Teaching Spring 2023: Electromagnetic Theory

(Physics 515A)

COURSE DESCRIPTION: Theory of classical electromagnetic phenomena, including time-dependent and static solutions of Maxwell's equations and radiation theory. A key goal of this course is to learn how to calculate an electromagnetic field for arbitrary boundary and initial conditions. One of the most important steps will be the introduction of the Green's function, which has important applications throughout Physics, not just electrodynamics. We shall also begin to assess symmetries and conservation laws, which will eventually culminate in a thorough examination of Noether's theorem in Phys 515B. INSTRUCTOR: Professor Fulvio Melia OFFICE HOURS: MW 10:00-11:00 in PAS 439 and most other times (but call 977-8269 or e-mail first to make sure I'm in) LECTURES: Mondays, Wednesdays, 3:00 pm - 4:15 pm in PAS 418. Please go to the bottom of this page for COVID-19 related policies HOMEWORK SOLUTIONS: Homework # 1: Solutions Homework # 2: Solutions Homework # 3: Solutions Homework # 4: Solutions Homework # 5: Solutions Extra Problems (A,B,C) Additional exam-style problems (not to be handed in) for you to practice on, in preparation for the final. USEFUL RESOURCE: The Academic Support Office, in the Physics Department at the University of Arizona. TEXTBOOKS: Melia, F., Electrodynamics Jackson, J. D., Classical Electrodynamics LEARNING OUTCOMES: 1. Students will demonstrate a familiarity with Maxwell's Equations. 2. Students will be able to derive the electromagnetic field for arbitrary boundary and initial conditions. 3. Students will be able to apply multipole expansions to solve for the angular and temporal distributions of radiation fields. 4. Students will be able to set up and solve equations describing the radiation produced by simple source geometries. 5. Students will understand the limitations of classical field theory due to restrictions on particle motions in the non-relativistic domain. UNIVERSITY POLICIES RELATED TO THIS SYLLABUS: Follow this link: https://academicaffairs.arizona.edu/syllabus-policies SUBJECT TO CHANGE NOTICE: Information contained in this course syllabus, other than the grade and absence policies, may be subject to change with reasonable advance notice, as deemed appropriate by the instructor of this course. TOPICS COVERED DURING THE SEMESTER: 1. INTRODUCTION 1.1 The Physical Basis of Maxwell's Equations 1.2 Maxwell's Equations in Matter 1.3 Subdivision of Electrodynamics---The Mathematical Structure 1.3.1 Electrostatic Phenomena 1.3.2 Magnetostatic Phenomena 1.3.3 Wave Phenomena 1.3.4 The General Case 1.3.5 The Mathematical Apparatus 2. TIME-INDEPENDENT ELECTRIC AND MAGNETIC FIELDS 2.1 Electrostatics 2.1.1 Method 1: Guesses and Symmetries 2.1.2 Method 2: Green's Function 2.1.3 Method 3: Expansions with Orthonormal Functions 2.2 Magnetostatics 2.2.1 Method 1: The Magnetic Scalar Potential 2.2.2 Method 2: The Magnetic Vector Potential 2.2.3 Method 3: Hard Ferromagnets 3. GENERAL PROPERTIES OF MAXWELL'S EQUATIONS 3.1 Time-Varying Fields 3.2 Time-dependent Green's Function 3.3 Conservation Laws 3.3.1 Field Energy Density and Poynting's Theorem 3.3.2 Conservation of Linear Momentum 3.3.3 The Maxwell Stress Tensor 3.3.4 Conservation of Angular Momentum 4. ELECTROMAGNETIC WAVES AND RADIATION 4.1 Electromagnetic Waves 4.2 Polarization and Stokes's Parameters 4.3 Reflection and Refraction 4.4 Time Harmonic Fields in Matter 4.5 Wave Guides 4.6 Radiation 4.6.1 Point Currents and Lienard-Wiechert Potentials 4.6.2 The Radiation Fields 4.6.3 Simple Radiating Systems PROBLEM SCHEDULE Sections I & II: Electrostatic Problems (due February 27) Jackson: 2.2, 2.7, 2.13, 3.2, 3.3, Problem A Section II (cont.): Magnetostatic Problems (due March 13) Jackson: 5.1, 5.19 Section III: General Properties of Maxwell's Equations (due April 3) Problem B, Problem C, Jackson: 6.11, 6.16, 6.20 parts (a) and (b) (But give c a try anyway!). Section IV (a): Plane Waves (due April 24) Jackson: 7.3, 7.5, 7.16, 7.20, 7.27 Section IV (b): Radiation (due May 3) Problem set with 4 problems METHOD OF EVALUATION Problems (20%) First written, in-class, open-book exam on Wednesday, March 15 (20%) Second written, in-class, open-book exam on Wednesday, April 12 (20%) Written, open-book Final, 9:00 am - 5:00 pm (May 5) (40%) GRADING SCALE: Grades will be assigned according to the scale shown below. A 85-100% B 70-85% C 60-70% D 50-60% E <50% COVID-19 Related Policies: 1. Meeting Times We will be meeting remotely throughout the semester. We will meet on Mondays and Wednesdays, beginning August 24th, for lectures conducted via ZOOM. The lectures will be recorded, and will be made available on D2L. 2. Face coverings are required in our classroom Per U Arizona’s Administrative Directive, face coverings that cover the nose, mouth, and chin are required to be worn in all learning spaces at the University of Arizona (e.g., in classrooms, laboratories and studios). Any student who violates this directive will be asked to immediately leave the learning space, and will be allowed to return only when they are wearing a face covering. Subsequent episodes of noncompliance will result in a Student Code of Conduct complaint being filed with the Dean of Students Office, which may result in sanctions being applied. The student will not be able to return to the learning space until the matter is resolved. The Disability Resource Center is available to explore face coverings and accessibility considerations if you believe that your disability or medical condition precludes you from utilizing any face covering or mask option. DRC will explore the range of potential options as well as remote course offerings. Should DRC determine an accommodation to this directive is reasonable, DRC will communicate this accommodation with your instructor. 3. Physical distancing is required in our classroom During our in-person class meetings, we will respect CDC guidelines, including restricted seating to increase physical distancing. Any student who does not maintain physical distance from others may be asked to immediately leave the learning space. Noncompliance may result in a Student Code of Conduct complaint being filed with the Dean of Students Office, which may result in sanctions being applied. 4. Classroom attendance If you feel sick, or may have been in contact with someone who is infectious, stay home. Except for seeking medical care, avoid contact with others and do not travel. Notify your instructors if you will be missing an in-person or online course. Campus Health is testing for COVID-19. Please call (520) 621-9202 before you visit in person. Visit the UArizona COVID-19 page for regular updates. 5. Life challenges If you are experiencing unexpected barriers to your success in your courses, please note the Dean of Students Office is a central support resource for all students and may be helpful. The Dean of Students Office can be reached at 520-621-2057 or DOS-deanofstudents@email.arizona.edu. 6. Physical and mental-health challenges If you are facing physical or mental health challenges this semester, please note that Campus Health provides quality medical and mental health care. For medical appointments, call (520-621-9202. For After Hours care, call (520) 570-7898. For the Counseling and Psych Services (CAPS) 24/7 hotline, call (520) 621-3334. 7. Exams All of our exams, the two midterms and the final, will be open-book. The first two will have a time-limit of 1.5 hours, while the final will be an all-day test, beginning at 9:00 am and ending at 5:00 pm.