PHY 712 Electrodynamics

MWF 10-10:50 PM OPL 103 http://www.wfu.edu/~natalie/s07phy712/

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

Homework Assignments

Information about Computational Project

PHY 712 -- Assignment #1

January 17, 2007

Read Chapters I and 1 in Jackson.

  1. Jackson Problem #1.5

PHY 712 -- Assignment #2

January 19, 2007

Complete Chapter 1 in Jackson.

  1. PDF

PHY 712 -- Assignment #3

January 22, 2007

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. 4-8 of the notes.
  2. Extra credit given for checking more non-trivial terms.

PHY 712 -- Assignment #4

January 24, 2007

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 29, 2007

Start reading Chapter 2 in Jackson.

  1. PDF

PHY 712 -- Assignment #6

January 31, 2007

Continue reading Chapter 2 in Jackson.

  1. Work problem 2.15 in Jackson.

PHY 712 -- Assignment #7

February 2, 2007

Continue reading Chapter 2 in Jackson.

  1. Work problem 2.16 in Jackson.

PHY 712 -- Assignment #8

February 12, 2007

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 #11 \& 12 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 4πε0 Φ 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 14, 2007

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 #10

February 16, 2007

Continue reading Chapter 3 in Jackson.

  1. PDF

PHY 712 -- Assignment #11

February 19, 2007

Start reading Chapter 4 in Jackson.

  1. Consider Problem 4.1 in Jackson. Choose either Fig. (a) or (b). Write expressions for the largest multipole contribution to the potential in cartesian and spherical-polar representations.

PHY 712 -- Assignment #12

February 21, 2007

Continue reading Chapter 4 in Jackson

  1. Work Problem #4.7(a) in Jackson. (Extra credit for working parts (b) and (c).)

PHY 712 -- Assignment #13

February 23, 2007

Continue reading Chapter 4 in Jackson

  1. Work Problem 4.8 of Jackson.

PHY 712 -- Assignment #14

February 26, 2007

Finish reading Chapter 4 in Jackson

  1. Find the molecular susceptibility of pentane using the data in Problem 4.11 of Jackson.

PHY 712 -- Assignment #15

February 28, 2007

Continue reading Chapter 5 in Jackson.

  1. PDF

PHY 712 -- Assignment #16

March 2, 2007

Continue reading Chapter 5 in Jackson.

  1. In Lecturenotes 15 & 16, we derived expressions for A(r) for an electron in a particular excited state of a H atom. Pick another excited state and evaluate the corresponding vector potential A(r).

PHY 712 -- Assignment #17

March 19, 2007

Finish reading Chapter 5 in Jackson

  1. Work Problem 5.14 of Jackson.

PHY 712 -- Assignment #18

March 21, 2007

Continue reading Chapter 6 in Jackson.

  1. PDF

PHY 712 -- Assignment #19

March 23, 2007

Finish reading Chapter 6 in Jackson

  1. Consider Equation 8.46 in Jackson which describes an electromagnetic field in a "wave guide" which has permittivity ε and permeability μ, propagating along the z-axis and confined for 0 ≤ x ≤ a and 0 ≤ y ≤ a. This wave satisfies Maxwell's equations within the waveguide with the wavevector k given by Eq. 8.39 and the cut-off frequency given in Eq. 8.45. Here H0 is a given constant. Find the time-averaged Poynting vector for this field within the waveguide.

PHY 712 -- Assignment #20

March 26, 2007

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 #21

March 28, 2007

Continue reading Chapter 7 in Jackson

  1. Work problem 7.22(a) in Jackson.

PHY 712 -- Assignment #22

April 9, 2007

Continue reading Chap. 11 in Jackson

  1. Work problem 11.5 in Jackson.

PHY 712 -- Assignment #23

April 11, 2007

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 13, 2007

Continue reading Chapter 11 in Jackson

  1. Work through the details of lecture notes 29 & 30 to verify to your own satisfaction that the electric and magnetic fields generated by a particle moving at constent velocity are the same when determined by the Lorentz transformation or from the Liénart-Wiechert potentials.

PHY 712 -- Assignment #25

April 18, 2007

Start reading Chapter 14 in Jackson

  1. Work problem 14.4 in Jackson.

PHY 712 -- Assignment #26

April 23, 2007

Finish reading Chapter 14 in Jackson

  1. Work problem 14.12 in Jackson.

PHY 712 -- Assignment #27

April 27, 2007

Complete Chap. 8 in Jackson

  1. Work problem 8.2(a) in Jackson. First determine the forms of the electric and magnetic fields in the dielectric, assuming that they are uniform in the azimuthal direction and propagating along the cable direction.
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