Physics 106bc
Winter and Spring Quarter, 2017
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 6
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 
Midterm due
Feb 13
3. Capacitance, Laplace's Equation, Uniqueness Theorem
Reading: G 2.5.4, 3.1, LN 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
(TA: Pouria)
Feb 20
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,
Separation of Variables in Spherical Coordinates w/o Azimuthal Symmetry
Reading: G3.3.2, LN 3.9-3.10
(J 3.1-3.3, 3.5-3.6)
Summary slides for lectures 3-6
Assignment 5
(TA: Feng) 
Feb 27
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)
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
(v2 updated 2017/03/01 18:00)
(TA: Pouria)
Mar 6
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
2016 final exam problems and solutions
2015 final exam problems and solutions
2014 final exam problems and solutions
(Poll for which problems to do during review session: Closes at midnight Mar 8/9.)

Assignment 7
(TA: Feng, Pouria)
Mar 13
No Lecture
OH by appt
No Lecture
OH by appt
(first page is instructions)
(v2 posted 4/18)
Due F Mar 17
(TA: Feng, Pouria, SG)

Back to the top.

Tuesday Lecture Thursday Lecture Homework
(due Friday 7 pm)
Apr 3
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 10
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: Pouria)
Apr 17
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: Pouria)
Apr 24
7. Magnetic Energy and Forces (cont.),
Maxwell's Equations
, Conservation Laws

Reading: G 7.2-7.3, 8.1-8.2, LN 7.5-7.7, 8.1-8.2.3
8. Conservation Laws (cont.),
Electromagnetic Waves in Vacuum
Reading: G 8.2.2-8.2.4, 9.1-9.2, LN 8.3-8.4, 9.1
Assignment 3
(TA: Feng)
May 1
9.  EM Waves in Nonconducting Matter,
EM Waves in Conductors
Reading: G 9.3, 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)
2016 midterm exam problems and solutions
2015 midterm exam problems and solutions
2014 midterm exam problems and solutions
(first page is cover sheet)
(TA: Feng/Yong-Liang)
May 8
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.
(TA: Feng)
May 15
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
(TA: Feng)
May 22
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
(TA: Yong-Liang)
May 29
17. Radiation (cont.),
Relativity Review
(Due to instructor absence, this lecture will occur on Thursday 6/1.)
Reading: G 11.1.2-11.1.4, LN 10.3 (HM 9.1, 9.8)
Reading: G 12.1-2, LN 12.1
Canceled due to instructor absence.
Assignment 7
(v. 2 2017/06/04 05:00)
(TA: Yong-Liang)
Jun 5
18. Relativity in Electrodynamics
Reading: G 12.3, LN 12.2
20. Review for Final
Practice final exams and solutions:
2016 final for GS, final for FSJ, solutions
2015 final for GS, final for FSJ, solutions
2014 final for GS, final for FSJ, solutions
Assignment 8
(FSJ only;
v 2 posted 6/8
(TA: Yong-Liang)
Final for GS
Due June 9
FSJ: do not download this exam!  It overlaps the FSJ exam.
(TA: Pouria)
June 12
No Lecture
No Lecture
Final for FSJ
Due June 16
Solutions for both Final Exams
(TA: Pouria)

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 9 pm, or 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.

Teaching Assistants:

Feng Bi
Pouria Dadras
Samuel Savitz

Office hours: Sam will run a weekly recitation section, W 4:20 pm in Watson 104, and office hours Friday 2 pm - 3 pm in Keck 142.
Feng Bi
Pouria Dadras
Yong-Liang Zhang

Office hours:
Wednesday 7-9 pm, 114 E. Bridge, Friday 3-4 pm in Keck 142 in addition to SG Th 9-11 pm.

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 Ph106ab.  Refinements and clarifications:
  • 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

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.  If that Monday is a holiday, then the set will be due Tuesday at the usual time.

  • 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.  The Friday office hours will be rescheduled for Sunday night.
    • 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 (2017):

Ph106c (only Midterm is updated for 2017):

Back to the top.

Announcements Archive