PHY 712 Electrodynamics

MWF 9-9:50 AM OPL 105 http://www.wfu.edu/~natalie/s18phy712/

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

Course schedule for Spring 2018

(Preliminary schedule -- subject to frequent adjustment.)
Lecture date
JDJ Reading
Topic
HW
Due date
Wed: 01/17/2018 No class Snow
1 Fri: 01/19/2018 Chap. 1 & Appen. Introduction, units and Poisson equation #1 01/26/2018
2 Mon: 01/22/2018 Chap. 1 Electrostatic energy calculations #2 01/26/2018
3 Wed: 01/24/2018 Chap. 1 Poisson's equation and Green's theorem #3 01/26/2018
4 Thu: 01/25/2018 Chap. 1 & 2 Poisson's equation in 2 and 3 dimensions
5 Fri: 01/26/2018 Chap. 1 & 2 Brief introduction to numerical methods #4 01/29/2018
6 Mon: 01/29/2018 Chap. 2 Method of image charges #5 01/31/2018
7 Wed: 01/31/2018 Chap. 2 & 3 Cylindrical and spherical geometries #6 02/02/2018
8 Fri: 02/02/2018 Chap. 3 & 4 Multipole analysis #7 02/07/2018
9 Mon: 02/05/2018 Chap. 4 Dipoles and Dielectrics #8 02/09/2018
10 Wed: 02/07/2018 Chap. 4 Dipoles and Dielectrics
11 Fri: 02/09/2018 Chap. 1-4 Review
12 Mon: 02/12/2018 Chap. 5 Magnetostatics #9 02/16/2018
13 Wed: 02/14/2018 Chap. 5 Magnetic dipoles and hyperfine interaction #10 02/19/2018
14 Fri: 02/16/2018 Chap. 5 Magnetic dipoles and dipolar fields #11 02/21/2018
15 Mon: 02/19/2018 Chap. 6 Maxwell's Equations #12 02/23/2018
16 Wed: 02/21/2018 Chap. 6 Electromagnetic energy and forces
17 Fri: 02/23/2018 Chap. 7 Electromagnetic plane waves
18 Mon: 02/26/2018 Chap. 7 Dielectric response of media Exam
19 Wed: 02/28/2018 Chap. 7 Complex dielectrics Exam
20 Fri: 03/02/2018 Chap. 1-7 Review Exam due
Mon: 03/05/2018 No class Spring Break
Wed: 03/07/2018 No class Spring Break
Fri: 03/09/2018 No class Spring Break
21 Mon: 03/12/2018 Chap. 8 Wave guides #13 03/16/2018
22 Wed: 03/14/2018 Chap. 9 Harmonic radiation #14 03/19/2018
23 Fri: 03/16/2018 Chap. 9 Harmonic radiation #15 03/21/2018
24 Mon: 03/19/2018 Chap. 9 & 10 Interference and Scattering #16 03/23/2018
25 Wed: 03/21/2018 Chap. 11 Special relativity #17 03/26/2018
26 Fri: 03/23/2018 Chap. 11 Special relativity #18 03/28/2018
27 Mon: 03/26/2018 Chap. 11 Special relativity
28 Wed: 03/28/2018 Chap. 14 Radiation from accelerated particles
Fri: 03/30/2018 No class Good Friday
29 Mon: 04/02/2018 Chap. 14 Synchrotron radiation #19 04/06/2018
30 Wed: 04/04/2018 Chap. 14 Synchrotron radiation #20 04/09/2018
31 Fri: 04/06/2018 Chap. 15 Radiation from collisions of charged particles
32 Mon: 04/09/2018 Chap. 13 Cherenkov radiation
33 Wed: 04/11/2018 Review
34 Fri: 04/13/2018 Review
35 Mon: 04/16/2018 Special topic: Superconductivity
36 Wed: 04/18/2018 Special topic: Superconductivity
37 Fri: 04/20/2018 Special topic: Optical properties of materials
38 Mon: 04/23/2018 Special topic: Optical properties of materials
39 Wed: 04/25/2018 Special topic: Optical properties of materials
Fri: 04/27/2018 Presentations I
Mon: 04/30/2018 Presentations II
Wed: 05/02/2018 Presentations III

PHY 712 -- Assignment #1

January 17, 2018

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 22, 2018

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 24, 2018
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 23 Jan 2018, 17:16.
No Title PDF VERSION
January 26, 2018
PHY 712 - Problem Set #4
Continue reading Chaper 1-3 in Jackson
  1. Consider a two-dimensional charge distribution of the form:
    ρ(x) = ρ0 sin⎛
    ⎝     		πx
    a
    		⎞
    ⎠     		sin⎛
    ⎝     		2 πy
    a
    		⎞
    ⎠     		,
    where ρ0 represents a density constant and a represents a length constant. In the problem, you are asked to determine the electrostatic potential Φ(x,y) for 0 ≤ x ≤ a and 0 ≤ y ≤ a, which satisfies the Poisson equation for the charge density ρ(x,y). and statisfies the boundary conditions Φ(0,y)=Φ(a,y) = Φ(x,0)=Φ(x,a)=0.
    1. Find the analytic form of the electrostatic potential Φ(x,y) for 0 ≤ x ≤ a and 0 ≤ y ≤ a.
    2. Using the finite difference method for the two grids discussed in class, find Φ(x,y) on the grid points.
    3. Using the finite element method for the two grids discussed in class, find Φ(x,y) on the grid points.
    4. Compare the accuracy of the numerical solutions for this example.


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On 25 Jan 2018, 16:22.

PHY 712 -- Assignment #5

January 29, 2018

Continue reading Chap. 2 in Jackson.

  1. Eq. 2.5 was derived as the surface change density on a sphere of radius a due to a charge q placed at a radius y > a outside the sphere. Determine the total surface charge on the sphere surface.
  2. Now consider the same system except assume y < a representing the charge q being placed inside the sphere. What is the surface charge density and the total surface charge in this case?
No Title
January 31, 2018
PDF VERSION
PHY 712 - Problem Set #6
Continue reading Chapters 1-3 in Jackson
  1. Consider a static charge distribution of cylindrical symmetry extended uniformly along the z-axis. In term the cylindrical radius ρ and angle ϕ the charge density is given by
    d(ρ,ϕ) = ⎧
    ⎪
    ⎨
    ⎪
    ⎩
    0
    for         0 ≤ ρ < a
    d0
    for         a ≤ ρ ≤ b
    0
    for         ρ > b
    		(1)
    Here d0 represents a charge density constant and a and b represent constant lengths with b > a. Find the corresponding electrostatic potential Φ(ρ,ϕ) and electrostatic electric field which are well behaved for ρ→ ∞, by directly solving the differential equation or by using the appropriate Green's function.


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On 30 Jan 2018, 21:42.

PHY 712 -- Assignment #7

February 2, 2018

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 #8

February 5, 2018

Continue reading Chapter 4 in Jackson .

  1. Supply some of the detailed steps that result in Eq. 4.20 of Jackson or the equivalent equations in the lecture notes.

PHY 712 -- Assignment #9

February 12, 2018

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 #10

February 14, 2018

Continue reading Chapter 5 in Jackson .

  1. Work problem #5.13.

PHY 712 -- Assignment #11

February 16, 2018

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.

PHY 712 -- Assignment #12

February 19, 2018

Start reading Chapter 6 in Jackson .

  1. Consider Maxwell's equations in vacuum as given on slide 5 of the lecture notes. Suppose that in a region of space where there are no charge or current sources, the E field is purely in the x-direction with the form Ex(r,t)=K sin(k(z-ct)), where K and k are given constants and c denotes the speed of light in vacuum. Find the corresponding B field, including its direction and its functional form.
No Title
March 12, 2018
PDF VERSION
PHY 712 - Problem Set # 13
Start reading Chapter 8 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 10 Mar 2018, 21:28.

PHY 712 -- Assignment #14

March 14, 2018

Start reading Chapter 9 in Jackson .

  1. Fill in some of the details of the derivations of the dipolar radiation potentials on slides 17-20 of the lecture notes for Lecture 22. Extra credit for correcting typos.

PHY 712 -- Assignment #15

March 16, 2018

Continue reading Chapter 9 in Jackson .

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

PHY 712 -- Assignment #16

March 19, 2018

Finish reading Chapters 9 and 10 in Jackson .

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

PHY 712 -- Assignment #17

March 21, 2018

Start reading Chap. 11 in Jackson .

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

PHY 712 -- Assignment #18

March 23, 2018

Continue reading Chap. 11 in Jackson .

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

PHY 712 -- Assignment #19

April 2, 2018

Continue reading Chap. 14 in Jackson .

  1. Supply some of the intermediate steps in deriving the synchrotron intensity expression given by Eq. 14.79 in Jackson or equivalently on slide 11 of the lecture notes for Lecture 29.

PHY 712 -- Assignment #20

April 4, 2018

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 its total energy. Evaluate the expression for an electron with total energy 200 GeV in a synchroton of radius ρ=103 m.
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Last modfied: Saturday, 07-Jan-2017 16:38:51 EST