Physics 106bc
Winter and Spring Quarter, 2016
Course Homepage


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 update the details of the topics covered in lectures, suggested reading, problem sets, and solutions as the term progresses. Assignments 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 we can make other arrangements.

Targets for the links below will not be present until they are needed.  If you find a broken link, try refreshing your browser first.  If the target is still not present, email me.

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, and J for Classical Elecrodynamics by Jackson.  Reading given in parentheses is optional (intended only to tell you where I am drawing material from).

Week Tuesday Lecture Thursday Lecture
(E&M due Friday 4 pm)
Feb 1

1. Electric Field, Gauss's Law, Dirac Delta Function, Curl E = 0
Reading: G §2.1-2.2, LN §2.1-2.5 

HW 4 due
(5 pm)
Feb 8
2. Boundary Conditions, Electric Potential, Electric Potential Energy, Conductors
Reading: G §2.3-2.5, LN §2.6-2.9 
3. Capacitance, Laplace's Equation, Uniqueness Theorem
(makeup lecture 2/13 1:00 pm in 107 Downs)
Reading: G §2.5.4, §3.1, LN §3.1-3.2
(J §1.8-1.9, §1.11)

Mechanics Midterm Due
(5 pm)
Feb 15
4. Method of Images, Green Functions 
Reading: G §3.2, LN §3.3-3.4
(J §2.1-2.4, §1.10)
5. Obtaining Green Functions from the Method of Images,
Separation of Variables in Cartesian Coordinates
Reading: G §3.3, LN §3.5-3.7
(J §2.6, 2.8-2.9)

Assignment 5
(TA: Zachary)
Feb 22
6. Separation of Variables in Spherical Coordinates, General Theory,
Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry,
Separation of Variables in Spherical Coordinates w/o Azimuthal Symmetry
Reading: G§3.3.2, LN §3.9-3.10
(J §3.1-3.3, 3.5-3.6)
Summary slides for lectures 3-6
7. Separation of Variables in Spherical Coordinates w/o Azimuthal Symmetry: Spherical Harmonic Expansion of Green Function
Reading: LN §3.10
(J §3.9, 3.10)

Assignment 6
(TA: Yongliang) 
Feb 29
8. Multipole Expansion,
Electric Fields in Matter I

Reading: G §3.4, 4.1-4.3, LN §3.11, 4.1-4.2
(J §4.1-4.3)
9. Electric Fields in Matter II
Reading: G §4.4, LN §4.3-4.5
(J §4.4-4.7)

Assignment 7
(TA: Kevin)

Mar 7
10. Review and Example Final Problem Session (TAs)
2015 final exam problems and solutions
2014 final exam problems and solutions
2013 final exam problems and solutions
(Poll for which problems to do during review session: Poll closes on morning of Mon Mar 7.)
No Lecture
(OH 10:30-12:00 in 308 Cahill)

Assignment 8
Due W Mar 9
(TA: Zachary)
Mar 14
No Lecture
OH by appt
No Lecture
OH by appt

(first page is instructions)
Due W Mar 16
(TA: Yong-Liang, SG)

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Tuesday Lecture Thursday Lecture Homework
(due Friday 4 pm)
Mar 28
1. Magnetostatics
Reading: G §5.1-5.4.1, LN §5.1-5.5
2. Magnetostatics (cont.)
Reading: G §5.4.2-5.4.3, LN §5.6-5.7

No assignment due
Apr 4
3. Magnetic Fields in Matter
Reading: G §6.1-6.4, LN §6.1-6.3
4. Magnetic Fields in Matter (cont.)
Reading: LN §6.4 (J §5.9-5.12)
Assignment 1
(TA: Zachary)
Apr 11
5. Currents and Ohm's Law, Electromotive Forces, Electromagnetic Induction
Reading: G §7.1-7.2, LN §7.1-7.2
6. Faraday's Law, Electric Fields in Charge-Free Regions, Inductance, Magnetic Energy and Forces
Reading: G §7.2, LN §7.3-7.5 (J §5.16)
Assignment 2
(TA: Kevin)
Apr 18
7. Maxwell's Equations, Conservation Laws
Reading: G §7.3, §8.1-8.2, LN §7.6-7.7, §8.1-8.4
8. Electromagnetic Waves in Vacuum,
EM Waves in Nonconducting Matter
Reading: G §9.1-9.3.1, LN §9.1-9.2
Assignment 3
(TA: Hsiao-Yi)
Apr 25
9.  EM Waves in Nonconducting Matter: Reflection and Refraction,
EM Waves in Conductors
Reading: G §9.3.2-9.3.3, 9.4.1, LN §9.2-9.3
10. EM Waves in Conductors cont'd,
EM Waves in Dispersive Matter
Reading: G §9.4, LN §9.3-9.4 (J §7.5)
2015 midterm exam problems and solutions
2014 midterm exam problems and solutions
2013 midterm exam problems (mistitled) and solutions
(first page is cover sheet)
(TA: Kevin, Hsiao-Yi, Zachary)
May 2
11. Confined Waves: Transmission Lines
Reading: G §9.5, LN §9.5 (HM §7.1)
12. Confined Waves: Waveguides
Reading: LN §9.6 (HM §7.3-7.5, J §8.1, 8.3-8.4)
Assignment 4
Section 8.3 of Griffiths 4th ed.
(TA: Zachary)
May 9
13. Confined Waves: Waveguides (cont.),
Potential Formulation
Reading: LN §9.6 (J §8.5)
Reading: G §10.1, LN §10.1
14. Potential Formulation (cont.),
Moving Point Charges
Reading: G §10.1-10.3.1, LN §10.1-10.2  (HM §8.2-8.3)
Assignment 5
(TA: Kevin)
May 16
15. Moving Point Charges (cont.)
Reading: G §10.3.2, LN §10.2
16. Moving Point Charges (cont.),
Reading: G §11.2.1, §11.1.1, §11.1.4, LN §10.2-10.3
G §11.2.2-11.2.3 are being skipped, you are not responsible for this material.
Assignment 6
(TA: Hsiao-Yi)
May 23
17. Dipole and Quadrupole Radiation,
Relativity Review

Reading: G §11.1.2-11.1.3, LN §10.3
Reading: G §12, LN §12.1
18. Relativity in Electrodynamics
Reading: G §12, LN §11.2
Assignment 7
(TA: Zachary)
May 30
19. Applications of Radiation:
Classical Scattering and Antennas
Reading: LN §12
20. Review for Final:
This will be held in the SFL Multimedia Conference Room (3rd floor) at 6 pm 6/4.
Practice final exams and solutions:
2015 final for GS, final for FSJ, solutions
2014 final for GS, final for FSJ, solutions
2013 final for GS, final for FSJ, solutions
Assignment 8
(FSJ only)
(TA: Kevin)
Final for GS
Due June 3
FSJ: do not download this exam!  It overlaps the FSJ exam.
(TA: Hsiao-Yi, SG)
June 6
No Lecture
No Lecture
Final for FSJ
Due June 10
Solutions for both Final exams
(TA: Hsiao-Yi, SG)

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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.

Office hours: Thursday 6:00-8:00, 126 Cahill.  Cahill is locked around 6 pm, but the west door of Cahill is visible from the conference room, so just knock and you will be let in.  The phone number in the conference room is x8884, you can call to be let in, too.

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:

Zachary Mark
Ke (Kevin) Ye
Yong-Liang Zhang
Hsiao-Yi Chen
Zachary Mark
Ke (Kevin) Ye
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 course will follow these policies:
  • Problem sets will be accepted for 50% credit up to 1 week late at the due date for the following week's set, and after that not at all. You do not need to contact me or the TAs to turn in a problem set late for 50% credit. You must hand in the assignment in one piece (i.e. not a fraction on time for full credit, and the rest late for partial credit).

  • You may take one full-credit one-week extension on a problem set during the term. No need to contact me or the TAs, just write it on your problem set. 
    • Since an extension policy has not been in effect for the first half of Ph106b, you may take the free extension for any of the E&M sets regardless of extensions you took during the mechanics sets. 
    • For Ph106c, it will be one free extension for the entire term.
    • You may not combine the free extension with the "50% credit for 1-week late" policy.  It's one or the other.

  • Other extensions will only be granted for extraordinary reasons -- documented health issues, family emergency, etc. You must consult me (not the TAs) in person or by e-mail, before the homework is due unless  conditions make this impossible.  Some proof of extenuating circumstances (e.g., note from the health center, counseling center, or Dean of Undergraduate Students) will be necessary.

  • 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.


    You must fi rst try the problems yourself.  If you get stuck, or are unsure of your answer, you may seek help from the TAs or the instructor (see office hours above). You may also seek help from other students in the course, but your solution must be the result your own understanding of the material and must be written up independently (e.g. not copied from someone else's solutions or from a jointly prepared solution). If you do work with other students on a problem set, you must identify the names of those with whom you worked with on the submitted work.

    These days, it is probably possible to find the solution to any reasonable problem in other textbooks, from previous years of Ph106, or on the internet. You must not seek solutions to the assigned problems from any such resource. In any case, this would be a foolish thing to do, since the assignments serve as practice for the midterm and final for which consulting outside sources is not allowed. You should also not consult others who have taken Ph106 in a previous year on the problem sets.

    Historically, performance on problem sets is much better than on exams (see below).  Some of this may be due to the exam time constraint, but some of it may also be due to problem set overcollaboration.  If you do not internalize the material via the problem sets, you will not do well on the exams.  So be very careful to follow the collaboration policies, not just because of the honor code, but for your own good.  Don't let your colleagues show you how to do the problems; make sure they are helping you by "Socratic Method" -- asking you questions that will lead you to the insight you need for a particular problem.

    Here are some elaborations of the collaboration and reference policies, intended to supplement, not replace, the above policies:

    • On consulting tutors, TAs, fellow students, etc:

      Remember what the collaboration policy says: you must first try the problems yourself.  You can consult the instructor, TAs, tutors, fellow students, etc., but your solution must be the result of your own understanding.  You cannot ask other people to show you how to do a homework problem, or watch them do it, only discuss general issues and concepts with them, or work different examples.

      Generally, homework problems appear difficult because either the underlying physics or the calculational technique has not been understood.  Understand those and the homework is doable on your own.

    • On assisting fellow students:

      The same rules apply.  Don't tell your fellow students how to do a problem.  You can help them figure it out themselves by discussing relevant concepts, other examples, etc.  Helping another student without explicitly showing them how to do a problem is helpful to your own understanding, also, as you must have the concepts and techniques clear in your own head in order to effectively explain them to another student.  Use the "Socratic Method" -- ask questions that will lead your colleague to the insight needed to figure out the problem on his/her own.


    Exams are strictly non-collaborative!

    Exams are "open-book": You may consult your own notes (both in-class and any additional notes you take), Griffiths, and handouts and solution sets on this website.  No other textbooks (not even Jackson and Heald & Marion, since they are optional), no web sites, no other resources.

    In some instances, you may make use of notes taken from online resources. In particular, if you take the initiative to do study beyond class material and you get lucky by finding or studying ahead of time a problem that is later assigned on homework or an exam, you get to benefit from your hard work. However, you may not go hunting for problems on the web after they have been assigned, and you must use your own notes (handwritten or electronic) on any materials you have found, not the original source material.

    The most extreme hypothetical is the case of finding on the web a problem that is assigned on homework or an exam.  If you find the problem before seeing the relevant homework or exam, and take notes on it in your own hand (real or “virtual”), then those notes are fair game for use while you are doing the homework or exam. If you see the homework or exam, then go searching on the web and find the problem, your notes on such a problem are not allowed. Even if you found the problem before you saw the exam and saved the solution on your computer, going back to that saved copy is also not allowed, since that would not be your own notes.

    While it follows the letter of the above policy, hunting down scores of problems ahead of time and copying them in one’s own hand is strongly discouraged. Doing so clearly violates the spirit of the law, and the large amount of time it takes to find and copy these solutions could be much better spent learning the material.

    If you do make use of electronic resources and save them, one idea would be to create a "forbidden" folder on your computer that you know you may not consult during an exam.  This will prevent even accidental violations of the honor code.

Problem sets are due 4 pm on Fridays to the locked homework box outside 307 Cahill.  Please label your problem sets (and exams) only with  your anonymous code.

Problem set pickup:
  • 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 SG’s AA in 307 Cahill.  She is generally there 8 am - 4 pm except 12-1 pm MWF.  If she is not there, you can look for SG in 308 Cahill and he can open her office for you.

  • Solution sets will be posted on the website.
The weighting for problem sets and exams in the final grade for Ph106b will be:
  • 50% first half problem sets and midterm (split between the two as indicated by Prof. Chen)
  • 25% second half problem sets
  • 25% final exam
For Ph106c, the split will be
  • 50% problem sets
  • 25% midterm exam
  • 25% final exam

Ditch day policy:

  • If ditch day falls on a lecture day, I will reschedule the lecture for the Saturday following ditch day at the usual lecture time, 10:30 am.  If ditch day falls on a problem set due day or the day before (Thursday or Friday), the set due date will be delayed to the following Monday, usual time: 4 pm.  If that Monday is a holiday, then the set will be due Tuesday at 4 pm.

  • Office Hours: If ditch day falls on a Thursday, office hours will be rescheduled.  If ditch day falls on a Friday, then causality requires that we not change the office hour schedule.  So, for those of you who might be making decisions on acausal information, don't assume we will have a second office hour after ditch day and before the HW is due.  Thursday will be your only chance.
Grade Distributions

Ph106b (2016):

Ph106c (2015, for reference):

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