Electricity and Magnetism:

K2 of physics (Feynman)

**Instructor: Lev Ioffe**
Homepage

Serin Physics 264E. Office hours: Monday and Wednesday 4:40-5:30.

**Textbooks: **

Main textbook (recommended):

Jackson "Classical Electrodynamics" (any edition)

For more theoretical approach:

L. D. Landau and E. M. Lifshits, "Field Theory" (any edition)

See also additional reading specific to lectures.

**Part 2 (Spring 2007). **

**Time and place:**

Monday and Wednesday 15:20-16:40 ARC 205.

**Exams: **

MidTerm: March 7th.

**Lectures and homeworks: **

1. Conservation laws and symmetries of Maxwell equations. Lorentz invariance.

2. Field transformation. Homework 1.

3. Field invariants. Lorentz-Invariant form of equations of motion.

4. Relativistic form of momentum-energy tensor for matter and fields. Homework 2.

5. Solution of homework problems. Dipolar radiation (review).

6. Radiation of a small antenna. Mossbauer effect. Homework 3.

7. Cherenkov radiation.

**Part 1 (Fall 2006). **

**Time and place:**

Tuesday and Friday 10:20-11:40 SEC 220.

**Exams: **

MidTerm: November 10th.

**Lectures and homeworks: **

1. Course setup. Course subject, Maxwell equations and their applicability limit. Homework 0 (review of basic math).

2. Coulomb law: review

3. Methods of solution of electrostatic problems: images. Homework 1.

4. General methods of solutions: symmetries and coordinate transformations.

5. General methods of solutions: coordinate transformations. Solution of Homework 1 problems. Homework 2.

6. General methods of solutions: conformal transformations.

7. Expansion in spherical functions. Solution of Homework 2 problems. Homework 3.

8. Multipole expansion, dipoles and quadrupoles. Energy of the system of charges in external field. Interaction between dipoles and quadrupoles.

9. Insulators, dielectric constant. Full set of equations and boundary conditions. Homework 4.

10. Energy of the insulators. Thermodynamic potentials as a function of external charge or electric field.

11. Magnetostatics: main equations. Homework 5.

12. Magnetostatics: field of magnetic dipoles. Magnetic moment and angular momentum, Larmor theorem.

13. Energy of particles in magnetic field. Bohr - van Leeuven theorem. Magnetization of the materials. Homework 6.

14. Magnetization of the materials. Tensor structure of the dielectric constant. Symmetry arguments.

15. Ferromagnets. Homework 7.

16. Domain wall in ferromagnets: thin films.

17. Domains in ferromagnets: non-zero fields, domain splitting near the surface. Homework 8.

18. Nucleation of domains in general and specifically in ferromagnets.

19. Magnetostatics of superconductors. Homework 9.

20. MidTerm exam. Problems and solutions.

21. Nucleation in ferromagnets: independent studies.

22. Magnetic properties of superconductors: critical field and domain structure in fields close to critical. Homework 10.

23. Magnetic properties of superconductors: penetration of magnetic field. London equations.

24. Magnetic properties of superconductors: vortices in type II superconductors. Homework 11.

25. Quasistatic magnetic field in conductors: skin depth.

26. Maxwell equations.

27. Solution of Maxwell equations. Dipole radiation.

28. Final exam. (Jackson Chapters 1-5).

__Additional reading for domain
structure of ferromagnets:__

Review by Privorotskii in Sov. Phys. Uspekhi v 15, 555 (1973) contains much more detailed exposition than needed for this course. See also Chapter V (Ferromagnetism and Antiferromagnetism) of Landau and Lifshitz course on Theoretical Physics, Volume VIII (Electrodynamics of Continuous Media) sections 40, 43, 44 (section numbers might vary from one edition to another).

__Additional reading for magnetic properties of
superconductors:__

1. V.V. Schmidt et al "The Physics of Superconductors: Introduction to Fundamentals and Applications": good introduction to the theory of superconductivity. In this course we discussed only the material of the introductory Chapter 1, selected sections from Chapters 2 (2.1, 2.2, 2.6) and the very beginning of Chapter 5 (5.1-5.3).

2. M. Tinkham "Introduction to superconductivity" gives more detailed treatment (advanced introductory level). The material included in this course can be found in Sections 2.1-2.3, 5.1.

**Part 2 (Spring 2007). **

**Time and place:**

Monday and Wednesday 15:20-16:40 ARC 205.

**Exams: **

MidTerm: March 9th.

**Lectures and homeworks: **

1. Conservation laws and symmetries of Maxwell equations. Lorentz invariance.

2. Field transformation. Field invariants. Homework 1.

3. Energy momentum stress tensor.

4. Energy-momentum stress tensor of electromagnetic field. Homework 2.

5. Solution of problems on field transformations (Homework 1)

6. Solution of problems in relativistic mechanics (Homework 2). Homework 3.

7. Mossbauer effect. Cherenkov radiation.

8. Cherenkov radiation (cont'd). Solution of problems: Kompton effect, Complex Doppler effect. Homework 4.

9. Solutions of Homework 4: Cherenkov radiation of moving dipoles.

10. Plane waves. Reflection and refraction.

11. Reflection and refraction (cont'd), Fresnel formulas. Causality, Kramers-Kronig relations.

12. Application of Kramers-Kronig relations: optical sum rule. Electromagnetic wave propagation in plasma in magnetic field: atmospheric whistles. Homework 5.

13. Magneto-hydrodynamics.

14. Mid Term Exam: relativistic equation of motion of particles, field transformations, radiation of moving charges in vacuum (last lecture of the Fall term) and in optically active media.

15. Electromagnetic properties of collisionless plasma: main equations.

16. Electromagnetic properties of collisionless plasma: Landau damping. Solution of Homework 6.

17. Waveguides: main equations.

18. Transverse magnetic and electric modes in waveguides. Homework 6.