Physics 106bc
Winter and Spring Quarter, 2020
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! 

The only difference between Ph106b and Ph106c (EM) is the range and the level of complexity of the physical configurations considered and the range of techniques taught.

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Announcements

Syllabus and Schedule, Problem Sets, and Solutions

Note that this is the first year of a reorganization of Ph106bc, shifting basic EM material entirely into the required Ph106b course and leaving more advanced EM material for the first half of the optional Ph106c course.  There will no doubt be challenges with such a reorganization, so please bear with us as we try to better adapt the courses to student needs and interests.

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 (modestly) as the term progresses.  Homework and exam due dates will not change.

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 may 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)
Jan 6
1.
Ba
sic Electrostatics I:
LN 2.2: Assumptions
LN 2.3:
Electric Field
LN 2.4: Gauss's Law, Dirac Delta Function
LN 2.5: Curl E = 0
(28+6)
Reading: G 2.1-2.2
2.
Ba
sic Electrostatics II:

LN 2.6: Boundary Conditions
LN 2.7: Electric Potential
LN 2.8: Electric Potential Energy
LN 2.9: Conductors
(24+7)
Reading: G 2.3-2.5.3
N/A
Jan 13
3.
Basic Electrostatics III:
LN 2.10: Capacitance
(12+2)
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)
PS, W OH: Xiuqi
4.
Advanced Electrostatics II:
LN 3.2: Uniqueness Theorem (2+3)
LN 3.3:
Method of Images (10+2)
LN 3.4: Separation of Variables in Cartesian Coordinates (10+6)
Reading: G 3.1.5-3.1.6 (J 1.8-1.9)
Reading: G 3.2-3.3.1 (J 2.1-2.4, 2.8-2.9)
F OH: Xiuqi
Assignment 1
Solutions
(TA: Xiuqi)
Jan 20
5.
Advanced Electrostatics III:
LN 3.8: Separation of Variables in Spherical Coordinates: General Theory (4+2)
LN 3.9: Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry (19+2)

Reading: G 3.3.2 (J 3.1-3.3)
PS, W OH: Yanlong
PS is Tuesday night due to Monday holiday
6.
Advanced Electrostatics IV:
LN 3.11:
Multipole Expansion (
12+3)
Electric Fields in Matter I:

LN 4.1: Polarizability, Bound Charges, and Potential of Polarizable Matter (6+1)

Reading: G 4.1-4.2 (J 4.1-4.3)
F OH: Yanlong
Assignment 2
Solutions
(TA: Yanlong) 
Jan 27
7.
Electric Fields in Matter II:

LN 4.2: Displacement Field, Boundary Conditions (4+2)
LN 4.3: Linear Dielectrics (7+4)
LN 4.4: Boundary Value Problems with Dielectrics (6+2)
LN 4.5:
Electrostatic Energies and Forces on Dielectrics (4+4)

Reading: G 4.3-4.4 (J 4.3-4.4, 4.7)
PS, W OH: Yongliang
8.
Electric Fields in Matter III:
LN 4.5: Electrostatic Energies and Forces on Dielectrics (cont.) (8)
Magnetostatics I:
LN 5.1-5.4: Currents, Fields, and Forces (18+3)
Reading: G 5.1-5.3.3 (J 5.1-5.3)
F OH: Yongliang
Assignment 3
Solutions
(TA: Yongliang)
Feb 3
9.
Magnetostatics II:
LN 5.5: Potentials (11+1)
LN 5.6: Boundary Conditions (5+0; drop BC on vector potential)
LN 5.7: Magnetic Multipole Expansion (15+5)

Reading: G 5.3.2, 5.3.4-5.4 (J 5.4-5.6)
PS, W OH: Xiuqi
This week will focus on:
2019 final exam problems and solutions
2018 final exam problems and solutions
2017 final exam problems and solutions
(Poll for which problems to do during review session: Closes at 1 pm Feb 3.)
10.
Magnetostatics II:
LN 5.7: Magnetic Multipole Expansion (15+5)
Magnetic Fields in Matter I:

LN 6.1-6.2: Potentials and Fields of Magnetized Materials (9+1)
LN 6.3: Auxiliary Field and Permeability (15+4)

Reading: G 5.4.3 (J 5.7)
Reading: G 6.1-6.4.1 (J 5.8-5.10)
F OH: None this week due to midterm.
Midterm
(first page is cover sheet)
Solutions
(TA: Yanlong, Yongliang)
Feb 10
11.
Magnetic Fields in Matter II:
LN 6.3: Auxiliary Field and Permeability ()
LN 6.4: Boundary Value Problems in Magnetic Matter (14+2)
Electrodynamics I:

LN 7.1: Currents and Ohm's Law (7)
LN 7.2: Electromotive Forces (6)

Reading: G 6.4 (J 5.9-5.11)
Reading: G 7.1 (J 5.15)
PS, W OH: Yongliang
12.
Electrodynamics II:
LN 7.2: Electromotive Forces (9)
LN 7.3: Electromagnetic Induction,
Faraday's Law (17)
LN 7.4:
Inductance (5)

Reading: G 7.1-7.2.3 (J 5.15, 5.17)
F OH:Yongliang
Assignment 4
Solutions
(TA: Yongliang)
Feb 17
13.
Electrodynamics III:
LN 7.5: Magnetic Energy, Magnetic Matter, and Magnetic Forces (14+2)
LN 7.6: Maxwell's Equations (8)

Reading: G 7.2.4-7.3.3 (J 5.16-5.17, J 6.1)
PS, W OH: Yongliang
14.
Electrodynamics IV:
LN 7.6: Maxwell's Equations (1)
LN 7.6: Maxwell's Equations in Matter (6)

Conservation Laws:

LN 8.1-8.2: Conservation of Charge, Energy (11)
EM Waves I:
LN 9.2: Electromagnetic Waves in Vacuum (15+1)

Reading: G 7.3.5-7.3.6 (J 6.1)
Reading: G 8.1 (J 6.7)
Reading: G 9.1-9.3.1
F OH:Yongliang
Assignment 5
Solutions
(TA: Yongliang)
Feb 24
15.
EM Waves II:
LN 9.2: EM Waves in Nonconducting Matter, Reflection and Refraction (21+4)
LN 9.3: EM Waves in Conductors (5)

Reading: G 9.3-9.4.1
PS, W OH: Yanlong
16.
EM Waves III:
LN 9.3: EM Waves in Conductors (11+1)
LN 9.6: Overview of Transmission Lines
and Waveguides (5)
Potential Formulation I:
LN 10.1: Potential Formulation (7)
LN 10.2.1:
Retarded Potentials (3+4)

Reading: G 9.4-9.5
Reading: G 10.1-10.2.1 (J 6.2-6.4, HM 8.1-8.2)
F OH: Yanlong
Assignment 6
Solutions
(TA: Yanlong)
Mar 2
17.
Potential Formulation II:
LN 10.2.2: Retarded Fields (6+2)
Special Relativity:
LN 11.1: Review of Special Relativity (11)
LN 11.2: Covariant Formulation of EM Sources and Fields (6)

Reading: G 10.2.2 (J 6.5, HM 8.2)
Reading: G 12.1, 12.3, 12.2
PS, W OH: Yanlong
18.
LN 11.2: Covariant Formulation of EM Sources and Fields (7+5)
LN 11.3: Relativistic Dynamics with EM Fields (7)

Radiation I:
LN 12.1: Potentials and Fields of a Moving Point Charge (19+2)

Reading: G 12.3, 12.2
Reading: G 10.3.2
F OH: Yanlong
Assignment 7
Solutions
(TA: Yanlong)
Mar 9
19. 
Radiation II:
LN 12.2: Power Radiated by an Accelerating Point Charge (4; skip brem and sync)
LN 12.3: Radiation: General Theory (10+1)

LN 12.4: Electric Dipole Radiation (5+1)
LN 12.5: Magnetic Dipole Radiation (4+1)
G 11.2.1, 11.1 (HM 8.4-8.6, 9.1)
G 11.2.2-11.2.3 are being skipped, you are not responsible for this material.
PS: Xiuqi
Special T OH: SG, 9-11 pm
W OH 3-4 pm because PS due on Wednesday
no F OH
Final Exam Review Session
during normal lecture time Th OH 10:30-noon (SG)
Location: 107 Downs
Practice final exams and solutions:
2019 midterm exam problems and solutions
2018 midterm exam problems and solutions
2017 midterm exam problems and solutions
2019 final for GS, final for FSJ, solutions
2018 final for GS, final for FSJ, solutions
2017 final for GS, final for FSJ, solutions
Assignment 8
Solutions
(TA: Xiuqi)
due Wednesday Mar 11 due to end of term!
Delayed to Fri Mar 13.
Mar 16
No Lecture
OH by appt
N/A Final exam including cover page
(first page is instructions)
Solutions
Due 3/18 7 pm
Delayed to 3/25 7 pm (ignore date on exam cover page).
(TA: Xiuqi, Yanlong)

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Ph106c syllabus now pretty solid, but adjustments will probably still be made.  Schedule delayed by 1 week due to COVID-19.
See below for how to access Zoom lectures and live PowerPoint slides.


Tuesday Lecture Thursday Lecture Homework
(due Friday 7 pm)
Apr 6
20.
Advanced Electrostatics IV:
LN 3.4: Green Functions (15+1)
LN 3.5:
Obtaining Green Functions from the Method of Images (6+2)
LN 3.9.1-3:
Separation of Variables in Spherical Coordinates w/o Azimuthal Symmetry (6)
Reading: (J 1.10, 2.6, 2.9, 3.1-3.2, 3.5-3.6)
21.
Advanced Electrostatics V:
LN 3.9.4-5: Spherical Harmonic Expansion of Green Function (16+12)

Reading: (J 3.9-3.10)

No assignment due
Apr 13
22.
Advanced Magnetostatics I:
LN 6.4.4: Advanced Boundary Value Problems in Magnetic Matter (16+4)
Advanced Conservation Laws in EM:
LN 8.3: Conservation of Linear Momentum (9)
LN 8.4: Conservation of Angular Momentum (3+2)

Reading: (J 5.12)
Reading: G 8.2 (J 6.7, 12.10)
PS, W OH: Yanlong
23.
Advanced EM Waves I:
LN 9.5: EM Waves in Dispersive Matter (14)

LN 9.6: Guided Waves Overview (1)
LN 9.7: Transmission Lines (23)
Reading: G 9.4.3 (J 7.5, HM 10.2, 10.4-10.5)
Reading: G 9.5 (HM 7.1)
Assignment 1
Solutions
(TA: Yanlong)
Apr 20
24.
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)
PS, W OH: Dongjun
25.
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)
Assignment 2
Solutions
(TA: Dongjun)
Apr 27
26.
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)
PS, W OH: Yanlong
27.
Applications of Radiation:
LN 12.2: Antennas (21)
Reading: (HM 9.4-9.5, 9.7, J 9.4)
Assignment 3
Solutions
(TA: Yanlong)
May 4
Ph106c taken over by Prof. Hutzler.
Midterm on EM material
OH/PS this week will focus on:
2019 Ph106b final exam problems and solutions
2018 Ph106b final exam problems and solutions
2017 Ph106b final exam problems and solutions
2019 Ph106c midterm exam problems and solutions
2018 Ph106c midterm exam problems and solutions
2017 Ph106c midterm exam problems and solutions
2019 Ph106c final for GS, final for FSJ, solutions
2018 Ph106c final for GS, final for FSJ, solutions
2017 Ph106c final for GS, final for FSJ, solutions
(Poll for which problems to do during problem session: Closes at 9 am M 5/4.)
M PS: Dongjun; W OH: Dongjun.  No Th, F OH.
Topics that we would have covered with one more week...
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)
Feel free to read about these topics in the Lecture Notes.
Reading: G 12.2 (J 12.1, 12.7, 12.10)
Midterm
(first page is cover sheet)
Solutions
(TA: Dongjun, Yanlong)

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Vital Information

Ph106c has a Moodle site.  Caltech-privileged information, including how to access online resources like the class sessions on Zoom and lists of students who are interested in forming collaboration groups, will be listed there since it is password-protected.  Otherwise all information will be posted to this site.

Location:
107 Downs On Zoom at location listed on Moodle page.

Time:
TuTh 10:30 am - 12:00 pm

Instructor:

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

Office hours: Thursday 9 pm - 11 pm, Cahill library.  If you don't have a key to Cahill, knock on the library windows (accessible from driveway on east side of Cahill).  On Zoom at location listed on Moodle page.  If no one shows by 10 pm, or no one sends an email requesting I stay past 10 pm, I will probably leave.

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:

Ph106b:
Xiuqi Ma
Yanlong Shi
Yongliang Zhang

Office hours:

Monday 10-11 pm, problem session, location Cahill library.  This is an interactive session in which the students will work together to solve problems.  Credit will be given for attending as noted below.  If you cannot attend, email Prof. Golwala to make special arrangements.  

Wednesday 9-11 pm, location Cahill library: office hour, no planned agenda.  If no one shows by 10 pm, or no one sends an email requesting the TA stay past 10 pm, the TA may leave.

Friday 3-4 pm, location TBD: office hour, no planned agenda.

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

If you don't have a key to Cahill, knock on the library windows (accessible from driveway on east side of Cahill).
Ph106c:
Dongjun Li
Yanlong Shi

Office hours:
Monday 7-8 pm, problem session, on Zoom at location listed on Moodle page for the TA covering that week's problem set.
This is an interactive session in which the students will work together to solve problems.  Credit will be given for attending as noted below.  
If you cannot attend, email Prof. Golwala to make special arrangements.  

Wednesday 4-6 pm, on Zoom at location listed on Moodle page for the TA covering that week's problem set: 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, on Zoom at location listed on Moodle page for the TA covering that week's problem set: office hour, no planned agenda.

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.

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.

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Textbook(s) and Lectures

Policies and Grading

The course will use the same policies at Prof. Weinstein's Ph106a.  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.  Sets that include identifying information, such as a name of a person who has not submitted a FERPA waiver, will be available from the PMA Undergraduate Student Affairs Administrator, Freddy Mora, in 156 Linde during normal business hours.
  • 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.
  • 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, the split will be
    • 50% problem sets
    • 25% midterm exam
    • 25% final exam
  • For Ph106c, the split is TBD but will likely be the same.
  • 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.  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 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.
    • 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

Ph106b (2020; refresh cache to make sure you get new versions):




Ph106c (2019):







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