Physics 106bc - Topics in Classical Physics - Electrodynamics
Winter and Spring Quarter, 2023
Course Homepage

Overview and Intended Learning Outcome

From the course catalog:
9 units (4-0-5) ... An intermediate course in the application of basic principles of classical physics to a wide variety of subjects. Ph106a will be devoted to mechanics, including Lagrangian and Hamiltonian formulations of mechanics, small oscillations and normal modes, central forces, and rigid-body motion. Ph106b will be devoted to fundamentals of electrostatics, magnetostatics, and electrodynamics, including boundary-value problems, multipole expansions, electromagnetic waves, and radiation. It will also cover special relativity. Ph106c will cover advanced topics in electromagnetism and an introduction to classical optics.
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.

This year marks the second time that the EM syllabus (neglecting optics), which for at least 20 years has been taught as a 1.5 term course, will be slowed down and extended to 2 full terms without any increase in the amount of material covered.  Ph106b will be restricted to electrostatics and magnetostatics, and Ph106c will cover electrodynamics including EM waves, special relativity, and radiation.  Classical optics will not be covered.  This change is intended to respond to concerns from prior years that too much material is packed into too short a time period.  The slower pace of the course will hopefully enhance learning and students' enjoyment of the course.

The intended learning outcome of both Ph106b and Ph106c is for students to acquire the ability to calculate electric and magnetic potentials, fields, energies, and forces in a variety of basic physical configurations combined with an understanding of the underlying physical principles and calculation techniques.  This outcome requires both an understanding of principles as well as the ability to apply them to do calculations! 

Quick Links

Announcements: see Canvas pages: Ph106b (accessible only to students registered for the course)

Syllabus and Schedule, Problem Sets, and Solutions

Below you will find the outline of Ph106bc.  I will update the details of the topics covered in lectures and suggested reading as the term progresses.  Assignments and exams will be made available via Canvas, about a week before the due date, so no effort is made here to list them.

The problem sets and solutions are only accessible via Canvas.  (Lecture notes are available to anyone.)

Note that, this year, the schedule is changing, now from a 3x55 minute class to 2x85 minutes, so please understand the syllabus is being refined as the lectures are being given.  You can view last year's syllabus here.  The ordering of topics will not change, but the distribution among lectures will, and there will be a half-week delay due to the date of start of term.  The specific material covered in each problem set will respond to the evolution of the syllabus, so problem sets will not be posted ahead of time.

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.

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 material is drawn from).  The numbers in parentheses after each LN section listing and at the end of each day's lecture is the number of LN slides (to manage lecture pace).

Ph106b: Electrostatics and Magnetostatics
Week/TA Tuesday Lecture Thursday Lecture
Jan 2
TA: N/A
No PS/OH this week!

1.
Introduction to Course
LN 1.1: Course Material (5)
LN 1.2: Notation (1)
Basic Electrostatics I:
LN 2.2: Assumptions (1)
LN 2.3: Coulomb's Law, Electric Field, Dirac Delta Function (8)
LN 2.4: Integral Form of Gauss's Law (6)
LN 2.4: Differential Form of Gauss's Law (4)
(27)
Reading: G 2.1-2.2.3
Jan 9
TA: Yanlong
2.
Basic Electrostatics II:
LN 2.4: Dirac Delta Function Redux (2)
LN 2.5: Curl E = 0 (4)
LN 2.6: Techniques (1)
LN 2.7: Electric Potential (5)
LN 2.8: Boundary Conditions (10)
LN 2.9: Poisson's and Laplace's Equations (2)
(24)
Reading: G 2.2.4-2.3
3.
Basic Electrostatics III:
LN 2.10: Electric Potential Energy (7)
LN 2.11: Conductors (10)
LN 2.12.1-2: Capacitance (6)
(23)
Reading: G 2.4-2.5 (J 1.11)
Jan 16
TA: Federico
PS delayed to Tuesday evening due to holiday
4.
Basic Electrostatics IV:
LN 2.12.3-5: Capacitance cont'd (13)
Advanced Electrostatics I:
LN 3.1: Laplace's Equation (6)
(19)
Reading: G 2.5.4 (J 1.11)
Reading: G 3.1.1-3.1.4 (J 1.7)
5. Advanced Electrostatics II:
LN 3.2: Uniqueness Theorem (5)
LN 3.3: Method of Images (11)
(21)
Reading: G 3.1.5-3.1.6 (J 1.8-1.9)
Reading: G 3.2 (J 2.1-2.5)
Jan 23
TA: Andrew
6. Advanced Electrostatics III:
LN 3.4: Green Functions (16)
LN 3.4: Obtaining Green Functions from the Method of Images (9)
(25)
Reading: (J 1.10)
Reading: (J 2.6-2.8)
7. Advanced Electrostatics IV:
LN 3.5: Separation of Variables: General Considerations (4)
LN 3.6: Separation of Variables in Cartesian Coordinates (13)
LN 3.7: Separation of Variables in Spherical Coordinates: General Theory (6)
(23)
Reading: G 3.3.1 (J 2.9)
Reading: G 3.3.2 (J 3.1-3.2)
Jan 30
TA: Yanlong
8. Advanced Electrostatics V:
LN 3.8.1-3.8.4: Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry (18)
Reading: G 3.3.2 (J 3.1-3.3)
9. Advanced Electrostatics VI:
LN 3.8.5: Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry (5)
LN 3.9.1-3: Separation of Variables in Spherical Coordinates w/o Azimuthal Symmetry (6)
LN 3.9.4: Spherical Harmonic Expansion of Green Function (8)
(19)
Reading: (J 3.3)
Reading: (J 3.5-3.6, 3.9-3.10)
Feb 6
TA: Federico
PS this week will focus on practice midterm problems
10. Advanced Electrostatics VII:
LN 3.9.4: Spherical Harmonic Expansion of Green Function (cont.) (6)
LN 3.9.5: Examples of Using the Spherical Harmonic Expansion of Green Functions (9+5)
(15+5)
Reading: (J 3.9-3.10)
11.
Advanced Electrostatics VIII:
LN 3.10: Multipole Expansion (12)
(12)
Reading: G 3.4 (J 4.2)
Feb 13
TA: Andrew
12.
Advanced Electrostatics IX:
 LN 3.10: Multipole Expansion (3)
Electrostatics in Matter I:
LN 4.1: Polarizability and Polarization (7)
LN 4.2: The Electric Displacement Field (5)
LN 4.3: Linear Dielectrics (4+4)
(19)
Reading: G 3.4 (J 4.2)
Reading: G 4.1-4.4.1 (J 4.3)
13.
Electrostatics in Matter II:
LN 4.3: Linear Dielectrics (cont.) (3)
LN 4.4: Boundary Value Problems with Dielectrics (7)
LN 4.5: Electrostatic Energies and Forces on Dielectrics (8)
(18)
Reading: G 4.4.1 (J 4.3)
Reading: G 4.4.2 (J 4.4)
Reading: G 4.4.3 (J 4.7)
Feb 20
TA: Federico
PS delayed to Tuesday evening due to holiday
14.
Electrostatics in Matter III:
LN 4.5: Electrostatic Energies and Forces on Dielectrics (cont.) (8)
Magnetostatics I:
LN 5.2: Lorentz Force, Currents (7)
LN 5.3: Continuity Equation (2)
LN 5.4: Fields and Forces (5)
 (22)
Reading: G 4.4.3 (J 4.7)
Reading: G 5.1-5.2.2 (J 5.1)
15.
Magnetostatics II:
LN 5.5: Divergence of Magnetic Field (1)
LN 5.5: Curl of Magnetic Field, Ampere's Law (7)
LN 5.6: Potentials (13)
(21)
Reading: G 5.2.2-5.4.1 (J 5.2-5.5)
Feb 27
TA: Andrew
16.
Magnetostatics III:
LN 5.7: Boundary Conditions (12)
LN 5.8: Magnetic Multipoles (10)
(22)
Reading: G 5.4.2 (J 5.8)
Reading: G 5.4.3 (J 5.6)
17.
Magnetostatics IV:
LN 5.8: Magnetic Multipoles (cont.) (9)
Magnetic Fields in Matter I:
LN 6.1: Paramagnetism and Diamagnetism (1+)
LN 6.2: Potentials and Fields of Magnetized Materials (6+3)
LN 6.3: Auxiliary Field (5)
(21+3)
Reading: G 5.4.3 (J 5.6-5.7)
Reading: G 6.1-6.3.2 (J 5.8, 5.10)
Mar 6
TA: Federico
18.
Magnetic Fields in Matter II:
LN 6.3: Boundary Conditions on Auxiliary Field (3)
LN 6.3: Magnetic Permeability (6+3)
LN 6.4: Boundary Value Problems in Magnetic Matter (17)
(23+3)
Reading: G 6.3.3 (J 5.8)
Reading: G 6.4.1 (J 5.9-5.11)
19.
Magnetic Fields in Matter III:
LN 6.4: Boundary Value Problems in Magnetic Matter (14+5)
 LN 6.5: Nonlinear Magnetic Permeability (7)
(21+5)
Reading: G 6.4.1-2 (J 5.11-5.12)
Mar 13
TA:
Yanlong
Final Exam Review during problem session
Problems from 2020-2022 exams, available on Canvas, will be used.
A poll will be sent out to determine which problems are of most interest.
N/A
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Ph106c: Electrodynamics
Week/TA
 Tuesday Lecture Thursday Lecture
Apr 3
TA: N/A
No PS/OH this week!


Apr 10
TA: TBD


Apr 17
TA: TBD


Apr 24
TA: TBD


May 1
TA: TBD


May 8
TA: TBD


May 15
TA: TBD


May 22
TA: TBD


May 29
TA: TBD


Jun 5
TA: TBD
PS delayed to Tuesday evening due to holiday

Final Exam Review during usual lecture time (SG)
Problems from 2020-2022 exams, available on Canvas, will be used.
A poll will be sent out to determine which problems are of most interest.
Reading: N/A
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Vital Information

Ph106b has a Canvas site.  Caltech-privileged information, including problem sets, will be listed there since it is password-protected.  All public information will be posted to this site.

Location: 107 Downs

Time: TuTh 10:30-11:55 am

Instructor:

Prof. Sunil Golwala, 308 Cahill, Mail Code 367-17.

Office hours: Thursday 9-11 pm, Cahill library.  If no one shows by the end of the first hour, or no one sends an email requesting the second hour, the OH may end early.  If you don't have access to Cahill, you can knock on the windows of the library to be let in (Cahill access will be requested for all Ph106b students.)

If conflicts prevent anyone from attending the above office hour, other arrangements can be made.  Contact the course instructor.

If you need to contact the course instruction outside of office hours, please try email first.  Meetings can be arranged outside of normal office hours, but spur-of-the-moment meetings are frequently not possible.  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:
Ph106b:
Federico Cima
Andrew Ivanov
Yanlong Shi

Office hours:
We will have one problem sessions (on Monday) and two office hours (Wednesday, Friday) each week in addition to the instructor office hours on Thursday.

The problem session and W/F office hours will be run by the TA who is grading that week's homework.  See the syllabus above for the relevant TA information.

Monday 8-10 pm, 107 Downs.  This is an interactive session in which the students will work together to solve problems.  The session may go past 1 hr depending on student and TA interest, but only attendance at the first hour is required to obtain credit as noted below.  If you cannot attend, email the course instructor to make special arrangements.

Wednesday 8-10 pm, Cahill Library.  If no one shows by the end of the 1st hour, or no one sends an email requesting the TA stay past the first hour, the OH may end early.  If you don't have access to Cahill, you can knock on the windows of the library to be let in (Cahill access will be requested for all Ph106b students.)

Friday. 3-4 pm, Cahill Library: office hour, no planned agenda; intended for last-minute questions for problem set due that day.

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

If conflicts prevent anyone from attending the above problem session or office hours, other arrangements can be made.  Contact the course instructor.

The problem session will switch to zoom if in-person instruction is suspended.  The office hours will switch too zoom for that reason or if weather precludes outside office hours.  The zoom links will be available on Canvas and an announcement will be sent in such situations.
Ph106c:
TBD

Office hours: Same as for Ph106b.

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.  There will be a request for volunteers for course ombudspersons and a mid-term survey that will provide an opportunity for anonymous feedback.

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Textbook(s) and Lectures

Other texts are included in the Course Reserves, but these are the most useful.

Policies and Grading

The course will use the following policies on collaboration, honor code, assignment due dates and extensions, and credit:
  • Homework is due Fri 7 pm PT via Canvas.

  • Extension requests should be sent to me, the course instructor, not the TAs.  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.

  • You may have one silver bullet extension each for Ph106b and one for Ph106c.  You do not need to request permission ahead of time, just note it at the top of the submitted problem set.  Let us know if it is occurring near the end of term so we don't miss giving credit for the work.

  • The grading split will be
    • 50% problem sets
    • 25% midterm exam
    • 25% final exam

  • Extra credit for problem session attendance: To encourage attendance at the Monday problem 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 Ph106b will be guaranteed one +/- grade increment of extra credit.  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 problem session time, contact the course instructor to identify an alternate solution.
  • Honor code and Collaboration policy

    • Use of mathematical software like Mathematica is allowed on homework, 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.

    • HOMEWORK COLLABORATION AND REFERENCE POLICY

      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.

      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.

    • EXAM COLLABORATION AND REFERENCE POLICY

      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.

    • You may use the previous years' exams and solutions posted on the Canvas 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 or the Canvas 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
Note the very strong final exam vs. midterm exam correlation and the weak total exam vs. homework correlation.  Too much collaboration on homework can leave one unprepared for the non-collaborative exams.

Ph106b (2023 -- updated 2023/03/23; note that all histograms are before extra credit):




Ph106c (2022 -- updated 2023/02/18; note that all histograms are before extra credit):





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