Physics 106bc
Winter and Spring Quarter, 2014
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From the course catalog:
An intermediate course in the application of basic principles of classical physics to a wide variety of subjects. Roughly half of the year will be devoted to mechanics, and half to electromagnetism. Topics include Lagrangian and Hamiltonian formulations of mechanics, small oscillations and normal modes, boundary-value problems, multipole expansions, and various applications of electromagnetic theory.
Ph106bc covers electrodynamics at a level of sophistication beyond the introductory Ph1bc sequence.  You will see much material that is familiar to you, but we will take a more rigorous approach, analyze more challenging physical situations, and also consider many topics not seen in Ph1bc.  It is impossible to emphasize how important the core physics courses Ph106 and Ph125 are: these teach you the basic frameworks and techniques that you must know to do any physics.

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Syllabus and Schedule, Problem Sets, and Solutions

Below you will find the outline of the E&M portion of Ph106bc.  I will fill in details of the topics covered in lectures, suggested reading, problem sets and solutions as the term progresses. The assignments will be due on Fridays, and will be available on the website about a week before the due date. Note that they are listed in the week they are due, rather than the week they are assigned. The schedule for the lectures and assignments may change as the term progresses.

The lecture notes, problem sets, and solutions are only accessible to computers with a Caltech IP address (either direct or by VPN). Please let me know if you are enrolled in the class and this causes problems for you, and I will make other arrangements.

In the suggested reading, G stands for Introduction to Electrodynamics by Griffiths, LN for Lecture Notes, HM stands for Classical Electromagnetism by Heald and Marion, J for Classical Elecrodynamics by Jackson, and LL for The Classical Theory of Fields by Landau and Lifshitz.  Reading given in parentheses is optional (intended only to tell you where I am drawing material from).

If you print out the problem sets and solutions in "2-up" format, the font size will be approximately 12 point.

Week Tuesday Lecture Thursday Lecture Homework
(due Friday 4 pm)
February 10
1. Electric Field, Gauss's Law, Dirac Delta Function, Curl E = 0
Reading: G 2.1-2.2, LN 2.1-2.5 
2. Boundary Conditions, Electric Potential, Electric Potential Energy, Conductors
Reading: G 2.3-2.5, LN 2.6-2.9 
No Assignment
Review G Ch 1
February 17
3. Capacitance, Laplace's Equation, Uniqueness Theorem, Method of Images
Reading: G 2.5, 3.1-3.2, LN 2.9, 3.1-3.3 (J 1.11, 1.8-1.9, 2.1-2.4)
4. Green Functions
Reading: LN 3.4-3.5 (J 1.10)
Assignment 6
(updated 2012/02/28)
(TA: Paraj)
February 24
5. Separation of Variables in Cartesian Coordinates, in Spherical Coordinates w/Azimuthal Symmetry
Reading: G 3.3, LN 3.6-3.8 (J 2.8-2.9, 3.1-3.2)
6. Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry (cont.),
Separation of Variables in Spherical Coordinates w/o Azimuthal Symmetry
Reading: LN 3.8-3.9 (J 3.3, 3.5-3.6, 3.9)
Summary slides for lectures 3-6
Assignment 7
(TA: Kevin)
March 3
7. Separation of Variables in Spherical Coordinates w/o Azimuthal Symmetry (cont.),
Reading: LN 3.9 (J 3.10, 4.1-4.2)
8. Multipole Expansion, Electric Fields in Matter
Reading: G 3.4, 4.1-4.2.1, LN 3.10, 4.1 (J 4.1-4.2)
Assignment 8
(TA: Chan)
March 10
9. Electric Fields in Matter cont'd
Reading: G 4.2.2-4.4.1, LN 4.1-4.3
No Lecture
Example final exam problem session.
107 Downs, 6:30-8:30 pm.
2013 final exam problems and solutions
impromptu problems/solutions (thanks to Yubo Su for taking excellent notes; corrections to notes are included)
Assignment 9
(shortened v.2 posted 3/7)
Due W Mar 12
(TA: Paraj)
March 17
No Lecture
No Lecture
(first two pages are instructions)
Due W Mar 19

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Tuesday Lecture Thursday Lecture Homework
(due Friday 4 pm)
April 1
1. Electric Fields in Matter cont'd
Reading: G 4.4.2-4.4.4, 5.1, LN 4.4-4.5, 5.1-5.2 (J 4.4, 4.7)
2. Magnetostatics
Reading: G 5.1-5.4.1, LN 5.1-5.5

No assignment due
April 7
3. Magnetostatics cont'd
Reading: G 5.4.2-5.4.3, LN 5.6-5.7
4. Magnetic Fields in Matter
Reading: G 6.1-6.4, LN 6.1-6.3
Assignment 1
(TA: Kevin)
April 14
5. Magnetic Fields in Matter cont'd
Reading: LN 6.4 (J 5.9-5.12)
6. Currents and Ohm's Law, Electromotive Forces, Electromagnetic Induction, 
Reading: G 7.1, LN 7.1-7.2
Assignment 2
(updated 4/15 with minor clarifications) Solutions
(TA: Feng)
April 21
7. Faraday's Law, Electric Fields in Charge-Free Regions, Inductance, Magnetic Energy, and Magnetic Forces, Maxwell's Equations
Reading: G 7.2-7.3, LN 7.3-7.7 (J 5.16)
8. Conservation Laws
Reading: G 8.1-8.2, LN 8.1-8.4
Assignment 3
(TA: Paraj)
April 28
9. Electromagnetic Waves
This lecture will take place on 4/26 at 4 pm in Downs 107.  No lecture on 4/29.
Reading: G 9.1-9.2, LN 9.1
10. EM Waves in Nonconducting Matter
Reading: G 9.3, LN 9.2
(first page is cover sheet, v 2 posted 4/28 6:00)
Due Monday May 5 at 4 pm
(TA: all)
May 5
11. EM Waves in Conductors
EM Waves in Dispersive Matter
Reading: G 9.4, LN 9.3-9.4
12. EM Waves in Dispersive Matter cont'd
Confined Waves: Transmission Lines
Reading: G 9.4-9.5, LN 9.4-9.5
Assignment 4
(v 3 posted 5/8 14:00)
Section 8.3 of Griffiths 4th ed.
(TA: Kevin)
May 12
13. Confined Waves: Transmission Lines cont'd
Confined Waves: Waveguides
Reading: G 9.5, LN 9.5-9.6
no lecture: Ditch Day

Assignment 5
(v 2 posted 5/16 17:00)
(v 2 posted 5/27)
(TA: Feng)
May 19
14. Confined Waves: Waveguides cont'd
Reading: G 9.5, LN 9.6
15. Potential Formulation
Reading: G 10.1-10.2, LN 10.1
Assignment 6
(v 4 posted 5/21 7:00)
(v 2 posted 6/1)
(TA: Paraj)
May 26
16. Moving Point Charges
Reading: G 10.3, LN 10.2
17. Moving Point Charges cont'd
Reading: G 11.2.1, LN 10.2
18. Dipole Radiation, Relativity Review (Makeup lecture on 5/31 at 4 pm in 107 Downs)
Reading: G 11.1, LN 10.3
G 11.2.2-11.2.3 are being skipped, you are not responsible for this material.
Reading: G 12, LN 11.1
Assignment 7
(TA: Kevin)
June 2
19. Relativity in Electrodynamics
Reading: G 12, LN 11.2
20. Review for Final Exam

Assignment 8
(FSJ only)
(v2 posted 6/8)
(TA: Feng)
Final for GS
v2 posted 6/1
Due June 6
FSJ: do not download this exam!  It overlaps the FSJ exam.
(TA: all)
June 9
No Lecture
No Lecture
Final for FSJ
v2 posted 6/11
Due June 13
Solutions for both Final exams
(TA: all)

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Vital Information

Location: 107 Downs

TuTh 10:30 am - 12:00 pm


Prof. Sunil Golwala, 308 Cahill, Mail Code 367-17, golwala at
Office hours: Thursday evenings, 6:30 pm - 8:30 pm, SFL 229 (#2-3).
If you need to contact me outside of office hours, please try email first.  I am happy to arrange meetings outside of normal office hours, but I am not always available on the spur of the moment.  Please include "Ph106" in the subject line of your email so that it is recognized and responded to quickly.

Teaching Assistants:

Paraj Bhattacharjee, pbhattac at, 155 W. Bridge
Feng Bi, bifnhlp at
Kevin Ye, kye at, 449 Lauritsen
Office hours: By appointment.

Feedback: I greatly appreciate student feedback; feedback prior to the end-of-term evaluations lets me modify the class to fit your needs.  In person, by email, by campus mail, whatever you like.  If you would like to preserve your anonymity, campus mail will usually work.  My mailbox is in the kitchen area near my office.

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Policies and Grading

The courses will continue the policies laid out by Prof. Cross for Ph106b.  In particular, problem set and exam policies given there apply to the second-half problem sets and final exam.

Note especially that the "one free extension" rule applies to the entire term, not to each half, for Ph106b.

Problem sets should be turned in by Friday at 4 pm to the Ph106 box outside 307 Cahill. 

Problem set pickup:
  • To satisfy Caltech privacy rules, if you did not take Ph106a this year, please choose a 6 digit code and e-mail this to the TAs before the first assignment. You will use this, and not your name, to label your assignments and exams.

  • Solution sets will be posted on the website. Graded problem sets will be available in class or in the Ph106 outbox outside 307 Cahill (second half of term). If your name, and not just your numerical code, appears on the assignment, you will have to pick it up directly from SGs AA in 307 Cahill.  She is generally there 8 am - 4 pm except 12-1 pm every day except Fridays.  If she is not there, you can look for SG in 308 Cahill and he can open her office for you.
The weighting for problem sets and exams in the final grade for Ph106b will be:
  • 25% first half problem sets
  • 25% midterm exam
  • 25% second half problem sets
  • 25% final exam
For Ph106c, the split will be
  • 50% problem sets
  • 25% midterm exam
  • 25% final exam
Use of mathematical software like Mathematica is allowed, but will not be available for exams.  From a former colleague: It is absolutely essential that you develop a strong intuition for basic calculations involving linear algebra, differential equations, and the like.  The only way to develop this intuition is by working lots of problems by hand; skipping this phase of your education is a really bad idea.

Grade Distribution

Ph106b (updated 2014/05/09):


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