PHY 712 Electrodynamics

MWF 12-12:50 PM OPL 107 http://www.wfu.edu/~natalie/s06phy712/

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

Homework Assignments

Information about Computational Project

PHY 712 -- Assignment #1

January 11, 2006

Read Chapters I and 1 in Jackson.

  1. Jackson Problem #1.5

PHY 712 -- Assignment #2

January 13, 2006

Complete Chapter 1 in Jackson.

  1. PDF

PHY 712 -- Assignment #3

January 18, 2006

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 20, 2006

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 23, 2006

Start reading Chapter 2 in Jackson.

  1. PDF

PHY 712 -- Assignment #6

January 25, 2006

Continue reading Chapter 2 in Jackson.

  1. Work Problem #2.7 in Jackson.

PHY 712 -- Assignment #7

January 27, 2006

Continue reading Chapter 2 in Jackson.

  1. Work Problem #2.16 in Jackson.

PHY 712 -- Assignment #8

January 30, 2006

Start reading Chapter 3 in Jackson.

  1. Work Problem #3.9 in Jackson.

PHY 712 -- Assignment #9

February 1, 2006

Continue reading Chapter 3 in Jackson.

  1. PDF

PHY 712 -- Assignment #10

February 3, 2006

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 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 #11

February 6, 2006

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 #12

February 8, 2006

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 10, 2006

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 #14

February 24, 2006

Finish reading Chapter 6 in Jackson

  1. Work problem 6.2 (parts a and b) in Jackson, Also, either work part c or instead, show how the Lienard-Wiechert results (Eqs. 16-17) in Lecture Notes 19 are related.

PHY 712 -- Assignment #15

March 1, 2006

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. Choose typical values of the refractive indicies and permeabilities and plot the reflectances as a function of i for the two polarizations showing the effects of Brewster's angle.

PHY 712 -- Assignment #16

March 3, 2006

Continue reading Chapter 7 in Jackson

  1. Work problem 7.2 in Jackson.

PHY 712 -- Assignment #17

March 20, 2006

Continue reading Chapter 7 in Jackson

  1. Work problem 7.22(a) in Jackson.

PHY 712 -- Assignment #18

Martch 24, 2006

Continue reading Chapter 8 in Jackson.

  1. PDF

PHY 712 -- Assignment #19

March 27, 2006

Complete Chap. 8 and start Chap. 11 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.

PHY 712 -- Assignment #20

March 29, 2006

Continue reading Chap. 11 in Jackson

  1. Work problem 11.5 in Jackson.

PHY 712 -- Assignment #21

March 31, 2006

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 #22

April 3, 2006

Finish reading Chapter 11 and start Chapter 14 in Jackson

Note: The original problem was not totally well-defined. In order to define the problem, assume all measurements are taken at t′ = 0.

In the following, assume that there is a particle at the origin in the "prime" frame (x′,y′, z′) and that we want to determine the fields (electric and magnetic) at the point r′=a′x′+ b′y′ as measured in the "prime" frame at t′ = 0.

  1. Suppose that the "prime" frame is moving with velocity vx relative to a "stationary" frame. Find the fields measured in the stationary frame, espressed in terms of the coordinates and time of that frame.
  2. Suppose that the "prime" frame is moving with velocity vz relative to a "stationary" frame. Find the fields measured in the stationary frame, espressed in terms of the coordinates and time of that frame.

PHY 712 -- Assignment #23

April 5, 2006

Continue reading Chapter 14 in Jackson

  1. Work problem 14.4 in Jackson.

PHY 712 -- Assignment #24

April 7, 2006

Continue reading Chapter 14 in Jackson

  1. Work problem 14.12 in Jackson. (Note: in order to make Maple work productively, you might want to mention that the magnitude of βcosθ is 0 ≤ βcosθ ≤ 1,)

PHY 712 -- Assignment #25

April 10, 2006

Start reading Chapter 9 in Jackson

  1. Work problem 9.16(a) in Jackson.

PHY 712 -- Assignment #26

April 12, 2006

Continue reading Chapter 9 in Jackson

  1. PDF

PHY 712 -- Assignment #27

April 19, 2006

Continue reading Chapter 9 in Jackson

  1. Work problem 9.2 in Jackson.

PHY 712 -- Assignment #28

April 21, 2006

Start reading Chapter 10 in Jackson

  1. Work problem 10.1 in Jackson.
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