PHY 712 Electrodynamics

MWF 11-11:50 AM OPL 107 http://www.wfu.edu/~natalie/s04phy712/

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

Homework Assignments

Information about Computational Project

PHY 712 -- Assignment #1

January 16, 2002

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 21, 2004

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 23, 2004

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 30, 2004

Start reading Chap 2 in Jackson

PDF file for assignment 5

PHY 712 -- Assignment #6

February 2, 2004

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 #7

February 4, 2004

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 #8

February 4, 2004

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 #9

February 6, 2004

Read Chapter 3 in Jackson.

  1. PDF

PHY 712 -- Assignment #10

February 9, 2004

Finish reading Chap 3 in Jackson

  1. Work Problem #3.9 in Jackson.

PHY 712 -- Assignment #11

February 11, 2004

Start reading Chap 4 in Jackson

  1. Find the multiple moments associated with the charge distribution given in Problem Set #9.
  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 #12

February 18, 2004

Continue reading Chap 4 in Jackson

  1. Work Problem #4.9 in Jackson.

PHY 712 -- Assignment #13

March 3, 2004

Continue reading Chap 5 in Jackson

  1. Work Problem #5.13 in Jackson.

PHY 712 -- Assignment #14

March 5, 2004

Continue reading Chap 5 in Jackson

  1. Work Problem #5.14 in Jackson.

PHY 712 -- Assignment #15

March 15, 2004

Finish reading Chapter 5 in Jackson.

  1. PDF

PHY 712 -- Assignment #16

March 17, 2004

Start reading Chapter 6 in Jackson.

  1. PDF

PHY 712 -- Assignment #17

March 19, 2004

Finish reading Chap 6 in Jackson

  1. Work through the derivations in lecture notes #22 (PDF file). Extra credit for correcting any possible errors.

PHY 712 -- Assignment #18

March 29, 2004

Start reading Chap 7 in Jackson

  1. Work Problem 7.2 in Jackson.

PHY 712 -- Assignment #19

March 31, 2004

Continue reading Chap 7 in Jackson

  1. Consider the "Fresnel" equations 7.39 & 7.41 in Jackson.
    1. For μ = μ' and ,n ≠ n', show that the reflectivity does not vanish for s-polarization, but does vanish at the Brewster's angle for p-polarization.
    2. Show that the time averaged Poynting vector component normal to the surface (⟨S ⋅ z⟩) is continuous at the surface boundary (z=0).

PHY 712 -- Assignment #20

April 2, 2004

Continue reading Chap 7 in Jackson

  1. Work Problem 7.22a in Jackson.

PHY 712 -- Assignment #21

April 7, 2004

Start reading Chap 11 in Jackson

  1. Work Problem 11.5 in Jackson.

PHY 712 -- Assignment #22

April 12, 2004

Read 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 #23

April 14, 2004

Continue reading Chapter 11 in Jackson

  1. Read the lecture notes for Lecture #28.
    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).

    PHY 712 -- Assignment #24

    April 19, 2004

    Continue reading Chapter 14 in Jackson

    1. Problem # 14.4 in Jackson.

    PHY 712 -- Assignment #25

    April 21, 2004

    Continue reading Chap 14 in Jackson

    1. Consider Eq. 14.79 in Jackson. Plot the spectrum as a function of frequency and angle for various values of the parameters or in suitably parameterized form in order to appreciate the dependence on the critical frequency and on the angle of observation.
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