Overview and
Intended Learning Outcome
From the course catalog:
9 units (405) ... 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 rigidbody motion. Ph106b will
be devoted to fundamentals of electrostatics,
magnetostatics, and electrodynamics, including
boundaryvalue 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
halfweek 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 2.12.2.3



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 2.2.42.3


3.
Basic Electrostatics III:
LN 2.10: Electric Potential Energy (7)
LN 2.11: Conductors (10)
LN 2.12.12: Capacitance (6)
(23)

Reading: G 2.42.5 (J 1.11)


Jan 16
TA: Federico
PS delayed to Tuesday evening due to
holiday


4.
Basic Electrostatics IV:
LN 2.12.35: 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 3.1.13.1.4 (J 1.7)


5. Advanced Electrostatics II:
LN 3.2: Uniqueness Theorem (5)
LN 3.3: Method of Images (11)
(21)

Reading: G 3.1.53.1.6 (J 1.81.9)
Reading: G 3.2 (J 2.12.5)



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 2.62.8)


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 3.13.2)



8. Advanced Electrostatics V:
LN 3.8.13.8.4:
Separation of Variables in Spherical
Coordinates w/Azimuthal Symmetry (18)

Reading: G 3.3.2
(J 3.13.3) 

9. Advanced Electrostatics VI:
LN 3.8.5:
Separation of Variables in Spherical
Coordinates w/Azimuthal Symmetry (5)
LN 3.9.13: 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 3.53.6, 3.93.10)


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
3.93.10)


11.
Advanced Electrostatics VIII:
LN 3.10:
Multipole Expansion (12)
(12)

Reading: G 3.4 (J 4.2)



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 4.14.4.1 (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
5.15.2.2 (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
5.2.25.4.1 (J 5.25.5)



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 5.65.7)
Reading: G
6.16.3.2 (J 5.8, 5.10)



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 5.95.11)


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 6.4.12 (J 5.115.12)




Final Exam Review during
problem session
Problems from
20202022 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!




























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



Final Exam Review during usual
lecture time (SG)
Problems from 20202022 exams, available on
Canvas, will be used.
A poll will be sent out to determine which
problems are of most interest. 
Reading: N/A 

Back to the
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Vital
Information
Ph106b has a Canvas site.
Caltechprivileged information, including problem sets,
will be listed there since it is passwordprotected.
All public information will be posted to this site.
Location: 107 Downs
Time: TuTh 10:3011:55 am
Instructor:
Prof.
Sunil Golwala, 308 Cahill, Mail Code 36717.
Office hours: Thursday 911 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
spurofthemoment 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 810 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 810 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.
34 pm, Cahill Library: office
hour, no planned agenda; intended for lastminute
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 inperson
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 endofterm 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
midterm survey that will provide an opportunity for anonymous
feedback.
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Textbook(s)
and Lectures
 Required: Introduction to
Electrodynamics, Griffiths (4th edition!) available
via the Caltech eCampus online textbook
store. No guarantees are made about whether the
3rd edition is sufficient for the course (though in the past
it has been).
 Optional (all these will
be available via the Course Reserves link in Canvas):
 Heald and Marion, Classical
Electromagnetic Radiation
 Jackson, Classical Electrodynamics: the bible,
but in general too advanced for this course.
While this is not a required text, many students in past
years have found it useful to buy it. If you stay
in physics, you will need it. In addition to
the hard copies, the library is able to make portions
available electronically. Those portions will be
synchronized with the course.
 Landau and Lifshiftz, The Classical Theory of Fields
 Landau and Lifshiftz, Electrodynamics of Continuous
Media
Other texts are included in the Course Reserves, but
these are the most useful.
 Lecture Notes and
Strategy:
2023 version, updated 2023/03/09 10:00 for Lecture 19: pdf
2022 final version: pdf
My lecture notes generally follow Griffiths. My
goals in making them available to you are:
 To provide clarification of points in Griffiths that I
thought deserved more or alternate explanation.
 To present additional explanation or material derived
from other texts; the references will be provided in the
notes and/or on the syllabus above.
 To get all the calculational work down on the page,
correctly, so that I don't have to do it in class.
In particular, text in magenta is calculational work
that I skip over in class but which you are
responsible. If steps are unclear, ask the TAs
or in the following lecture.
I do not consider
myself responsible for providing updated copies of the
lecture notes well ahead of class time  they are being
updated as the course is being given. The 2022
version of the notes is provided above and is
frozen. Change from 2022 will be minimal (aside from
lecture breaks). Updated notes will be posted
promptly after class.
The lecture
notes may relieve you of the obligation of coming to
lecture. That's your choice. Some students
benefit from being able to receive information aurally and
to interact during that process; others prefer to read it
off the page. I hope the interactive nature of the
lectures will make them worth the time to attend.
But whatever works for you. Grades are based only on
the written work you submit.
But please do
not delude yourself into thinking that, because the
lecture notes are available, you can just skim through all
the material for the week on the day before a problem set
or exam is due and expect to immediately become
expert. Learning requires time to mull over concepts
in your mind, for your subconscious to work on ideas and
problems. If you choose not to come to class, please
be disciplined about keeping up with the material in your
own study time.
Back to the top.
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 nonimmediate
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 first 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 noncollaborative!
Exams are "openbook": You may consult your own notes
(both inclass 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 noncollaborative 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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