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.

Quick Links


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
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)
4. Method of Images, Green Functions 
Reading: G 3.2, LN 3.3-3.4
(J 2.1-2.4, 1.10)
Assignment 4
Feb 25
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)
6. 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
Assignment 5
(TA: TBD) 
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)
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)
Assignment 6
Mar 11
9. Electric Fields in Matter II
Reading: G 4.4, LN 4.3-4.5
(J 4.4-4.7)
10. Review and Example Final Problem Session
during normal OH time slot
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 6 pm Mar 14.)

Assignment 7
Mar 18
No Lecture
OH by appt
No Lecture
OH by appt
(first page is instructions)
Due 3/20 7 pm.

Back to the top.

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
4. Magnetic Fields in Matter (cont.)
Reading: (J 5.9-5.12)
Assignment 1
Apr 15
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
Apr 22
7. Magnetic Energy and Forces (cont.),
Maxwell's Equations
, Conservation Laws

Reading: G 7.2-7.3, 8.1, LN 7.5-7.7, 8.1-8.2
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
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)
May 6
11. Confined Waves:
Transmission Lines
Reading: G 9.5.3, LN 9.5 (HM 7.1, 7.3, J 8.2)
12. Confined Waves:
Transmission Lines (cont.),
Waveguides (cont.)
Reading: G 9.5.1, LN 9.5-9.6 (HM 7.3-7.4, J 8.2-8.3)
Assignment 4
Section 8.3 of Griffiths 4th ed.
May 13
13. Confined Waves: Waveguides (cont.)
Reading: LN 9.6 (J 8.1, 8.5)
14. Potential Formulation,
Retarded Potentials
Reading: G 10.1.1-10.1.3, 10.2.1, LN 10.1 (HM 8.1)
Assignment 5
May 20
15. Retarded Fields,
Fields of Point Charges Moving at Fixed Velocity

Reading: G 10.2.2-10.3, LN 10.1-10.2 (HM 8.2-8.5)
16. Fields of and Power from Accelerating Point Charges,
Electric Dipole Radiation

Reading: G 10.3.2, 11.2.1, 11.1.1-11.1.2, LN 10.2-10.3 (HM 8.4, 8.6-8.8, 9.2)
G 11.2.2-11.2.3 are being skipped, you are not responsible for this material.
Assignment 6
May 27
17. Radiation (cont.),
Relativity Review
Reading: G 11.1.2-11.1.4, LN 10.3 (HM 9.1, 9.8)
Reading: G 12.1-2, LN 11.1
Reading: Chen Ph106b Lecture Notes for
Lecture 1, Lecture 2, Lecture 3, Lecture 4
18. Relativity in Electrodynamics
Reading: G 12.3, LN 11.2
Reading: Chen Ph106b Lecture Notes for Lecture 5
Assignment 7
Jun 3
19. Relativity in Electrodynamics (cont.); Applications of Radiation: Classical Scattering
Reading: LN 12
20. Applications of Radiation:
Antennas, Diffraction
Reading: TBD
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
Assignment 8
(FSJ only)
Final for GS
Due Jun 7
FSJ: do not download this exam!  It overlaps the FSJ exam.
June 10
No Lecture
No Lecture
Final for FSJ
Due Jun 14
Solutions for both Final Exams

Back to the top.

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:

Wednesday 7-8 pm, B157 West Bridge: problem session.  This is an interactive session in which the students will work together to solve problems.

Friday 3-4 pm, B157 West Bridge: open session.

Office hours:
Wednesday 7-8 pm, B157 West Bridge: problem session.  This is an interactive session in which the students will work together to solve problems.

Friday 3-4 pm, B157 West Bridge: open session.

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.

Back to the top.


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.
  • 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.

Ditch day policy (Ph106c):

  • If ditch day falls on a lecture day, I will reschedule the lecture for the Saturday following ditch day at the usual lecture time, 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 (2018):

Ph106c (2018):

Back to the top.

Announcements Archive