Syllabus/Reading Material

This is what has been covered in lectures. All references to Chapters, Sections, Applications, and Examples refer to Zangwill. All (unless I missed something) Examples and Applications we did in class are listed. If an Example or Application isn't listed, we didn't do it in class. Section N.N.0 (for example, 13.4.0) means the unnumbered initial part of Section N.N.

  1. Review of Chapter 10. Derivation of Biot-Savart law from Maxwell eqs. using Helmholtz theorem. Filamentary (1D) wire limit of Biot-Savart. Magnetic field of infinitely long solenoid. Integral form of magnetostatic Maxwell eqs, Ampere's law. Magnetic field of infinite straight wire and uniform sheet of current. Matching conditions for B-field. Vector potential, gauge freedom, Coulomb gauge. Magnetic scalar potential and its multivalued nature.  Reading: read this material in Chapter 10.
  2. Magnetic multipoles, magnetic dipole (read Sections 11.1, 11.2.0 and 11.2.1). Orbital and spin magnetic moments (Section 11.2.2). Point magnetic dipole (Section 11.2.3).  Point magnetic monopole (Application 11.1)
  3. Spherical multipoles (Section 11.4.2, 11.4.3, and 11.4.4) and azimuthally symmetric case (Section 11.4.5). Helmholtz Anti-Coil (Application 11.3)
  4. Interior magnetic multipoles, 2D case, 2N parallel wires on a cylinder (Section 11.5).
  5. Magnetic force and torque (Section 12.1). The Lorentz force does no work (Section 12.2.1).  Motion in uniform B-field (Section 12.2.2). Motion in crossed E and B-fields (Example 12.1). Force between steady currents (Section 12.3). Dipole force (Section 12.4.1). Dipole potential energy (Section 12.4.2). Magnetic Trapping (Application 12.2). Dipole torque (Section 12.4.4)
  6. Larmor precession (Section 12.4.5). Magnetic stress tensor (Section 12.5). Magnetic tension and pressure (Section 12.5.1). Fun solenoid - cut an infinite solenoid into two perpendicular to its symmetry axis. What is the force between the two parts of the solenoid?
  7. Magnetostatic total energy (Sections 12.6.0 and 12.6.1). Interaction energy and reciprocity (Section 12.6.2). Legendre transform from potential energy as a function of flux to a function of current (Sections 12.6.4, 12.7.1, and 12.7.2). Example 12.5.
  8. Inductance and self-inductance of a wire loop (Sections 12.8 and 12.8.1). Mutual inductance (Section 12.8.2 including Example 12.6)
  9. Magnetic matter - Introduction (Section 13.1), Magnetization (Sections 13.2.0, 13.2.1, 13.2.2, 13.2.3, and 13.2.4). The Field Produced by Magnetized Matter (Sections 13.30, 13.3.1). Fictitious Magnetic Charge (Sections 13.4.0 and 13.4.1 including Application 13.1). The total magnetic field (Sections 13.5.0 and 13.5.1). Simple Magnetic Matter (Sections 13.6.0, 13.6.1, 13.6.2, 13.6.3, 13.6.4, and 13.6.6). Energy of magnetic matter (Sections 13.7.1, 13.7.2, 13.7.3, and 13.7.4). A Simple Magnetic Sub-Volume (Sections 13.8.4 and 13.8.5 including Examples 13.5 and 13.6).
  10. Moving beyond electro- and magnetostatics. Full Maxwell eqs. and displacement current (Section 14.1 and beginning of Section 14.2.1). Polarization current (Section 14.2.2). Dielectric constant of plasma (Application 14.1). Faraday's law and the betatron (Sections 14.3.0 and 14.3.1). Faraday electromotive force (Section 14.4.1 including Example 14.1 and Application 14.2).
  11. Electromagnetic induction - Section 14.4 with Examples 14.1 and 14.3. Electromagnetic potentials (Section 15.3). Conservation of energy (Section 15.4). Conservation of linear momentum (Section 15.5). Conservation of angular momentum (Section 15.6.0). Conservation laws in matter (Sections 15.8.1 and 15.8.2).
  12. Waves in vacuum (Sections 16.1, 16.2, and 16.3). Polarization (Sections 16.4.1, 16.4.2, 16.4.3 and 16.4.6). Wave Packets (Sections 16.5.2, 16.5.3, 16.5.4, and 16.5.5). Beam-like waves (Sections 16.7.1, 16.7.2, and 16.7.4). Spherical waves (Section 16.8).
  13. Waves in matter. Plane waves (Section 17.2), Reflection and refraction, Snell's law (Sections 17.3.0 and 17.3.1), Fresnel equations (Section 17.3.2 and 17.3.3), Energy transport, reflection & transmission coefficients (Section 17.3.4), Polarization by reflection (Section 17.3.5), Total internal reflection (Section 17.3.6), Non-uniform and evanescent plane waves (Section 17.3.7), Radiation pressure (Section 17.4), Simple conducting matter (only Sections 17.6.0 and 17.6.1)
  14. The following topics we covered in last 2 lectures and in the extra lecture. These topics will NOT be on the exam. Hamilton's principle (Section 24.2). Lagrangian of a charged particle in a specified EM field (Section 24.3.2). Lagrangian of the free EM field (Section 24.3.3). The Lagrange equation for the fields (Section 24.3.4). The Coulomb-Lorentz and Maxwell equations (Section 24.3.5). Crush course on special relativity (see lecture notes from 05/04/2020). Covariant Formulation (Section 24.3.6).  Charge Conservation (Section 24.4.1), Noether's Theorem (Section 24.4.2), Conservation of Energy-Momentum (Section 24.4.3).

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