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.
- 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.
- 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)
- 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)
- Interior magnetic multipoles, 2D case, 2N
parallel wires on a cylinder (Section 11.5).
- 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)
- 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?
- 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.
- 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)
- 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).
- 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).
- 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).
- 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).
- 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)
- 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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