Physics 106bc
Winter and Spring Quarter, 2019
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 problem sets and solutions are only accessible to computers with a Caltech IP address (either direct or by VPN). (Lecture notes are available to anyone.) 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.

Keep a copy of the lecture notes and problem sets handy on your computer or a USB stick.  Websites go down occasionally (seemingly especially during holidays), and a very modest bit of foresight can prevent this from disrupting the problem set due date schedule.  If there is a problem set update, or a lecture notes update relevant to a problem set, at a very late date and there is an outage (in the 24 hrs before a set is due), this policy will be suspended.  We are looking into setting up a secure mirror website for the future.

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 Homework
(E&M due Friday 7 pm)
Feb 11
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 2.3-2.5.3, LN 2.6-2.9 
Midterm due
Feb 18
Note: this lecture was shifted to 2/21 due to instructor absence.
3. Capacitance, Laplace's Equation, Uniqueness Theorem
Reading: G 2.5.4, 3.1, LN 2.10, 3.1-3.2
(J 1.8-1.9, 1.11)
Note: this lecture will be shifted to 2/26 due to instructor absence on 2/19.
Method of Images, Green Functions 
Reading: G 3.2, LN 3.3-3.4
(J 2.1-2.4, 1.10)
Assignment 5
(TA: Yongliang)
Feb 25
Note: this lecture will be shifted to 2/28 due to instructor absence on 2/19.
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)
Tu Problem Session: Alex
W Problem Session: Alex
Note: this lecture will be made-up on 3/2 due to instructor absence on 2/19.
Separation of Variables in Spherical Coordinates: General Theory,
Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry
Reading: G3.3.2, LN 3.8-3.9
(J 3.1-3.3)
Summary slides for lectures 3-6
W OH: Sizheng
F OH: Sizheng
Assignment 6
(TA: Sizheng) 
Mar 4
7. Separation of Variables in Spherical Coordinates w/o Azimuthal Symmetry;
Spherical Harmonic Expansion of Green Function

Reading: LN 3.10
(J 3.5-3.6, 3.9-3.10)
Tu Problem Session: Yongliang
W Problem Session: Sizheng
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)
W OH: Sizheng
F OH: Yongliang
Assignment 7
(TA: Alex)
Mar 11
9. Electric Fields in Matter II
Reading: G 4.4, LN 4.3-4.5
(J 4.4-4.7)
Note: Problem Sessions and OH are shifted due to Weds due date for PS8.
M Problem Session: Alex
M 8-9 pm OH: Alex
Tu Problem Session: Alex
Tu 9-11 pm: instructor OH
W 3-4 pm OH: Alex
10. Review and Example Final Problem Session
during normal class time
2018 final exam problems and solutions
2017 final exam problems and solutions
2016 final exam problems and solutions
(Poll for which problems to do during review session: Closes at 9 am Mar 14.)
There will also be review sessions Saturday and Sunday evenings, times and locations to be announced.

Assignment 8
(TA: Alex)
Mar 18
No Lecture
OH by appt
Final exam cover page only
Final exam including cover page
(first page is instructions)
Due 3/20 7 pm.
(TA: Sizheng)

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Tuesday Lecture Thursday Lecture Homework
(due Friday 7 pm)
Apr 1
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 8
3. Magnetic Fields in Matter
Reading: G 6.1-6.4, LN 6.1-6.4
OH/PS: Kung-Yi
4. Magnetic Fields in Matter (cont.)
Reading: (J 5.9-5.12)
Assignment 1
(TA: Kung-Yi)
Apr 15
5. Currents and Ohm's Law, Electromotive Forces, Electromagnetic Induction, Faraday's Law, Electric Fields in Charge-Free Regions
Reading: G 7.1-7.2, LN 7.1-7.3
6. Inductance, Magnetic Energy
Reading: G 7.2, LN 7.3-7.5 (J 5.16)
Assignment 2
(TA: Ge)
Apr 22
7. Magnetic Forces, Maxwell's Equations, Conservation Laws
Reading: G 8.1, LN 7.5, 8.1-8.2 (J 5.16)
8. Conservation Laws (cont.),
Electromagnetic Waves in Vacuum
Reading: G 8.2, 9.1-9.2, LN 8.3-8.4, 9.1
Assignment 3
(TA: Anya)
Apr 29
9.  EM Waves in Vacuum (cont.),
EM Waves in Nonconducting Matter

Reading: G 9.1.4, 9.3, LN 9.1-9.2
10. EM Waves in Conductors,
EM Waves in Dispersive Matter
Reading: G 9.4, LN 9.3-9.4 (J 7.5)
2018 midterm exam problems and solutions
2017 midterm exam problems and solutions
2016 midterm exam problems and solutions
(first page is cover sheet)
(TA: Ge)
May 6
11. Confined Waves:
Transmission Lines
Reading: G 9.5.3, LN 9.5 (HM 7.1)
OH/PS: Kung-Yi
12. Confined Waves:
Transmission Lines (cont.),
Reading: G 9.5.1, LN 9.5-9.6 (HM 7.3-7.5, J 8.2-8.4)
Assignment 4
Section 8.3 of Griffiths 4th ed.
(TA: Anya)
May 13
13. Confined Waves: Waveguides (cont.)
Reading: LN 9.6 (J 8.1, 8.5)
OH/PS: Kung-Yi
14. Potential Formulation,
Retarded Potentials,
Retarded Fields
Reading: G 10.1-10.2, LN 10.1 (HM 8.1-8.2)
Assignment 5
(TA: Kung-Yi)
May 20
15. Fields of Point Charges Moving at Fixed Velocity,
Fields of Accelerating Point Charges
Reading: G 10.3, LN 10.2 (HM 8.3-8.6)
16. Power from Accelerating Point Charges,

Reading: G 11.2.1, 11.1.1, 11.1.4, LN 10.2-10.3 (HM 8.7-8.8)
G 11.2.2-11.2.3 are being skipped, you are not responsible for this material.
Assignment 6
(v. 2 posted 2019/05/23 03:00)
(TA: Ge)
See Brinson visualizations of triangular waveguide modes.
May 27
17. Radiation (cont.),
Applications of Radiation: Classical Scattering
Reading: G 11.1, LN 10.3 (HM 9.1, 9.8)
Reading: LN 11.1
Memorial Day is a holiday, so the Monday PS will be held during the 8-9 pm hour of the Weds OH.
18. Applications of Radiation: Antennas
Reading: LN 11.2
Assignment 7
(TA: Anya)
Jun 3
19. Final Exam Review (GS and FSJ)
Practice final exams and solutions:
2018 final for GS, final for FSJ, solutions
2017 final for GS, final for FSJ, solutions
2016 final for GS, final for FSJ, solutions
M PS: Golwala
OH incl. Th: Kung-Yi
20. Relativity Redux
Pizza will be served!
Reading: G 12, LN 12
Reading: Chen Ph106b Lecture Notes for
Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5
Prof. Chen covered in Ph106b the material that would normally be covered here, so we will do a quick review and augment it a bit, but we will not go back through it in detail (and we won't cover it in HW).
Assignment 8
(FSJ only)
(TA: Kung-Yi)
Final for GS
Due Jun 7
FSJ: do not download this exam!  It overlaps the FSJ exam.
(TA: Kung-Yi/Ge)
June 10
No Lecture
OH/PS: Kung-Yi
No Lecture
Final for FSJ
Due Jun 14
Solutions for both Final Exams
(TA: Kung-Yi/Ge)

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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 9 pm - 11 pm, 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 no one shows by 10 pm, or no one sends an email requesting I stay past 10 pm, I will probably leave.

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 rarely 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.  See comments below about email and extensions.

Teaching Assistants:

Sizheng Ma:
Alex Turzillo:
Yongliang Zhang:

Office hours:

Tuesday and Wednesday 7-8 pm, problem session.  This is an interactive session in which the students will work together to solve problems.  Credit will be given for attending.  You need only attend one session per week to get credit. 
Tuesday location: 351 W. Bridge
Wednesday location: B157 W. Bridge
Wednesday 8-9 pm, B157 West Bridge: office hour, no planned agenda.

Friday 3-4 pm, B157 West Bridge: office hour, no planned agenda.

If you would like to help before Weds 8-9 pm, feel free to contact the TAs to arrange a special appointment.
Ge Chen
Anya Mitskovets (grading only)
Kung-Yi Su

Office hours:
Monday 9-10 pm, problem session, location Cahill library.  This is an interactive session in which the students will work together to solve problems.  Credit will be given for attending.  If you cannot attend, email Prof. Golwala to make special arrangements. 

Wednesday 8-10 pm, location Cahill library: office hour, no planned agenda.

Friday 1-2 pm, location 319 Cahill: office hour, no planned agenda.

If you would like to help on Tuesday, feel free to contact the TAs to arrange a special appointment.

If you don't have a key to Cahill, knock on the library windows (accessible from driveway on east side of Cahill).

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 use the same policies at Prof. Weinstein's Ph106a and Prof. Chen's Ph106b.  Refinements and clarifications:
  • Homework is due Fridays at 7 pm to the Physics 106 IN box by the East Bridge mailboxes.  It will be returned to the Physics 106 OUT box by the East Bridge mailboxes.  Sets that include identifying information, such as a name, will be available from the PMA Undergraduate Student Affairs Administrator, Meagan Heirwegh, in 156 Linde during normal business hours.
  • Extension requests should be sent to me, the course instructor.  I do not check email continuously, and typically not after 5:30 pm on weeknights (until possibly after 8 pm), so your extension requests must allow time for non-immediate response.
  • Only one silver bullet extension is allowed for all of Ph106b, not one for each half of the class.
  • The Ph106b final will not be comprehensive: it will only cover E&M.
  • 50% of the Ph106b course grade will be based on E&M material.  The E&M grade will have equal weight of homework and the final exam (i.e. E&M HW = 25% of Ph106b grade, E&M Final Exam = 25% of Ph106b grade).
  • For Ph106c, the split will be
    • 50% problem sets
    • 25% midterm exam
    • 25% final exam
  • Extra credit for problem session attendance: To encourage attendance at the Wednesday problem-solving sessions, we will offer extra credit.  Here are the rules on the extra credit:
    • The extra credit will be added after the letter grade boundaries are decided, so students who do not attend will not be penalized.
    • Students who miss no more than one problem session in Ph106c will be guaranteed one +/- grade increment of extra credit.  For Ph106b, since the problem session policy is being instituted partway through, the max credit will be half a +/- grade increment. 
    • Students who attend fewer sessions will receive a proportional point increment.  This may or may not result in a +/- grade increment depending on the details of the person's numerical grade.
      If you have a time conflict with the proposed time, contact me and we will find an alternate solution.
  • Honor code and Collaboration policy tweaks
    • You may use the previous years' exams and solutions posted on this website when doing problem sets or exams, but only those!  You may not use previous years' exams or solutions that are not available from this website.
    • You may use any other materials provided by the instructor or TAs, including material from the problem sessions or office hours.

Ditch day policy (Ph106c):

  • If ditch day falls on a lecture day, I will reschedule the lecture for the Saturday following ditch day, probably at 2:00 pm.  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.  If that Monday is a holiday, then the set will be due Tuesday at the usual time.

  • A delayed problem set due date due to ditch day has no impact on later problem set due dates, including 50% credit and silver bullet extensions.  If ditch day falls just before a holiday weekend, pushing the due date to Tuesday, there is the prospect of a very short following week to do the next set.  Plan accordingly by starting the next set over the weekend while finishing the set that was due during the week of ditch day.

  • Office Hours:
    • If ditch day falls on a Thursday, Thursday and Friday office hours will be rescheduled for Saturday/Sunday. 
    • If ditch day falls on a Friday, then causality requires that we not change the Thursday office hour schedule.
    • If Monday is a holiday, shift the above by one day, availability permitting. 
    • So, for those of you who might be making decisions on acausal information, take account of the above information.
Grade Distributions

Ph106b (2019; refresh cache to make sure you get new versions):

Ph106c (2018 except for Midterm, which is from 2019):

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