiation from moving charges #23 04/10/2017
32 Mon: 04/10/2017 Chap. 15 Radiation from collisions
33 Wed: 04/12/2017 Chap. 13 Cherenkov radiation
Fri: 04/14/2017 Good Friday Holiday -- no class
34 Mon: 04/17/2017 Superconductivity
35 Wed: 04/19/2017 Superconductivity
36 Fri: 04/21/2017 Review
Mon: 04/24/2017 Presentations I
Wed: 04/26/2017 Presentations II

PHY 712 -- Assignment #1

January 11, 2017

Read Chapters I and 1 and Appendix 1 in Jackson.

  1. Jackson Problem #1.5. Be careful to take into account the behavior of Φ(r) for r-->0.

PHY 712 -- Assignment #2

January 13, 2017

Continue reading Chap. 1 in Jackson.

  1. Using the Ewald summation methods developed in class, find the electrostatic interaction energy of a NaCl lattice having a cubic lattice constant a. Check that your result does not depend of the Ewald parameter η. You are welcome to copy (and modify) the maple file used in class. A FORTRAN code is also available.
No Title PDF VERSION
January 18, 2017
PHY 712 - Problem Set #3
Continue reading Chaper 1 & 2 in Jackson
  1. Consider a one-dimensional charge distribution of the form:
    ρ(x) = ⎧
    ⎪
    ⎨
    ⎪
    ⎩
    0     
    for  
    x < −a/2
    ρ0 x/a     
    for   
    −a/2 ≤ x ≤ a/2
    0       
    for   
    x > a/2,
    where ρ0 and a are constants.
    1. Solve the Poisson equation for the electrostatic potential Φ(x) with the boundary conditions [(d Φ)/dx](−a/2) = 0 and [(d Φ)/dx](a/2) = 0.
    2. Find the corresponding electrostatic field E(x).
    3. Plot Φ(x) and E(x).
    4. Discuss your results in terms of elementary Gauss's Law arguments.


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On 17 Jan 2017, 12:06.

PHY 712 -- Assignment #4

January 20, 2017

Continue reading Chap. 1 & 2 in Jackson.

  1. Jackson Problem #2.16. Note: as long as you show that your result is equivalent to the result given in the text, it is not necessary to put your result in the identical form.

PHY 712 -- Assignment #5

January 23, 2017

Review last section of Chap 1 in Jackson .

  1. Work Problem #1.24 in Jackson. Note that you can set this up as a linear algebra problem as we did in the lecture notes and can be solved directly for the three unknown values in Maple or Mathematica. It is not then necessary to use iteration methods. Also note that it is convenient to multiply the entire equation by 4πε0 so that the values of 4πε0 Φ are calculated directly. Also note that in these units, ρ = 1. These can be compared to the exact results in part (c) and to the series solution of the same system in Jackson problem 2.16.

PHY 712 -- Assignment #6

January 25, 2017

Finish reading Chapters 1-2 in Jackson .

  1. Work Problem #2.30 in Jackson after correcting the equation for SI units. Choose ρ=1 in these units and compare your results with those from previous homework sets involving Jackson's problems 2.16 and 1.24.

PHY 712 -- Assignment #7

January 27, 2017

Continue reading Chapter 3 in Jackson .

  1. Work Problem #3.9 in Jackson. Work out a general expression for the potential Φ(ρ,φ,z); then evaluate the unknown constants for the particular boundary potential

    Φ(ρ=b,φ,z)=V(φ,z)= V0 sinh(z/L) sinh(1-z/L),

    where V0 and L are given potential and length constants, respectively and "b" is the cylinder radius given in the problem.

PHY 712 -- Assignment #8

January 30, 2017

Complete reading Chapter 3 and start Chapter 4 in Jackson .

  1. Consider the charge density of an electron bound to a proton in a hydrogen atom -- ρ(r) = (1/πa03) e-2r/a0, where a0 denotes the Bohr radius. Find the electrostatic potential Φ(r) associated with ρ(r). Compare your result to HW#1.

PHY 712 -- Assignment #9

February 1, 2017

Continue reading Chapter 4 in Jackson .

  1. Work problem #4.1 (parts a and b), in Jackson. For each case, find the lowest order multipole moment qlm and its cartesian equivalent.

PHY 712 -- Assignment #10

February 3, 2017

Finish reading Chapter 4 in Jackson .

  1. Work problem #4.9(a) in Jackson. In order to slightly simplify the analysis, you can assume that the point charge is in the z direction so that you can use the expansion given in equation 3.33 instead of a full spherical harmonic expansion. Check your result in the limits ε/ε0 → 1 and ε/ε0 → ∞.

PHY 712 -- Assignment #11

February 6, 2017

Start reading Chapter 5 in Jackson .

  1. Consider an infinitely long wire with radius a, oriented along the z axis. There is a steady uniform current inside the wire. Specifically, in terms of ρ the radial parameter of the cylindrical coordinates of the system the current density is j(ρ)=J0 , where J0 is a constant vector along the z-axis, for ρ ≤ a and zero otherwise.
    1. Find the vector potential (A) for all ρ.
    2. Find the magnetic flux field (B) for all ρ.

PHY 712 -- Assignment #12

February 8, 2017

Continue reading Chapter 5 in Jackson .

  1. Work problem #5.13.

PHY 712 -- Assignment #13

February 10, 2017

Finish reading Chapter 5 in Jackson .

  1. Work through the details of the magnetic shielding example given in Section 5.12 of your textbook. Verify Eq. 5.121 and 5.122.
No Title PDF VERSION
February 13, 2017
PHY 712 - Problem Set #14
Start reading Chaper 6 in Jackson
  1. This problem relates to the evaluation of the retarded time Green's function for a charged particle as given in Eq. 6.44 of Jackson and in the lecture notes. Suppose that the particle trajectory is given by
    Rq(t′) = R0+v0 t′,
    where R0 and v0 are fixed constant position and velocity vectors respectively. Write an expression for the integral
    ⌠
    ⌡     		∞

    −∞ 
    		 dt′  f(t′) δ(t′−(t−|r− Rq(t′)|/c) ),
    expressing your answer in terms of the arbitrary function f and the field time t and position r.


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No Title PDF VERSION
February 15, 2017
PHY 712 - Problem Set # 15
Finish reading Chapter 6 and start reading Chapter 7 of Jackson.
  1. Suppose that an electromagnetic wave of pure (real) frequency ω is traveling along the z-axis of a wave guide having a square cross section with side dimension a composed of a medium having a real permittivity constant ϵ and a real permeability constant μ. Suppose that the wave is known to have the form:
    E(r,t) = ℜ⎧
    ⎨
    ⎩     		H0 ei k z − i ωt (i μω) a
    π
    		 sin⎛
    ⎝     		πx
    a
    		⎞
    ⎠
    ^
    y
     
    		⎫
    ⎬
    ⎭

    H(r,t) = ℜ⎧
    ⎨
    ⎩     		H0 ei k z − i ωt ⎡
    ⎣     		−ik a
    π
    		 sin⎛
    ⎝     		πx
    a
    		⎞
    ⎠
    ^
    x
     
    		 + cos⎛
    ⎝     		πx
    a
    		⎞
    ⎠
    ^
    z
     
    		⎤
    ⎦     		⎫
    ⎬
    ⎭     		.
    Here H0 denotes a real amplitude, and the parameter k is assumed to be real and equal to
    k ≡   ⎛
    √
    μϵω2 − ⎛
    ⎝     		π
    a
    		⎞
    ⎠     		2

     
     
    		 ,
    for μϵω2 > ([(π)/a] )2.
    1. Show that this wave satisfies the sourceless Maxwell's equations.
    2. Find the form of the time-averaged Poynting vector
      〈S 〉avg ≡ 1
      2
      		 ℜ{ E(r,t)×H*(r,t) }
      for this electromagnetic wave.


File translated from TEX by TTH, version 4.01.
On 13 Feb 2017, 22:27.

PHY 712 -- Assignment #16

February 17, 2017

Start reading Chapter 7 in Jackson .

  1. Consider the reflectivity of a plane polarized electromagnetic wave incident from air (n=1) on a material with refractive index n'=1.5 at an angle of incidence i, Plot the reflectance

    R(i)=|E"0/E0|2

    as a function of i for both cases of polarization (E0 in the plane of incidence or perpendicular to the plane of incidence). What is the qualitative difference between the two cases?

PHY 712 -- Assignment #17

March 20, 2017

Start reading Chapter 9 in Jackson .

  1. Work problem # 9.10(b) in Jackson.

PHY 712 -- Assignment #18

March 24, 2017

Finish reading Chapters 9 and 10 in Jackson .

  1. Work problem # 9.16(a) in Jackson.

PHY 712 -- Assignment #19

March 27, 2015

Start reading Chap. 11 in Jackson .

  1. Work problem 11.5 at the end of Chapter 11 in Jackson.

PHY 712 -- Assignment #20

March 31, 2017

Continue reading Chap. 11 in Jackson .

  1. Verify Eq. 11.148 in Jackson by evaluating the transformation equations.

PHY 712 -- Assignment #21

April 3, 2017

Continue reading Chap. 14 in Jackson .

  1. "Prove" equation 14.66 in Jackson.

PHY 712 -- Assignment #22

April 5, 2017

Continue reading Chap. 14 in Jackson .

  1. Consider an electron moving at constant speed βc ≈ c in a circular trajectory of radius ρ. Its total energy is E= γ m c2. Determine the ratio of the energy lost during one full cycle to the total energy. Evaluate the expression for an electron with total energy 200 GeV in a synchroton of radius ρ=103 m.

PHY 712 -- Assignment #23

April 7, 2017

Continue reading Chap. 14 in Jackson .

  1. Supply some of the intermediate steps to derive the Thompson formula for scattering of radiation by a free electron in Eq. 14.125 in Jackson.
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Last modfied: Saturday, 07-Jan-2017 16:38:51 EST