PHY 712 Electrodynamics

MWF 9-9:50 AM OPL 107 http://www.wfu.edu/~natalie/s05phy712/

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

Homework Assignments

Information about Computational Project

PHY 712 -- Assignment #1

January 12, 2005

Read Chapters I and 1 in Jackson.

  1. Jackson Problem #1.5

PHY 712 -- Assignment #2

January 16, 2004

Complete Chapter 1 in Jackson.

  1. PDF

PHY 712 -- Assignment #3

January 19, 2005

Continue Reading Chap 1 in Jackson

  1. Complete the proof of the "mean value theorm" for a solution of the Laplace equation, following "Lecture Notes #3". In particular, carry out several of the angular integrals that result in Eqs. 9-13 of the notes.
  2. Extra credit given for checking more non-trivial terms.

PHY 712 -- Assignment #4

January 21, 2005

Continue reading Chap 1 in Jackson

  1. Read the lecturenotes for the Ewald summation "Lecture Notes #4" (pdf file) . Check the result for the CsCl structure, using the maple script as a guide.
  2. Extra credit -- Evaluate the interaction energy for another crystal form such as the NaCl structure, for example. If you are interested in further study in this area, you might want to use a fortran90 code which is also available -- ewaldsum.f90. sample run.

PHY 712 -- Assignment #5

January 24, 2005

Continue reading Chapter 1 in Jackson.

  1. Jackson Problem #1.4

PHY 712 -- Assignment #6

January 26, 2005

Start reading Chap 2 in Jackson

PDF file for assignment 6

PHY 712 -- Assignment #7

January 28, 2005

Continue reading Chap.2 in Jackson

  1. Consider a two-dimensional system for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 . Find a solution to the Laplace equation which satisfies the conditions Φ(x=0,y)=0, Φ(x=1,y)=0, Φ(x,y=0)=V0, and Φ(x,y=1)=V0.
  2. Plot your solution as a function of (x,y) using Maple.

PHY 712 -- Assignment #8

January 31, 2005

Complete 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 Lecture Notes #8&9 and solve 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 4πε0Φ are calculated directly. Also note that in these units, ρ = 1. These can be compared to the exact results in part (c).

PHY 712 -- Assignment #9

February 2, 2005

Finish reading Chap 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 of 2.16 and 1.24.
  2. Extra credit: Work Problem #2.16 in Jackson so that you can make a quantitative comparison with the finite element results.

PHY 712 -- Assignment #10

February 7, 2005

Begin reading Chapter 3 Jackson.

  1. PDF

PHY 712 -- Assignment #11

February 9, 2005

Finish reading Chap 3 in Jackson

  1. Work Problem #3.9 in Jackson.

PHY 712 -- Assignment #12

February 14, 2005

Start reading Chap 4 in Jackson

  1. Find the multiple moments associated with the charge distribution given in Problem Set #10.
  2. Find the lowest order multipole moment associated with the charge distribution given in Fig. (b) for Problem #4.1 in Jackson.

PHY 712 -- Assignment #13

February 16, 2005

Continue reading Chap 4 in Jackson

  1. Work Problem #4.9 in Jackson.

PHY 712 -- Assignment #14

February 18, 2005

Finish reading Chap 4 in Jackson

  1. Work Problem #4.11 or 4.12 in Jackson.

PHY 712 -- Assignment #15

March 14, 2005

Continue reading Chapter 6 Jackson.

  1. PDF

PHY 712 -- Assignment #16

March 16, 2005

Continue reading Chap.6 in Jackson

  1. Problem 6.9 in Jackson.
  2. (Extra credit: problem 6.10)

PHY 712 -- Assignment #17

March 18, 2005

Finish reading Chap.6 in Jackson

  1. Work through the derivations in lecture notes #23 (PDF file). Extra credit for correcting any possible errors.

PHY 712 -- Assignment #18

March 28, 2005

Start reading Chap 7 in Jackson

  1. Work Problem 7.2 in Jackson.

PHY 712 -- Assignment #19

March 30, 2005

Continue reading Chap 7 in Jackson

Consider the lecture notes on Reflection and refraction from an isotropic medium.

  1. Work through the derivations to make sure they make sense.
  2. Determine how the anisotropic dielectric tensor κ is related to the refractive indices n and n' of Equations 7.38 and 7.39 in Jackson. In particular, determine the parameters nx and ny for the case that the medium is isotropic.

PHY 712 -- Assignment #20

April 1, 2005

Finish reading Chap 7 in Jackson

  1. Work Problem 7.22a in Jackson.

PHY 712 -- Assignment #21

April 6, 2005

Continue reading Chapter 8 Jackson.

  1. PDF

PHY 712 -- Assignment #22

April 8, 2005

Finish reading Chap 8 in Jackson

  1. Work Problem 8.4 in Jackson.

PHY 712 -- Assignment #23

April 11, 2005

Continue reading Chap 11 in Jackson

  1. Work Problem 11.5 in Jackson.

PHY 712 -- Assignment #24

April 11, 2005

Continue reading Chapter 11 in Jackson

  1. Verify Eq. 11.148 in Jackson, showing the relationship between the electric and magnetic fields in two frames of reference moving at a velocity βc relative to each other, by evaluating the matrix multiplication of Eq. 11.147.

PHY 712 -- Assignment #25

April 15, 2005

Continue reading Chapter 11 in Jackson and the lecture notes for Lecture #32.

  1. Convince yourself that the electric and magnetic fields due to a charge moving at constant velocity derived using the Lorentz transformations are equivalent are equivalent the the fields derived from the Liénard-Wiechert potentials as measured in a stationary frame of reference.
  2. Do the same analysis in the moving frame of reference (in which the charged particle is at rest).
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