# PHYS 100C

## **RECENT UPDATES:**

- June 1: Reminder that there will be a brief review on Tuesday, June 5th in class.

Lecture 17 PDF introduced 2nd rank tensors for transforms of E, B. 4-vector of charge-current density. HW #5 Solutions: PDF HW #6: Solutions to 11.9, 11.13: PDF Solutions to 12.6 and 12.7

- May 23: Lecture 15 (PDF). Lecture 16 (PDF) dealt with how to transform E, B fields from one frame of reference to another, and included a revelation that magnetic field is just a relativistic consequence of electrostatics.

Links: LIGO, the largest interferometer project ever built, in search of gravitational waves. Early reports of gravity wave discoveries in 1970ies were flawed. Michelson-Morley experiment. Einstein on Michelson-Morley: What did he know and when did he know it?

- May 16: Special theory of relativity (12.1). Lecture 14 (PDF).
- May 14: Today we got through two sets of notes for Lecture 11 (PDF) and Lecture 12 (PDF), skipping some repetitive mathematical details and focusing on the physics instead.

- May 9: Midterm Solutions (PDF). Please note that in problem 2 due to some ambiguity in wording of the problem we will accept solutions that assume that transmitted wave is eventually adsorbed (therefore contributing to radiation pressure on the slab) as well as solution that assumes that the transmitted wave is not adsorbed and therefore does NOT contribute the pressure, as correct. Let me know if you are missing points for assuming one of those two scenarios and following through (correctly, within the initial assumptions) to the answer.

- May 9: Homework #5: 10.13, 10.17, 10.20, 11.1. Hints for 10.13: v is perpendicular to r. Hints for 10.17 - consider value of |r|, using the fact that |r|=sqrt(r*r), and differentiate it with respect to time. Hints for 10.20: r is perpendicular to v and parallel to a.

- May 9: 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 30: Lecture 9 (PDF) Summary: Lienard-Wiechert potentials for moving charge, expanded. Velocity and acceleration contributions to E derived.

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).

- For those interested in deep discussions related to the fact that Maxwell equations are time-reversible, but our experiences are not (these are obviously not required for this course!) - you may read up 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 23: 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 22: Group vs. phase velocity animation.

- April 22: The Homework grades are posted here: GoogleDrive

- April 20: Lecture 6 (PDF) covered waveguides.

- April 16 Lecture 5 (Tuesday) will be delivered by Prof. Sunil Sinha (I am out of town). I will be back for Thursday April 18 (Homework #2 is due on Thursday).

Lecture 5 (PDF) summary: we considered a simple mass-on-a-spring model for electron driven by electromagnetic wave to calculate dependence of index of refraction and attenuation as a function of frequency, leading to dispersion (rainbows etc.) We started deriving propagation of EM waves in a hollow metallic waveguide.

- April 11: Lecture 4 (PDF) Summary (with a tilda): we considered E&M waves propagating in conducting materials. Wavevector k becomes complex, with imaginary part of k representing exponential attenuation of the wave (skin depth introduced). E&M are still transverse but no longer in phase. Re-deriving the boundary conditions (Lecture 2/3 with complex k) get 100% reflection - explains why metal objects/mirrors are shiny. The physics explanation is that the surface currents "conspire" to screen out the EM fields from entering the bulk of the metal - the superposition of the incident fields and these currents produces all the new effects: out of phase E, B; rapidly decaying fields as a function of distance from the interface, and strongly reflecting surface, as a result.

- April 9: Lecture 3 (PDF) summary: we considered boundary conditions for a plane EM wave incident on an interface at arbitrary incident angle. We have derived three laws of reflection/refraction and derived Fresnel Law for p-wave.

(p stands for parallel, s stands for senkrecht, German word for "perpendicular" - to the plane of incidence). We have considered Brewster angle physics which included polarized sunglasses and Brewster Angle Microscopy.

- Historic Perspective (not required, but could be of interest for those of you who like the history of science): the fact that light is E&M wave was *almost* derived by Wilhelm Eduard Weber and Rudolf Kohlrausch in 1856. Maxwell made the connection in 1861.

Einstein wrote about this prediction:Of Maxwell's work:

"Imagine [Maxwell's] feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarised waves, and at the speed of light! To few men in the world has such an experience been vouchsafed... it took physicists some decades to grasp the full significance of Maxwell's discovery, so bold was the leap that his genius forced upon the conceptions of his fellow-workers."

Maxwell's conjecture was proven by Hertz in 1887, who was only 4 years old in 1861, when Maxwell first postulated that light is Electromagnetic Wave.

- April 4: Lecture 2 (PDF) summary: we considered energy and pressure carried by radiation / EM wave. We have looked at propagation of waves in media; We started derving the properies of transmitted and reflected wave equations for a plane EM wave normal-incident at the boundary between two media (using boundary conditions from Eq. 7.64) - we stopped half-way through derivation though, will pick up the calculation next Tuesday in class!

April 2: Lecture 1 (PDF) 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).

## **COURSE SUMMARY:**

**PHYS 100C, Electromagnetism, Spring 2013, UC San Diego**

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

**Office:** Mayer Hall 3210, ext. 4-3066 (**Where is it**?)

**Office Hours:** Mondays 4-5PM as well as Discussion Session on Friday, 2PM-2:50PM, YORK 4080A

**TA (Grader):** Leandra Boucheron, lboucheron@gmail.com

**Text:** Introduction to Electrodynamics, 3rd Edition, by David J. Griffiths. (also check abebooks for used copies)

**Lectures:** Tue, Thu, 11:00AM-12:20PM, SOLIS 110

**Discussion Session:** Fridays, 2-2:50PM, YORK 4080A

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

**Midterm:** May 7th 11AM (in class). Open book exam. Bring your textbook only, and a bluebook.

**Final:** TBD. Open book exam. Bring your textbook, notes, 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. 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 | April 2, 4 | Wave Equations, Electromagnetic Waves in Vacuum and in Matter. Reflection/Transmission coefficients at normal incidence. (9.1-9.2). | (No homework during the first week) |

2 | April 9, 11 | Electromagnetic Waves in Matter, Reflection and Transmission. Adsorption and Dispersion (9.3-9.4). Lecture 3 PDF.Lecture 4 (PDF). | HW #1: 9.3, 9.5, 9.9 (do not have to do the sketch part), 9.10, Due Thursday April 11, before lecture. Homework #1 Solutions (PDF) |

3 | April 16, 18 | Waveguides and Antenna (9.5) Lecture 5 (PDF), Lecture 6 PDF) | HW #2: 9.13, 9.14, 9.15, 9.16, 9.21, Due Thur, Apr. 18 before lecture. HW #2 solutions (PDF). |

4 | April 23, 25 | Potential formulation of Maxwell's equations and retarded potentials (10.1-10.2) Lecture 7 (PDF) and Lecture 8 (PDF) Summary: derived Jefimenko Eqs (fields from retarded potentials) 10.2.2. | Homework #3: Problems 9.19, 9.24, 9.27, 9.28, 9.30. Due Thursday, April 25. Solutions PDF |

5 | Apr 30, May 2 | Lienard-Wiechert potentials and fields of a moving point charge (10.3). Lecture 9 (PDF)No Lecture on Thursday - please use the time to prepare for Midterm next week. There will be a discussion session on Friday. | Homework #4: 10.1, 10.3, 10.5, 10.7, 10.10. Due Thursday, May 2nd. Solutions PDF |

6 | May 7, 9 | May 7 is midterm, in class 1hr 20min. No homework assigned this week. May 9: Radiation (11) - Lecture 10. (PDF) | No Homework Due this Week (due to Midterm). Midterm Solutions (PDF) |

7 | May 14, 16 | Lecture 11 (PDF)& Lecture 12 (PDF). Lecture 14 (PDF). (No Lecture 13 for good luck!) | Homework #5: 10.13, 10.17, 10.20, 11.1. Due May 16. HW#4 Solutions PDF |

8 | May 21, 23 | Relativity. Lecture 15 (PDF). : Lecture 16 (PDF) | Homework #6: 11.9, 11.13, 12.6, 12.7. Due May 23. Solutions to 11.9, 11.13: PDF Solutions to 12.6 and 12.7 |

9 | May 28 | Relativity. Lecture 17 [ http://x-ray.ucsd.edu/mediawiki/images/b/ba/PHYS_100C_Lecture_17_June_2.pdf PDF] should be final lecture (no lecture on Thursday) | No Homework |

10 | June 5 | Review on Tuesday June 5, 11AM, in class. | No Homework |