# Classical Electrodynamics Homework Solutions

## Physics 209

## Fall 2002

## University of California, Berkeley

- Instructor: Robert Littlejohn
- Office: 449 Birge
- Office Hours: MWF 12-1
- Telephone: 642-1229
- Email: physics209@wigner.berkeley.edu

- Lecture: 308 LeConte
- Time: MWF 11-12
- Discussion Section: Thursdays, 5:00-6:30pm, 329 LeConte

- TA: Alfredo Correa, alfredo@wigner.berkeley.edu
- Office Hours: Tu 2-3
- Office: 277 LeConte

- Text:
*Classical Electrodynamics*by J. D. Jackson

#### Prerequisites

The prerequisites for the course are a one-semester undergraduate course in Electricity and Magnetism(preferably a two-semester course) at the level of Griffiths,

*Introduction to Electrodyamics*or Lorraine,

Corson and Lorraine,

*Fundamentals of Electromagnetic Phenomena.*

#### Grade, Exams

The**grade**will be based on homework, the midterm Exam, and the final Exam (40% homework, 15%

midterm, and 45% final).

The **final exam** will he held on Wednesday, December 11, 12:30-3:30pm, in 150 GSPP (Goldman

School of Public Policy).

#### Homework Policy

Homework will be posted on this web site normally by Saturday of each week. The first homeworkwill be due on Saturday, September 7 at 5:00pm. All subsequent homeworks will be due on Friday

at 5:00pm. Homeworks should be placed in the box labelled Physics 209 on the second floor of

LeConte, just before the breezeway going over to Birge. Late homeworks will be accepted at 50%

credit up to one week late. Homeworks more than one week late will not be accepted.

**Exception:**

each student is allowed one free late homework (up to one week late), no questions asked.

#### Course Outline

- Review of electrostatics and magnetostatics
- Special Relativity
- Radiation
- Scattering
- Diffraction
- Special Topics

#### Homework Assignments

- 0. Read Chapters 1 and 2 of Jackson by Saturday, August 31. There is nothing to be turned in this week.
- 1. Homework in postscript or pdf format, due Saturday, September 7.
- 2. Homework in postscript or pdf format, due Friday, September 13 at 5:00pm.
- 3. Homework in postscript or pdf format, due Friday, September 20 at 5:00 pm.
- 4. Homework in postscript or pdf format, due Friday, September 27 at 5:00 pm.
- 5. Homework in postscript or pdf format, due Friday, October 4 at 5:00pm.
- 6. Homework in postscript or pdf format, due Friday, October 11 at 5:00pm.
- 7. Homework in postscript or pdf format, due Friday, October 18 at 5:00pm.
- 8. Homework in postscript or pdf format, due Friday, October 25 at 5:00pm.
- 9. Homework in postscript or pdf format, due Saturday, November 2 at 5:00pm.
- 10. Homework in postscript or pdf format., due Friday, November 8 at 5:00pm.
- 11. Homework in postscript or pdf format, due Friday, November 22 at 5:00pm.
- 12. Homework in postscript or pdf format, due Friday, November 22 at 5:00pm.
- 13. Homework in postscript or pdf format, due Friday, December 6 at 5:00pm.

#### Homework Solutions

Homework solutions are available in pdf format only.- Solutions to Homework #1.
- Solutions to Homework #2.
- Solutions to Homework #3.
- Solutions to Homework #4.
- Solutions to Homework #5.
- Solutions to Homework #6.
- Solutions to Homework #7.
- Solutions to Homework #8.
- Solutions to Homework #9.
- Solutions to Homework #10.
- Solutions to Homework #11.
- Solutions to Homework #12

#### Notes

- 1. Notes on
**Green's Functions**in postscript or pdf format. - 2. Notes on
**SI and Gaussian Units**in postscript or pdf format. - 3. Notes on the
**Levi-Civita Symbol**in postscript or pdf format. - 4. Notes on
**Tensor Analyis**in postscript or pdf format. - 5. Notes on
**Thomas Precession**in postscript or pdf format.

**Lecture Notes**are Professor Littlejohn's hand-written notes for lectures. They are not available for all

lectures, and no guarantees are made about how accurately they reflect the actual lectures. Go to the

lecture notes web page.

**Optional Notes**are not required reading, they are just for your edification if you are interested. The first set is

taken from an earlier Physics 221A course. They concern the theory of

**rotations**, which explains things like the

deeper theory underlying

**multipole expansions**, how to get

**Y_lm**'s with raising and lowering operators, how to

derive the

**addition theorem**for spherical harmonics, the meaning of

**irreducible tensors**,and many other things.

Much of this is standard fare in 221A, and you may find these notes useful also for that course.

- 1. Notes on
**Rotations in 3D Space and Classical Mechanics**, in postscript or pdf format. - 2. Notes on
**Rotations of Spin 1/2 Systems**, in postscript or pdf format. - 3. Notes on
**Representations of Rotations**in postscript or pdf format. - 4. Notes on
**Orbital Angular Momentum and Spherical Harmonics**in postscript or pdf format. - 5. Notes on
**Coupling of Angular Momenta**in postscript or pdf format. - 6. Notes on
**Irreducible Tensor Operators**in postscript or pdf format.

**g-factors**and such things.

The notes on the Stark effect explain how

**molecular polarizabilities**are computed in quantum mechanics. The

notes on the hyperfine structure explain the use of the

**Fermi contact term**for the magnetic field of a particle.

The notes on the Electromagnetic Field Hamiltonian contain a discussion of

**Coulomb gauge**and

**transverse and**

**longitudinal**vector fields. The notes on the Lorentz covariance of the Dirac equation contains a discussion of

the

**Lie algebra of the Lorentz group**.

- 7. Notes on
**Spins in Magnetic Fields**in postscript or pdf format. - 8. Notes on the
**Stark Effect**in postscript or pdf format. - 9. Notes on
**Hyperfine Structure**in postscript or pdf format. - 10. Notes on the
**Electromagnetic Field Hamiltonian**in postscriptor pdf format. - 11. Notes on the
**Lorentz Covariance of the Dirac Equation**in postscript or pdf format.

**action-at-a-distance electrodynamics**tell the interesting story of the Feynman-Wheeler theory.

- 12. The
**Feynman-Wheeler theory**, in pdf format only (taken from Jagdish Mehra,*The Beat of a Different* *Drum*(Clarendon Press, Oxford, 1994))..

John David Jackson's "Classical Electrodynamics" (3rd ed., Wiley, ISBN 0-471-30932-X, with errata) is a rite of passage for graduate students. Those who pass enjoy forcing the same pain on the next generation. Well, here's some help in that regard. Solutions from the problems assigned during the 2001-2000, 2003-2004, 2005-2006, and first half of 2007-2008 classes at the University of Michigan, taught by different professors. For the lazy among you, zip files of each section are provided for bulk download, but as these were added in later no guarantee is made as to the equivalence of filenames between the zipfiles and the linked files.

I have posted every solution that I have available, so while I do appreciate any feedback and comments about this page and its contents, please don't e-mail me asking for solutions that haven't been posted. This is all I have.

9/11/2007 UPDATE: I had no idea when I first posted this site that it'd be so popular. I've had e-mails from students around the world either thanking me for making this available or asking questions about the solutions. I want to thank everyone for making this the #1 Jackson solutions site in the world! If anyone has an equivalent solution set (i.e. from a whole semester) that they'd like to contribute, I'd be happy to add it to the collection with attribution.

10/11/2007 UPDATE: There is another student at the UM who has a Jackson solutions page up. He has solutions entirely different from the ones I have collected (from the 2004-2005 year), and his site is: http://www-personal.umich.edu/~jbourj/em.htm.

12/19/2007 UPDATE: Thanks to a current Jackson student at the University of Michigan, we now have the Fall 2007 Physics 505 solutions!

04/20/2008 UPDATE: The Fall 2007 solutions now include problem assignments and the final, and we now have Winter 2008 solutions as well!

The solutions for the 2001-2002 year were by Jianming Qian, 2003-2004 by Georg Raithel, 2005-2006 and 2007-2008 by James Liu.

06/04/11 UPDATE: A Rutgers student, Philip Naudus, has donated his Jackson solutions for the 2010-2011 school year. They can also be found at his Ephysics Wiki page for discussion and erratas.

03/21/11: Now that I am no longer a student, I have to pay to maintain this page. People from around the world use this resource, and I'd love to keep it available for everyone. It has been paying for itself since March 2010, and will stay up as long as it continues to do so. If you use this site, and have a few dollars to spare, please consider donating via the paypal button below. It'll only take 30 seconds. Thanks!

Physics 505 (a.k.a. "the first half") 2007-2008 solutions

Problem Set 1 and solution : 1.5, 1.7, 1.11, 1.12

Problem Set 2 and solution : 2.2, 2.8, 2.10, 2.11

Problem Set 3 and solution : 2.14, 2.15, 2.22, 2.23

Problem Set 4 and solution : 3.1, 3.2, 3.4, 3.7

Problem Set 5 and solution : 3.13, 3.17, 3.26, 3.27

Problem Set 6 and solution : 4.1, 4.7, 4.8, 4.9

Problem Set 7 and solution : 5.4, 5.7, 5.8, 5.9

Problem Set 8 and solution : 5.14, 5.14, 5.15, 5.16

Problem Set 9 and solution : 5.19, 5.21, 5.22, 5.27

Problem Set 10 and solution : 6.1, 6.4, 6.13, 6.18

Problem Set 11 and solution : 7.3, 7.4, 7.6, 7.8

Practice Midterm and solution

Real Midterm solutions.

Practice Final and solution

Real Final solutions.

Bulk download zipfile for Fall 2007 solutions.

And the 2005-2006 solutions

Problem Set 1 and solution : 1.4, 1.5, 1.10, 1.14

Problem Set 2 and solution : 2.3, 2.4, 2.7, 2.10

Problem Set 3 and solution : 2.12, 2.13, 2.15, 3.1

Problem Set 4 and solution : 3.4, 3.6, 3.9, 3.10

Problem Set 5 and solution : 3.14, 3.26, 3.27, 4.1

Problem Set 6 and solution : 4.2, 4.6 (a and b), 4.7 (a and b), 4.8

Problem Set 7 and solution : 4.10, 5.3, 5.6, 5.7

Problem Set 8 and solution : 5.10, 5.14, 5.17, 5.19

Problem Set 9 and solution : 5.20, 5.22, 5.26, 6.1

Problem Set 10 and solution : 6.3, 6.4, 6.14, 6.18

Problem Set 11 and solution : 7.3, 7.5, 7.8, 7.16

Practice Midterm and solution

Real Midterm solutions.

Practice Final and solution

Bulk download zipfile for Fall 2005 solutions.

And the 2003-2004 solutions

Class Notes

Problem Set 1 and solution : 1.3, 1.5, 1.6, 1.11, 1.12, tailored problem

Problem Set 2 and solution : 1.17, 1.22, 2.1, 2.2, tailored problem

Problem Set 3 and solution : 2.7, 2.8, 2.9, 2.12, 2.30

Problem Set 4 and solution : 2.13, 2.23, 2.24, 3.2, 3.3

Problem Set 5 and solution : tailored problem, 3.17, 3.23

Problem Set 6 and solution : 4.1, 4.6, 4.8, 4.10

Problem Set 7 and solution : 5.1, 5.3, 5.8, 5.13

Problem Set 8 and solution : 5.10, 5.15, 5.19

Problem Set 9 and solution : 5.22, tailored problem, 6.1, 6.2 (a) and (b)

Problem Set 10 and solution : 6.8, 6.15, 6.18, 7.3, 7.4

Midterm and final solutions for Physics 505.

Bulk download zipfile for Fall 2003 solutions.

And now the 2001-2002 solutions

Problem Set 1 solutions : 1.5, 1.6, 1.7, 1.9

Problem Set 2 solutions : 2.2, 2.4, 2.5, 2.9

Problem Set 3 solutions : 2.10, 2.11, 2.13, 2.21

Problem Set 4 solutions : 3.1, 3.4, 3.7, 3.9

Problem Set 5 solutions : 3.10, 3.14, 3.22, 3.24

Problem Set 6 solutions : 4.1, 4.2, 4.10, 4.13

Problem Set 7 solutions : 5.6, 5.13, 5.18, 5.19

Problem Set 8 solutions : 5.10, 5.20, 5.22, 5.27, 5.29

Problem Set 9 solutions : 6.4, 6.8, 6.11, 6.13

Problem Set 10 solutions : 6.14, 7.2, 7.3, 7.4

Problem Set 11 solutions : 7.12, 7.13, 7.28

Bulk download zipfile for Fall 2001 solutions.

Contributed Solutions, 2010-2011

Problem Set 1 solutions : 1.4, 1.5, 1.6, 1.9

Problem Set 2 solutions : 1.14, 2.1, 2.2

Problem Set 3 solutions : 2.7, 2.9, 2.10

Problem Set 4 solutions : 2.13, 2.14, 2.23

Problem Set 5 solutions : 3.1, 3.3

Problem Set 6 solutions : 3.17, 3.26, 3.27

Problem Set 7 solutions : 4.1, 4.7

Problem Set 8 solutions : 4.9, 5.3, 5.6

Problem Set 9 solutions : 5.13, 5.15, 5.19

Problem Set 10 solutions : 5.21, 5.27

Bulk download zipfile for Fall 2010 solutions.

Physics 506 (a.k.a. "the second half") 2007-2008 solutions

Problem Set 1 and solution : 8.2, 8.4

Problem Set 2 and solution : 8.5, 8.6, 8.7

Problem Set 3 and solution : 8.18, 8.20, 9.1, 9.3

Problem Set 4 and solution : 9.6, 9.11, 9.16, 9.17

Problem Set 5 and solution : 9.22, 9.23, 9.24, 10.1

Problem Set 6 and solution : 10.2, 10.3, 10.8, 10.9a

Problem Set 7 and solution : 10.12, 10.14, 10.18, 11.3

Problem Set 8 and solution : 11.5, 11.13, 11.14, 11.18

Problem Set 9 and solution : 11.27, 11.30, 12.2, 12.3

Problem Set 10 and solution : 12.10, 12.13, 12.16, 12.19

Problem Set 11 and solution : 13.1, 13.2, 13.3, 13.5

Problem Set 12 and solution : 14.4, 14.5, 14.8, 14.11

Practice Midterm and solution

Real Midterm solutions.

Practice Final and solution

Bulk download zipfile for Winter 2008 solutions.

And the 2005-2006 solutions

Problem Set 1 and solution : 8.2, 8.4, 8.5

Problem Set 2 and solution : 8.6, 8.8

Problem Set 3 and solution : 8.18, 8.19, 9.3, 9.6

Problem Set 4 and solution : 9.8, 9.9, 9.16, 9.17

Problem Set 5 and solution : 9.19, 9.22 (a and b), 9.23, 10.1

Problem Set 6 and solution : 10.2, 10.3, 10.7, 10.10

Problem Set 7 and solution : 10.14, 10.16, 11.4, 11.5

Problem Set 8 and solution : 11.13, 11.16, 11.18, 11.27

Problem Set 9 and solution : 12.2, 12.9, 12.13, 12.14

Problem Set 10 solution : 12.15, 12.16, 12.19, 12.20

Problem Set 11 and solution : 13.1, 13.2, 13.3, 13.9

Problem Set 12 and solution : 14.2, 14.4, 14.6, 14.12

Practice Midterm and solution

Real Midterm solution

Practice Final and solution

Bulk download zipfile for Winter 2006 solutions.

And the 2003-2004 solutions

Class Notes

Problem Set 1 and solution : 8.2, 8.4, 8.5

Problem Set 2 and solution : 8.6, 8.12, 8.13, 8.20

Problem Set 3 and solution : 9.1, 9.2, 9.3, 9.5

Problem Set 4 and solution : 9.10, 9.16, 9.17, 9.22

Problem Set 5 and solution : 10.2, 10.3, 10.8, 10.9a

Problem Set 6 and solution : 10.10a, 10.12, 10.16

Problem Set 7 and solution : 11.3, 11.5, 11.6, 11.9

Problem Set 8 and solution : 11.13, 11.14, 11.18, 11.19

Problem Set 9 and solution : 12.1, 12.5, 12.9, 12.14, 14.4, 14.12

Midterm solutions for Physics 506.

Bulk download zipfile for Winter 2004 solutions.

And now the 2001-2002 solutions

Problem Set 01 solutions : 8.2, 8.5, 8.8, 8.18

Problem Set 02 solutions : 8.3, 8.4, 8.16a, 8.20

Problem Set 03 solutions : 9.1, 9.2, 9.3, 9.10

Problem Set 04 solutions : 9.12, 9.16, 9.17, 9.22

Problem Set 05 solutions : 10.3, 10.9a, 10.12, 10.18

Problem Set 06 solutions : 10.15, 11.3, 11.5

Problem Set 07 solutions : 11.6, 11.8, 11.13, 11.16

Problem Set 08 solutions : 11.23, 12.2, 12.3, 12.6b

Problem Set 09 solutions : 12.5, 12.9, 12.11, 12.14

Problem Set 10 solutions : 14.4, 14.5, 14.12, 14.13

Problem Set 11 solutions : 14.14, 14.26, 13.1, 13.11

Bulk download zipfile for Winter 2002 solutions.

Contributed Solutions, 2010-2011

Problem Set 1 solutions : 6.1, 6.4, 6.5

Problem Set 2 solutions : 7.3, 7.16, 8.5

Problem Set 3 solutions : 8.9, 8.14

Problem Set 4 solutions : 9.1, 9.7

Problem Set 5 solutions : 11.8a

Problem Set 6 solutions : 11.6, 11.11,11.14

Problem Set 7 solutions : 12.7, 12.9a, 12.10, 12.14

Problem Set 8 solutions : 13.9, 14.4, 14.10, 14.21

Bulk download zipfile for Winter 2011 solutions.

I hope all of this was as useful to you as it was to me. Help the next generation by putting your own solutions online for their enlightenment. The only way to survive Jackson E&M is by standing on the shoulders of those who've gone before.

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