PHY 712 Electrodynamics

MWF 10-10:50 PM OPL 103 http://www.wfu.edu/~natalie/s08phy712/

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, 2008

Read Chapters I and 1 in Jackson.

  1. Jackson Problem #1.5

PHY 712 -- Assignment #2

January 23, 2008

Continue reading Chapters 1 in Jackson.

  1. Read the lecturenotes for the Ewald summation "Lecture Notes #2" (pdf file) . Check the result for the CsCl structure, using the maple script as a guide.
  2. 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 #2

January 25, 2008

Continue reading Chapters 1 in Jackson.

PDF file for HW problem

PHY 712 -- Assignment #4

January 28, 2008

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 #5". In particular, carry out several of the angular integrals that result in Eqs. 4-8 of the notes.
  2. Extra credit given for checking more non-trivial terms.

PHY 712 -- Assignment #5

January 30, 2008

Start reading Chap 2 in Jackson

  1. Work problem 2.16 in Jackson using the appropriate Green's function as discussed in class.

PHY 712 -- Assignment #6

February 1, 2008

Continue reading Chap 2 in Jackson

  1. Work problem 2.1 in Jackson.

PHY 712 -- Assignment #7

February 4, 2008

Continue reading Chap 2 in Jackson

  1. Work problem 2.20 (a) in Jackson. (Extra credit for working parts (b) and (c).)

PHY 712 -- Assignment #8

Febrary 6, 2008

Continue reading Chapter 3 in Jackson.

PDF file for HW problem

PHY 712 -- Assignment #9

February 11, 2008

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 Lecture Notes #10 & 11 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 #10

February 13, 2008

Finish reading Chapters 1-3 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 problems 2.16 and 1.24.

PHY 712 -- Assignment #11

Febrary 15, 2008

Continue reading Chapter 4 in Jackson.

  1. Work problem 4.7 in Jackson.

PHY 712 -- Assignment #12

Febrary 29, 2008

Continue reading Chapter 5 in Jackson.

  1. Work problem 5.14 in Jackson.

PHY 712 -- Assignment #13

March 3, 2008

Finish reading Chapter 5 in Jackson.

PDF file for HW problem

PHY 712 -- Assignment #14

March 5, 2008

Start reading Chapter 6 in Jackson.

PDF file for HW problem

PHY 712 -- Assignment #15

March 17, 2008

Continue reading Chapter 6 in Jackson.

PDF file for HW problem

PHY 712 -- Assignment #16

March 19, 2008

Start reading Chapter 7 in Jackson

  1. Use the results in section 7.3 to calculate the reflectance as a function of incident angle i. Assuming μ=μ'=&mu0 choose typical values of the refractive indicies n and n' and plot the reflectances as a function of i for the two polarizations showing the effects of Brewster's angle.

PHY 712 -- Assignment #17

March 24, 2008

Continue reading Chapter 7 in Jackson

  1. Work problem 7.2 in Jackson.

PHY 712 -- Assignment #18

March 26, 2008

Continue reading Chapter 7 in Jackson

  1. Work problem 7.22(a) in Jackson.

PHY 712 -- Assignment #19

March 28, 2008

Continue reading Chapter 7 in Jackson

  1. Work problem 7.4 in Jackson.

PHY 712 -- Assignment #20

March 31, 2008

Start reading Chapter 8 in Jackson

  1. Work problem 8.2(a) in Jackson.

PHY 712 -- Assignment #21

April 2, 2008

Finish reading Chapter 8 and start Chapter 11 in Jackson

  1. Find the form of the TM cavity fields within a rectangular parallelopiped cavity of dimension 0 ≤ x ≤ a, 0 ≤ y ≤ b, and 0 ≤ z ≤ c analogous to the fields we found in class for the TE modes.

PHY 712 -- Assignment #22

April 4, 2008

Continue reading Chapter 11 in Jackson

  1. Work problem 11.5 in Jackson.

PHY 712 -- Assignment #23

April 7, 2008

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 #24

April 18, 2008

Continue reading Chapter 14 in Jackson

  1. Work problem 14.12a in Jackson. For the same system, derive a general expression for the frequency distribution (as defined by Eq. 14.67) as a function of ω. Show that the result is related to a Bessel function when ω=ω0.

PHY 712 -- Assignment #25

April 21, 2008

Finish reading Chapter 14 and start Chapter 9 in Jackson

  1. Consider a synchrotron light source (such as the "Advanced Light Source" in Berkeley CA -- http://www-als.lbl.gov/als/aboutals/index.html) which has a ring radius of ρ=100m and the radiating electrons have energy E=2GeV. Determine the critical frequency ωc. With the help of Maple, plot the spectral intensity as a function of ω for θ=0 and for at least one other angle.

PHY 712 -- Assignment #26

April 23, 2008

Continue reading Chapter 9 in Jackson.

PDF file for HW problem

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