PHY 712 Electrodynamics

MWF 10-10:50 AM OPL 107 http://www.wfu.edu/~natalie/s14phy712/

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

Course schedule for Spring 2014

(Preliminary schedule -- subject to frequent adjustment.) Please note that makeup lectures (indicated in red) are scheduled for Tuesdays or Thursdays at 11 AM - 12:15 PM in Olin 107,
while makeup lectures (indicated in green) are scheduled for
Mondays, Wednesdays, or Fridays at 9 AM - 10:00 AM in Olin 102.
Lecture date
JDJ Reading
Topic
Assign.
Due date
1 Wed: 01/15/2014 Chap. 1 Introduction, units and Poisson equation #1 01/31/2014
2 Thu: 01/16/2014 Chap. 1 Electrostatic energy calculations #2 01/31/2014
3 Fri: 01/17/2014 Chap. 1 Poisson equation and Green's theorm #3 01/31/2014
Mon: 01/20/2014 MLK Holiday - no class
4 Wed: 01/22/2014 Chap. 1 Green's functions for cartesian coordinates #4 01/31/2014
5 Thu: 01/23/2014 Chap. 1 Brief introduction to numerical methods #5 01/31/2014
6 Fri: 01/24/2014 Chap. 2 Method of images #6 01/31/2014
Mon: 01/27/2014 NAWH out of town - no class
Wed: 01/29/2014 NAWH out of town - no class
7 Fri: 01/31/2014 Chap. 3 Cylindrical and spherical geometries #7 02/05/2014
8 Mon: 02/03/2014 Chap. 4 Multipole analysis of charge distributions #8 02/05/2014
9 Wed: 02/05/2014 Chap. 4 Dipoles and dielectrics #9 02/07/2014
10 Fri: 02/07/2014 Chap. 4 Dipoles and dielectrics #10 02/10/2014
11 Mon: 02/10/2014 Chap. 5 Magnetostatics #11 02/12/2014
12 Wed: 02/12/2014 Chap. 5 Magnetostatics #12 02/14/2014
Fri: 02/14/2014 Class cancelled because of weather
13 Mon: 02/17/2014 Chap. 5 Magnetostatics #13 02/28/2014
14 Mon: 02/17/2014 Chap. 6 Maxwell's equations #14 02/28/2014
15 Wed: 02/19/2014 Chap. 6 Electromagnetic energy and force #15 02/28/2014
16 Fri: 02/21/2014 Chap. 7 Electromagnetic plane waves #16 02/28/2014
17 Fri: 02/21/2014 Chap. 7 Dynamic dielectric media and their effects #17 02/28/2014
Mon: 02/24/2014 No class -- NAWH out of town
Wed: 02/26/2014 No class -- NAWH out of town
18 Fri: 02/28/2014 Chap. 7 Complex dielectrics; TEM modes
Mon: 03/03/2014 APS Meeting Take-home exam (no class meeting)
Wed: 03/05/2014 APS Meeting Take-home exam (no class meeting)
Fri: 03/07/2014 APS Meeting Take-home exam (no class meeting)
Mon: 03/10/2014 Spring Break
Wed: 03/12/2014 Spring Break
Fri: 03/14/2014 Spring Break
19 Mon: 03/17/2014 Chap. 8 Wave guides;Take-home exam due #18 3/21/2014
20 Wed: 03/19/2014 Chap. 9 Sources of Electromagnetic Waves #19 3/21/2014
21 Fri: 03/21/2014 Chap. 9 Sources of Electromagnetic Waves #20 3/28/2014
22 Mon: 03/24/2014 Chap. 11 Special Theory of Relativity #21 3/28/2014
23 Wed: 03/26/2014 Chap. 11 Special Theory of Relativity #22 3/28/2014
24 Fri: 03/28/2014 Chap. 11 Special Theory of Relativity #23 4/04/2014
25 Mon: 03/31/2014 Chap. 14 Radiation from moving charges #24 4/04/2014
26 Wed: 04/02/2014 Chap. 14 Radiation from moving charges #25 4/04/2014
27 Fri: 04/04/2014 Chap. 14 Radiation from moving charges #26 4/11/2014
28 Mon: 04/07/2014 Chap. 14 Radiation from moving charges #27 4/11/2014
29 Wed: 04/09/2014 Chap. 15 Radiation due to collision processes #28 4/16/2014
30 Fri: 04/11/2014 Chap. 13 Cherenkov radiation #29 4/16/2014
31 Mon: 04/14/2014 Special topic -- E&M of superconductivity
32 Wed: 04/16/2014 Special topic -- E&M of superconductivity
Fri: 04/18/2014 Good Friday Holiday -- no class
33 Mon: 04/21/2014 Special topics and review
34 Wed: 04/23/2014 Special topics and review
35 Fri: 04/25/2014 Special topics and review
Mon: 04/28/2014 Presentations Part I
Wed: 04/30/2014 Presentations Part II

PHY 712 -- Assignment #1

January 15, 2014

Read Chapters I and 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 16, 2014

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
January 17, 2014
PDF Version
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.


File translated from TEX by TTH, version 4.01.
On 16 Jan 2014, 23:50.

PHY 712 -- Assignment #4

January 22, 2014

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, 2014

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. 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 24, 2014

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 31, 2014

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

February 3, 2014

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 5, 2014

Continue reading Chapter 4 in Jackson .

  1. Work problem #4.9 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.

PHY 712 -- Assignment #10

February 7, 2014

Finish 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. Comment on other non-vanishing higher multipole moments qlm.

PHY 712 -- Assignment #11

February 10, 2014

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 the current is along the z-axis with the magnitude of J0 for ρ ≤ a and zero for ρ > a, where ρ denotes the radial parameter of the natural cylindrical coordinates of the system.
    1. Find the vector potential (A) for all ρ.
    2. Find the magnetic flux field (B) for all ρ.

PHY 712 -- Assignment #12

February 12, 2014

Continue reading Chapter 5 in Jackson .

  1. Work problem #5.13.

PHY 712 -- Assignment #13

February 17, 2014

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 #14

February 17, 2014

Start reading Chapter 6 in Jackson .

  1. Supply the intermediate steps to derive Eq. 6.105.

PHY 712 -- Assignment #15

February 19, 2014

Finish reading Chapter 6 in 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:

    Here H0 denotes a real amplitude, and the parameter k is assumed to be real and equal to

    1. Show that this wave satisfies the sourceless Maxwell's equations.
    2. Find the form of the time-averaged Poynting vector

      for this electromagnetic wave.

PHY 712 -- Assignment #16

February 21, 2014

Continue 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

February 21, 2014

Continue reading Chapter 7 in Jackson .

  1. Work problem 7.22(a) in Jackson .

PHY 712 -- Assignment #18

March 17, 2014

Start reading Chapter 8 in Jackson .

  1. Work problem 8.2(a) in Jackson .

PHY 712 -- Assignment #19

March 19, 2014

Continue reading Chapter 8 in Jackson .

  1. Following section 8.4 of Jackson which works out the form of the electromagnetic fields for the TE1,0 mode. Find the corresponding fields for the TM mode with the lowest cutoff frequency.

PHY 712 -- Assignment #20

March 21, 2014

Start reading Chapter 9 in Jackson .

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

PHY 712 -- Assignment #21

March 24, 2014

Start reading Chapter 11 in Jackson .

  1. Work out the details of the derivation of the velocity transformation equations 11.31 in Jackson.

PHY 712 -- Assignment #22

March 26, 2014

Continue reading Chap. 11 in Jackson .

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

PHY 712 -- Assignment #23

March 26, 2014

Continue reading Chap. 11 in Jackson .

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

PHY 712 -- Assignment #24

March 28, 2014

Continue reading Chap. 11 in Jackson .

  1. Using the Lienard-Wiechert fields, verify the equations for the electric and magnetic fields given by Eq. 11.152 in Jackson. Some of the details are given in the lecture notes for Lecture 24.

PHY 712 -- Assignment #25

March 31, 2014

Start reading Chap. 14 in Jackson .

  1. In class we assumed that the electric field E produced by a moving charge at the field point R has the relationship

    Is this an approximation or is it exact. Show the algebraic justification for your answer.

PHY 712 -- Assignment #26

April 2, 2014

Continue reading Chap. 14 in Jackson .

  1. "Prove" equation 14.66 in Jackson.

PHY 712 -- Assignment #27

April 7, 2014

Continue reading Chap. 14 in Jackson .

  1. Consider an electron moving at constant velocity 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 #28

April 9, 2014

Start reading Chap. 15 in Jackson .

  1. Work problem 15.2 in Jackson.

PHY 712 -- Assignment #29

April 11, 2014

Read sections of Chap. 13 in Jackson .

  1. Examine the derivation of the scalar and vector potentials for a charged particle moving in a medium discussed in slides 5-8 of Lecture 30, supplying the intermediate steps.
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Last modfied: Wednesday, 15-Jan-2014 09:01:56 EST