Physics 106bc - Topics in Classical Physics - Electrodynamics
Winter and Spring Quarter, 2021
Course Homepage

Overview and Intended Learning Outcome

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.

The intended learning outcome of both Ph106b and Ph106c (EM) 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! 

Ph106b covers the basics undergraduate syllabus in electrodynamics.  Ph106c (EM) extends some topics considered in Ph106b, introduces additional topics, and covers additional techniques where required.  Ph106c (EM) will increase a student's readiness for advanced work in areas that rely heavily on electrodynamics (quantum optics, AMO, some quantum information science platforms such as superconducting RF qubits) or field theory.

Quick Links

Announcements: see Canvas pages: Ph106b, Ph106c

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 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 is the first year that Ph106bc is being taught on a MWF schedule, and the second year of the reorganization in which only Ph106b is a required course, so please bear with me as the syllabus is refined to satisfy these new constraints.  The distribution of topics among weeks is not likely to change much, but the distribution of topics among lectures is being worked out as the term progresses.  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 I am drawing material from).  The numbers in parentheses after each LN section listing is the number of LN slides (for my benefit).

Week/TA Monday Lecture Wednesday Lecture Friday Lecture
Jan 4
No PS/OH this week!
Introduction to Course
LN 1.1: Course Material (5)
LN 1.2: Notation (1)
sic Electrostatics I:
LN 2.2: Assumptions (1)
LN 2.3:
Coulomb's Law, Electric Field,
Dirac Delta Function (7+1)
LN 2.4: Gauss's Law (8+2)
Reading: G 2.1-2.2.3
sic Electrostatics II:

LN 2.4: Dirac Delta Function Redux (2)
LN 2.5: Curl E = 0 (3+1)
LN 2.6: Techniques (1)
LN 2.7: Boundary Conditions (7)
LN 2.8: Electric Potential (4+1)
Reading: G 2.2.2-4, 2.3.1-2, 2.3.4-5
sic Electrostatics III:

LN 2.8: Electric Potential (3+1)
LN 2.9: Electric Potential Energy (7)
LN 2.10: Conductors
LN 2.10: Capacitance (9)
Reading: G 2.3.5, 2.4, 2.5.1-4 (J 1.11)
Jan 11
TA: Sophie
Basic Electrostatics III:
LN 2.10: Capacitance
Advanced Electrostatics I:
LN 3.1: Laplace's Equation (6)
Reading: G 2.5.4 (J 1.11)
Reading: G 3.1.1-3.1.4 (J 1.7)
Advanced Electrostatics II:
LN 3.2: Uniqueness Theorem (5)
LN 3.3:
Method of Images (10+1)
LN 3.5: Separation of Variables (3+1)
Reading: G 3.1.5-3.1.6 (J 1.8-1.9)
Reading: G 3.2 (J 2.1-2.4, 2.8)
Advanced Electrostatics III:
LN 3.5: Separation of Variables in Cartesian Coordinates (11+1)
LN 3.8: Separation of Variables in Spherical Coordinates: General Theory (5+1)
LN 3.8: Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry (3)
Reading: G 3.3.1 (J 2.9)
Reading: G 3.3.2 (J 3.1-3.3)
Jan 18
TA: Yanlong
PS is Tuesday night due to Monday holiday
MLK Holiday, no lecture
Advanced Electrostatics IV:
LN 3.8: Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry (cont.) (18+2)
Reading: G 3.3.2 (J 3.1-3.3)
Advanced Electrostatics V:
LN 3.10:
Multipole Expansion (

Reading: G 3.4 (J 4.1)
Reading: G 4.1.3 (J 4.2)
Jan 25
TA: Jaeha
Electric Fields in Matter I:

LN 4.1: Polarizability, Bound Charges, and Potential of Polarizable Matter (7)
LN 4.2:
Displacement Field, Boundary Conditions (3+2)
LN 4.3: Linear Dielectrics (4+7)
LN 4.4: Boundary Value Problems with Dielectrics (8)

Reading: G 4.1-4.4.2 (J 4.3-4.4)
Electric Fields in Matter III:
LN 4.5: Electrostatic Energies and Forces on Dielectrics (14+3)
Magnetostatics I:
LN 5.2: Lorentz Force, Currents (7)
Reading: G 4.4.3-4.4.4 (J 4.7)
Reading: G 5.1 (J 5.1)
Magnetostatics II:
LN 5.3: Continuity Equation (2)
LN 5.4: Fields, and Forces (5+1)
LN 5.5: Curl and Divergence of Magnetic Field, Ampere's Law (4+1)

LN 5.6: Potentials (11+1)
Reading: G 5.1-5.4.1 (J 5.2-5.5)
Feb 1
TA: Sophie
PS/OH this week will focus on 2018-2020 exams and solutions (see Canvas).
Magnetostatics III:
LN 5.6: Potentials (cont.) (1+2)
LN 5.7: Boundary Conditions (5+1; skip BC on vector potential)
LN 5.8: Magnetic Multipole Expansion (13+5)

Reading: G 5.4.2-3 (J 5.4-5.7)
Magnetic Fields in Matter I:
LN 6.1: Paramagnetism and Diamagnetism (1)
LN 6.2: Potentials and Fields of Magnetized Materials (5+4)
LN 6.3: Auxiliary Field and Permeability (9+4)

Reading: G 6.1-6.4.1 (J 5.8)
Magnetic Fields in Matter II:

LN 6.3: Auxiliary Field and Permeability (cont.) (11)
LN 6.4: Boundary Value Problems in Magnetic Matter (10+1)
Reading: G 6.4 (J 5.8-5.9, 5.11)
Feb 8
TA: Yanlong
Electrodynamics I:

LN 7.1: Currents and Ohm's Law (7)
LN 7.2: Electromotive Forces (16)

Reading: G 7.1 (J 5.15)
Electrodynamics II:
LN 7.3: Electromagnetic Induction,
Faraday's Law (17)
LN 7.4:
Inductance (3)

Reading: G 7.2.1-3 (J 5.15, 5.17)
Electrodynamics III:
LN 7.4: Inductance (cont.) (2)
LN 7.5: Magnetic Energy, Magnetic Matter, and Magnetic Forces (14+2)

Reading: G 7.2.3 (J 5.17)
Reading: G 7.2.4 (J 5.16-5.17)
Feb 15
TA: Jaeha
Presidents' Day Holiday, no lecture
Electrodynamics IV:
LN 7.5: Magnetic Energy, Magnetic Matter, and Magnetic Forces (cont.) (3)
LN 7.6: Maxwell's Equations (14)

Reading: G 7.2.4 (J 5.16-5.17)
Reading: G 7.3.1-7.3.3 (J 6.1)
Conservation Laws:
LN 8.1-8.2: Conservation of Charge, Energy (11)
EM Waves I:
LN 9.2: Electromagnetic Waves in Vacuum (12+2)

Reading: G 8.1 (J 6.7)
Reading: G 9.1-9.2 (J 7.1)
Feb 22
TA: Sophie
EM Waves II:
LN 9.2: Electromagnetic Waves in Vacuum (cont.) (3)
LN 9.3:
EM Waves in Nonconducting Matter,
Reflection and Refraction (19+3)
Reading: (J 7.2)
Reading: G 9.3 (J 7.3)
EM Waves III:
LN 9.3: EM Waves in Nonconducting Matter, Reflection and Refraction (5+7)
LN 9.4: EM Waves in Conductors (15+1)

Reading: G 9.3 (J 7.3)
Reading: G 9.4.1-2 (J 8.1)
EM Waves IV:
Overview of Transmission Lines and Waveguides
(optional: LN 9.6)
Potentials Revisited:

LN 10.1.1-4: Potential Formulation (8)
LN 10.2: Retarded Potentials and Field (9+12)
Reading: none required; optional: G 9.5 (J 8.1-8.5)
Reading: G 10.1-10.2 (J 6.2-6.3, 6.5, HM 8.1-8.2)
Mar 1
TA: Yanlong
Relativity and Electrodynamics I:
LN 11.2: Fundamentals of Special Relativity (22+13)

Reading: G 12.1-2
Relativity and Electrodynamics II:
LN 11.2: Fundamentals of Special Relativity (cont.) (3+2)
LN 11.3: Covariant Formulation of EM Sources and Fields (12+6)

LN 11.4: Relativistic Dynamics with EM Fields (3)

Reading: G 12.3, 12.2
Radiation I:
LN 12.1: Potentials, Fields, and Power Radiated by an Accelerating Point Charge (21+4)

Reading: G 10.3.2, 11.2.1 (HM 8.4-8.6)
Mar 8
TA: Jaeha
Th/F OH shifted to Tu/W at nominal times; no W 4-6 pm OH
Radiation I

LN 12.2: General Theory of Radiation including Electric and Magnetic Dipole Radiation (19+3)

G 11.1 (HM 9.1-9.2)
G 11.2.2-11.2.3 are being skipped, you are not responsible for this material.
Final Exam Review Session
during normal lecture time (SG)

Mar 15
No Lecture
OH by appt


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Monday Lecture Wednesday Lecture Friday Lecture
Mar 29
Advanced Electrostatics VI:
LN 3.4: Green Functions incl.
Obtaining Green Functions from the Method of Images (21+4)
Reading: (J 1.10, 2.6)
Advanced Electrostatics VII:
LN 3.5: Relation between Separation of Variables in Cartesian Coordinates and Green Functions (2)
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 (11)

Reading: (J 2.9, 3.1, 3.5-3.6, 3.9)
Advanced Electrostatics VIII:
LN 3.9.5: Spherical Harmonic Expansion of Green Function: Examples (11+5)

LN 3.4 redux: Obtaining Green Functions from the Method of Images (4) (we'll go over the material skipped on 3/29)
Reading: (J 3.10, 2.6)
Apr 5
TA: Sophie
Advanced Magnetostatics I:
LN 6.4.4: Advanced Boundary Value Problems in Magnetic Matter (16+4)

Reading: (J 5.9-5.10, 5.12)
Advanced Conservation Laws in EM:
LN 8.3: Conservation of Linear Momentum (9)
LN 8.4: Conservation of Angular Momentum (3+2)

Reading: G 8.2 (J 6.7, 12.10)
Advanced EM Waves I:
LN 9.5: EM Waves in Dispersive Matter (16)
LN 9.6: Guided Waves Overview (1)
LN 9.7: Transmission Lines (7)
Reading: G 9.4.3 (J 7.5, HM 10.2, 10.4-10.5)
Reading: G 9.5 (HM 7.1)
Apr 12
TA: Dongjun
Advanced EM Waves II:
LN 9.7: Transmission Lines (cont.) (23)
LN 9.8.1-9.8.2: Waveguides: General Properties of Solutions (5+1)
Reading: G 9.5 (HM 7.1, J 8.2)
Advanced EM Waves III:
LN 9.8.3-9.8.8: Waveguides: General Properties of Solutions (5+1)
LN 9.8.9: Waveguides: Propagation Properties (3)
LN 9.8.10-11: Waveguides: Example Solutions (6+1)
LN 9.8.12: Energy in Waveguides (5+1)

Reading: (J 8.2-8.3, 8.4, 8.5)

Apr 19
Advanced EM Waves IV:
LN 9.8.13-15: Waveguides with Finite Conductivity (13)

Advanced Potentials and Fields of Moving Charged Particles:
LN 12.2: Bremsstrahlung and Synchrotron Radiation, Lienard's Formula (7)
Applications of Radiation:
LN 13.1: Classical Scattering Theory (16+1)
Reading: (J 8.1, 8.5)
Reading: G 11.2 (HM 8.7-8.8)
Reading: (HM 10.1, J 14.8)
Applications of Radiation:
LN 12.2: Antennas (21)
Reading: (HM 9.4-9.5, 9.7, J 9.4)

Apr 26
Advanced Potential Formulation:
LN 10.1.5: Lorentz Force Law in Potential Form (7);
LN 10.1.6: Gauge Transformations and Coupling of Matter to EM Fields (7);

Advanced Special Relativity:
LN 11.3: Relativistic Dynamics with EM Fields (7)
LN 11.4: Relativistic Conservation Laws (5+4)

Reading: G 12.2 (J 12.1, 12.7, 12.10)
Reading: TBD

May 3
Ph106c taken over by Prof. Hutzler.
Midterm on EM material
OH/PS this week will focus on 2018-2020 exams and solutions (see Canvas)
(Poll for which problems to do during problem session: Closes at 9 am M 5/3.)

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Vital Information

Ph106b and Ph106c have Canvas sites.  Caltech-privileged information, including problem sets and how to access online resources like the class sessions on Zoom, will be listed there since it is password-protected.  All public information will be posted to this site.

On Zoom at location listed on Canvas page.

MWF 11:00-11:55 am


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

Office hours: Thursday 9 pm - 11 pm, on Zoom as listed on Canvas page.  If no one shows by 10 pm, or no one sends an email requesting I stay past 10 pm, I will probably leave. 

Zoom sessions will be recorded and posted to the course Canvas page unless a student requests an unrecorded breakout room.

If time zones prevent anyone from attending the above office hour, other arrangements can be made.  Contact me.

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:

Sophie Hourihane
Jaeha Lee
Yanlong Shi

Office hours:

The MWF problem sessions and office hours will be run by the TA that is grading that week's homework using that TA's zoom link.  See the syllabus above for the relevant TA information.  Zoom links are available on the course Canvas page.

Zoom sessions will be recorded and posted to the course Canvas page unless a student requests an unrecorded breakout room.

Monday 7-8 (-9) pm: problem session. 
This is an interactive session in which the students will work together to solve problems.  The session may go past 8 pm depending on student and TA interest, but only attendance at the first hour is required to obtain credit as notedIf you cannot attend, email me to make special arrangements.  

Wednesday 4-6 pm: office hour, no planned agenda.  If no one shows by 5 pm, or no one sends an email requesting the TA stay past 5 pm, the TA may leave.

Friday 3-4 pm: 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 time zones prevent anyone from attending the above problem session or office hours, other arrangements can be made.  Contact the course instructor.

Sophie Hourihane
Dongjun Li

Office hours: same as above, with one modification: the 2nd hour of the Monday Problem Session, which will not be required to obtain extra credit, will consist of a non-interactive run-through of additional problems so students can get more experience with how problems can be approached.

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 mid-term survey that will provide an opportunity for anonymous feedback.

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Textbook(s) and Lectures

Policies and Grading

The course will use the same policies at Prof. Fuller's Ph106a policies, available from his course's Canvas site.  Refinements and clarifications:
  • 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 for Ph106b and one for Ph106c.  Only one silver bullet extension is allowed for all of Ph106c, not one for each half of the class (E&M vs. optics).
  • For Ph106b and 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 Monday 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 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 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 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.
Grade Distributions

Ph106b (2021):

Ph106c (2020):

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