# PHYS 100C 2009

**Welcome to Physics 100C webpage for Spring'2009 Quarter.**

** Spring'2009 Quarter is over. This webpage is archived/protected **

## Contents |

## **RECENT UPDATES:**

in reverse chronological order

- June 11: Final Exam and Total Scores/Rankings are posted here. Letter grades will be posted later tonight.
- June 11: Final exam and solution are posted (PDF). The problems were more real-world related than your typical Griffith problem sets, and the physicsy head-scratching, model-building component may have gotten most of you by surprise - there were really no "simply turn the math crank here" type problems. I expect post the exam grades and letter grading tonight. You are welcome to stop by and talk to me today or tomorrow (should be in my office) if you want to discuss the final.
- June 9: Homeworks 1-7 and midterm grades posted. Let me know if you find any errors.
- June 9: Reminder that the final exam is 3 hrs, on Thursday, May 11, from 8AM to 11AM (make sure to set those alarm clocks) in the same classroom as usual (HSS 2154). Exam is open book - use the textbook, your notes, my note printouts, homeworks - whatever helps. See you bright and early on Thursday.
- June 4: HW#7 Solutions (PDF)
- June 4: there will be no discussion session tomorrow, Fri, June 5th. Instead we will hold an extra discussion hour on Tuesday, at 10AM, in my office Mayer Hall Addition (MHA) 3681, ext. 4-3066 (possibly we will end up using MHA 4681, 4th floor conference room next to north side stairwell of MHA).
- June 3: Lecture 17 PDF introduced 2nd rank tensors for transforms of E, B. 4-vector of charge-current density.
- June 3: HW#6 Solutions PDF posted.
- May 27: Lecture 16 PDF dealt with how E, B fields transform from one reference frame to another. Reminder that there will be no lecture on Thursday, May 28, and no discussion session on Friday, May 29, as I am out of town.

## **OLDER UPDATES:**

- May 22: Jeff asked - why was there a Newtonian value for deflection of light near a star (precisely 1/2 of the value predicted by Einstein's general relativity)? The short answer is: because within this model physicists considered light as composed of particles ("corpuscules") with mass travelling at speed of light - massless nature of photons wasn't discovered until much later. The deflection value was derived by Von Soldner in 1801, here's the (modern) summary of this relatively trivial calculation, along with the original by von Soldner (in German).
- May 22: Lecture 15 (PDF) Summary: Michelson-Morley experiment. "Proper" velocity. Relativistic momentum and energy. Origin and derivation of E=mc^2. (Sect. 12.2)
- May 22: Homework #7, due Tue June 2nd (this one has 7 - yes, seven (!) problems, but most of them are relatively easy - as those who show up to discussion session can confirm - and you have extra time and it's the last E&M homework you have to suffer through... until grad school).
- May 22: To Calvin and others - to get a feel for (or visualize) radiation arising from an accelerating charge try these: applet 1, applet 2.

Those interested in history of science, there was a recent Physics Today article about two 1919 eclipse expeditions that aimed to verify (or disprove) Einstein. Those interested in LIGO - scaled up version of Michelson-Morley aimed to detect gravity waves, read more about it here. Here's the Michelson-Morley experiment paper. The most important physics experiment is a failure! (negative result is often extremely important in science). Michelson-Morley discovery was also the most exciting thing to come out of Cleveland, Ohio. By far. (distant 2nd place goes to Drew Carey).

- May 22: Since we are running ahead of schedule, there will be
**NO lecture**on Thursday, May 28 and NO discussion session on Friday, May 29. There will be a lecture on Tuesday, May 26, as scheduled. Homework #7 will be due Tuesday, June 2. - May 19: Lecture 14 (PDF), Secttion 12.1
- May 19: For Scott and anyone else interested, this is the original, not previously released (director's cut) version of midterm exam (PDF).
- May 19: I will be holding an additional office hour on Wed., May
**20**from 1PM to 2PM in my office (Where is it?) - May 19: HW #5 solutions (PDF), Midterm (PDF), Midterm solutions (PDF) are posted.
- May 18: wiki is back (server reinstalled due to being hacked into)
- May 14: HW6 (11.9, 11.10, 11.13, 11.16, 11.25), due Thursday, May 21.
- May 14: There will be NO discussion session on Friday, May 15.
- May 13: You are allowed to use the textbook and hand-written notes (either yours or printouts of mine) during midterm. Good luck!
- May 9: Midterm will cover Chapters 9 and 10. Problems will be similar to homework.
- May 8: wiki server hosting PHYS 100C was not available in the evening of May 7th and for most of May 8th. Sorry for inconvenience. Backup depository of lecture notes and homeworks (in case something were to happen to server while I am away) is here.
- May 7: Lecture 12 (PDF) Notes: radiation reaction force and synchrotron radiation.
- May 7: tomorrow's (Friday May 8th)
**discussion session**will still be held as usual, at 11AM. We will discuss the troubling points of "flies on the garbage truck" analogy and solve some problems related to radiating charges - or address whatever other pre-midterm questions you may have. - May 5: I will be on leave throughout the week of May 11-15. Reminder that the midterm is going to be held on Thur., May 14 in class (8AM-9AM). Prof. (his Lordship) Sunil Sinha will substitute for me on May 12th. There will be no homework due the week of midterm (May 11-15), the next homework will be due on Thursday, May 21st in class. This week's homework is due Thur, May 7th, as previously scheduled.
- May 5: HW 4 Solutions (PDF)
- May 5: Lecture 11 (PDF) Summary: magnetic dipole radiation is not important (11.1.3), radiation from arbitrary "cloud" of charge (11.1.4).
- April 30: HW #5: 10.13, 10.17, 10.20, 11.1 (finalized!). Due Thur, May 7, 8AM.
**Update:**in Problem 10.17 you only need to derive the relationship shown in the problem, no need to derive full Eq. 10.63. Also note that there are now only four problems (problems 10.21 and 10.25 originally listed have been eliminated in**final-final**version). - April 30: Lecture 10 (PDF) Summary: we derived the radiated E, B fields for oscillating dipole, using retarded potential formalism (11.1.1, 11.1.2 in the textbook). Result is spherical EM wave (transverse), intensity ~ fourth power of frequency (Rayleigh scattering and the reason for why the sky is blue), decays as inverse square of distance, has sin
^{2}(theta) angular anisotropy with respect to dipole orientation. - April 28: I will be holding additional office hour, Wednesday, April 29th, at 3PM (Mayer Hall Addition 3681), for students who would like to discuss homework, lectures or complain about horrible Lienard-Wiechert potentials. I should also be in my office from 11AM to noon tomorrow (Wed. Apr. 29) for those who have conflict with PHYS 120A, but would like to talk to me.
- April 28: Homework #3 Solutions (PDF) posted.
- April 28: Lecture 9 (PDF) Summary: Lienard-Wiechert potentials for moving charge, expanded. Velocity and acceleration contributions to E derived.
- April 26: Midterm tentatively (re)scheduled for Thursday,
**May 14th**, in class (8AM-9AM). - April 23: HW #4 posted: 10.1, 10.3, 10.5, 10.7, 10.10 (finalized), Due Thur, Apr. 30, 8AM.
- April 23: Lecture 8 (PDF) Summary: derived Jefimenko Eqs (fields from retarded potentials) 10.2.2. Derived general expression for Lienard-Wiechert potentials for moving charges. (10.3.1)
- April 21: For those interested in deep discussions (obviously not required for this course!) on nature and direction of arrow of time see here, here, here, or here, or google "Boltzmann's Brain", "Arrow of time" or "Gibbs paradox".
- April 21: Lecture 7 (PDF) Summary: we introduced gauge transformations (10.1.2), Coulomb and Lorentz gauges, and Maxwell equations in these gauges (10.1.3). Introduced "retarded" potentials in Lorentz gauge and demonstrated that they are a solution to Maxwell equations for potential V(r,t) (10.2.1).
- April 21: Homework #2 Solutions posted.
- April 17: In Homework #3, Problem 9.28, the frequency 1.7E10 Hz is not the angular frequency, omega, but rather the inverse of period, "regular" frequency, usually described by greek letter nu. In Problem 9.30 you may assume that a > b (rectangular dimensions of waveguide).
- April 16: Lecture 6 (PDF) summary: continued description of waveguides, applied to specific example of rectangular waveguides (9.5.2). Treatment of coaxial transmission line (9.5.3) is left to class. Started discussion of potentials and fields in electrodynamics, gauge transformations (10.1.1 and 10.1.2).
- April 16: Homework #3 posted: 9.23, 9.24, 9.27, 9.28, 9.30. In Prob. 9.23 ignore the last question, answer only the first two - see PDF.
- April 14: Votes are in! We will keep having discussion session at original timeslot, 11-11:50 on Fridays.
- April 14: Homework #1 Solutions are posted.
- April 14: Group velocity animations - see applets here and here, and also wikipedia page with relevant references about slowing down light to bike/running velocities and "negative" speed of light.
- April 14: for any questions/conflicts about homework grading first contact the grader (Houdong Hu, hhu@physics.ucsd.edu), then email/talk to me.

**Homework #2, extra credit problem:** derive the most *general* solution of equation Ax"+Bx'+Cx=D*cos(wt) by solving homogeneous form of this 2nd order differential equation (D=0 - undriven/damped harmonic oscillator) first, and then finding general form of x(t) for when driving force parameter D is not equal to 0. (The question/objections raised by Jeff and Andrew in class.) Separate **transient** part due to some initial conditions (at short t as compared to the damping time constant) from solution describing long-term, **steady-state** behavior we are interested in (large t). Compare this long-term behavior to the solution introduced in class.
This extra credit for mathematically motivated students is due Thursday 8AM - I will post/discuss solution on Friday during our Discussion Session.

- April 14: Lecture 5 (PDF) summary: We derived dispersion relation for a simplistic "mass on a spring" model for electron in EM waves (Section 9.4.3). We also started deriving Maxwell equations for EM waves in waveguide (conducting tube). (Section 9.5.1)
- April 13: Homework #2 Hints - in Prob. 9.16 you may assume that both reflected and transmitted waves are also s-polarized (we did Prob. 9.14 that deals with this proof during Discussion session on Friday). You may also want to do Prob. 9.19 before proceeding to 9.21 (silver is a very good conductor).
- April 10: Q&A Notes (PDF) (mostly some answers to questions Jeff keeps asking me during the lectures - not required reading material by any means, for general education only).
- April 9: Lecture 4 (PDF) summary: We derived equations for EM waves in conducting media. The solutions for wavevector now have imaginary component, which means the wave amplitudes are exponentially decaying over "skin depth" near the surface. E and B are still mutually perpendicular, but are out of phase. (9.4.1)

We also derived equations for transmitted and reflected waves for EM wave normally incident at an insulator-conductor interface. Perfect conductor has 100% reflection coefficient. (9.4.2).

- April 7: Lecture 3 (PDF) summary: We derived equations for transmitted and reflected EM waves for a case of normal incidence (cont'd from Lecture 2), See section 9.3.2. We then derived a more general case of oblique incidence, p-polarized wave; Discussed Brewster angle and applications (polarized glasses and Brewster Angle Microscopy). Section 9.3.3.

**Reminder** that HW#1 is due Thur April 9 at the beginning of the lecture, 8AM.

- April 4: Feel free to add feedback, comments or suggestions regarding the PHYS 100C course in the discussion section (anonymously or not). Please do not edit this (main) page.
- April 2: Problems
**9.3, 9.5, 9.9 (sketch optional), 9.10, 9.15**(note that 9.13 will be deferred for HW #2) will be due as HW #1 next Thursday, Apr. 9 before lecture. - April 2: Lecture 2 (PDF) summary: we have derived energy density, energy flux, momentum density and radiation pressure of EM waves (9.2.3), propagation of EM waves in Linear Media (9.3.1), defined boundary conditions for EM wave traveling across media boundary and formulated the Incident, Transmitted and Reflected waves (9.3.2).
- April 1: Lecture 1 (March 31) summary: we covered waves in 1D (9.1.1-9.1.2), discussed transverse/longitudinal waves (9.1.4), derived EM waves in vacuum from Maxwell Eqs. (9.2.1, 9.2.2).
- March 31:
**Change in policy**- during the discussion session we will be breaking into small groups and solving problems, including (sometimes) upcoming homework problems. Therefore, student collaborations on homeworks is now**allowed**. Participation in discussion sessions is optional. - March 31: Lecture 1 Notes posted.
- March 31: Discussion session: Fridays 11:00-11:50, WLH 2110.
- March 31: RSS and Atom feeds allowing you to subscribe to/monitor changes to this page are available from this webpage (links in lower left panel)
- March 25: Syllabus has been posted.

## **COURSE SUMMARY:**

**PHYS 100C, Electromagnetism, Spring 2009, UC San Diego**

**Professor:** **Oleg Shpyrko**, oleg@physics.ucsd.edu

**Office:** Mayer Hall Addition (MHA) 3681, ext. 4-3066 (Where is it?)

**Office Hours:** Combined with Discussion Session, and on Mondays 3PM-4PM. For additional time see me after lectures or on demand.

**TA (Grader):** Houdong Hu, hhu@physics.ucsd.edu

**Text:** Introduction to Electrodynamics, 3rd Edition, by David J. Griffiths.

**Lectures:** Tue, Th 8:00am-9:20am, HSS 2154

**Discussion Session:** Fridays 11-11:50,WLH 2110.

**Homework:** Assigned weekly, due Thursday, at the START of lecture. Will also be accepted at the following lecture, but with a 20% penalty.

**Midterm:** Tue, May **14th** 8:00AM – 9:00AM (60 min), HSS 2154 (in class). Open book exam. Bring your textbook only, and a bluebook.

**Final:** June 11, 8:00AM – 11:00AM. Open book exam. Bring your textbook only, and a bluebook.

**Grading:** Homework=20%, Midterm =30%, Final=50%.

**Academic Dishonesty:** Please read the section entitled "UCSD Policy on Integrity of Scholarship" located in the2008-2009 General Catalog, www.ucsd.edu/catalog
(More specifically, see page 69 of PDF document)
The rules on academic dishonesty will be strictly enforced!

**Course Webpage:** x-ray.ucsd.edu/PHYS_100C (RSS/Atom feeds available)
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## **COURSE SCHEDULE:**

Week # | Dates | Topic (Chapter.Section) | Homework Assignment |
---|---|---|---|

1 | 3/30-Apr 3 | Wave Equations, Electromagnetic Waves in Vacuum (9.1-9.2) | No homework during the first week |

2 | Apr 6-10 | Electromagnetic Waves in Matter, Reflection and Transmission. Adsorption and Dispersion (9.3-9.4) | HW #1: Problems 9.3, 9.5 (!), 9.9 (sketch is optional), 9.10, 9.15 (finalized). Due Thur, Apr. 9, 8AM (before lecture) HW #1 Solutions |

3 | Apr 13-17 | Waveguides and Antenna (9.5). Lecture 5 (PDF). Lecture 6 (PDF). | HW #2: 9.13, 9.16 (!), 9.19, 9.21 (finalized), Due Thur, Apr. 16 8AM (before lecture) |

4 | Apr 20-24 | Potential formulation of Maxwell's equations and retarded potentials (10.1-10.2) Lecture 7 (PDF). Lecture 8 (PDF). | HW #3: 9.23 (ignore last question), 9.24, 9.27, 9.28, 9.30. Due Thur, Apr. 23 8AM. Homework #3 Solutions (PDF). |

5 | Apr 27 - May 1 | Lienard-Wiechert potentials and fields of a moving point charge (10.3). Lecture 9 (PDF). Lecture 10 (PDF). | HW #4: 10.1, 10.3, 10.5, 10.7, 10.10 (finalized), Due Thur, Apr. 30, 8AM. HW #4 Solutions (PDF) |

6 | May 4-8 | Radiation (11). Lecture 11 (PDF). Lecture 12 (PDF). | HW #5: 10.13, 10.17, 10.20, 11.1 (finalized!). Due Thur, May 7, 8AM. HW #5 Solutions (PDF). |

7 | May 11-15 | Lecture 13: Special Guest Lecturer, Lord Sunil K. Sinha. Midterm (PDF), (May 14th). | No homework due this week. Midterm (PDF), Midterm solutions (PDF). |

8 | May 18-22 | Special theory of relativity (12.1-12.2). Lecture 14 (PDF). Lecture 15 (PDF). | HW #6 (11.9, 11.10, 11.13, 11.16, 11.25), due Thursday, May 21. HW #6 Solutions (PDF). |

9 | May 25-29 | Special theory of relativity (12.1-12.2). Lecture 16 (PDF). May 28 lecture canceled. | HW #7 X (see PDF), 12.6, 12.7, 12.10, 12.17, 12.29, 12.30 due Tue June 2nd. HW#7 Solutions (PDF). |

10 | June 1-5 | Relativistic Electrodynamics (12.2-12.3). Lecture 17 (PDF). | No Homework (last homework - #7 - is due this week, Tue June 2nd) |