Electrodynamics (11279) - Spring 2022

Department of Physics, University of Basel

*** Office hours by appointment on Wed and Thu afternoon.

Literature:

1) David Jeffrey Griffiths, Introduction to Electrodynamics, 3rd Edition, Pearson (2008).

2) John David Jackson, Classical Electrodynamics, 3rd edition, John Wiley & Sons (1999).

3) Richard Phillips Feynman, Robert Benjamin Leighton, and Matthew Sands, The Feynman Lectures on Physics - Vol.II, Pearson (2006). Available online at: https://www.feynmanlectures.caltech.edu/

Homework:

Exercise sheets are going to be distributed every Wednesday in the exercise classes. The solved exercises are to be returned the following Monday per email to the TAs. A minimum of 60% of exercise points is required to qualify for the final exam. Please refer to the schedule below for dates and responsible TA.

Exam:

Scheduled: Wednesday 06-08 Jul 2022 (9:30-17:00)

Dept. Physik, St. Johanns-Ring 25, Seminar Room 3.12

This is an oral exam and no auxiliary material is allowed.

Here is the schedule according to the matriculation number:

Exam Schedule (last updated 17/06/2022)

Summary of lectures:

Lecture #1 (23/02/2022): Organizational aspects of the course (see information above). Discussion of the literature and on the choice of different systems of units by different references (see discussion in Appendix C of Griffiths or Appendix of Jackson). "SI" redefinition (see for example: https://www.nist.gov/si-redefinition/ampere-introduction). Brief discussion on the Maxwell Equations and how this set of equations is at the core of this course. General discussion of multiple aspects that connects to electrodynamics: unification of law's of physics, Standard Model of particle physics, symmetries, fields, optics, material's properties, among others (see prefaces of Griffiths, Jackson, and Feynman Lectures). Revision of electrostatics and introduction of the electric field for discrete and continuous charge distributions. Reading material: Griffiths 2.1.

Lecture #2 (24/02/2022): Examples of electric fields generated by continuous charge distributions evaluated directly from the charge distributions. Example 1: finite line of charge (Griffiths example 2.1). Example 2: charged disk (Griffiths problem 2.6, and in the process also solved problem 2.5). Introduction of the notion of electric field lines. Discussion and derivation of Gauss' law. Solved examples 1 and 2 using Gauss' law (Griffiths problem 2.13 and example 2.5, respectively). Reading material: Griffiths 2.2.1-3.

Lecture #3 (02/03/2022): Solved Example 1 (infinite line of charge) and Example 2 (infinite charged plane) using Gauss' law. The rotational of the electric field and the definition of the electric potential. Discussed the choice of different reference points for the potential. Solved Example 1 (finite line of charge) and Example 2 (charged disk) by evaluating the electric potential first and later the electric field (Griffiths problem 2.25 b and c). Reading material: Griffiths 2.4.4 and 2.3.1-4.

Lecture #4 (03/03/2022): Summary of electrostatics, its basic quantities (charge, electric field, electric potential) and the equations connecting them. Boundary conditions for the electric field. Material interlude #1: Metals/Conductors. Discussed the basic properties of metals and how the charges in conductors respond to the presence of external charges and electric fields. Solved Griffiths Problem 2.38. Reading material: Griffiths 2.3.5 and 2.5.1-2.

Basler Fasnacht (07 - 11/03/2022): No lectures

Lecture #5 (16/03/2022): General properties of the solutions of the Laplace Equation. Uniqueness Theorem given boundary conditions. The method of images with example of a point charge near an infinite grounded conducting plane. Reading material: Griffiths 3.1 and 3.2.

Lecture #6 (17/03/2022): Method of images with example of a point charge near a grounded conducting sphere (Griffiths Example 3.2 in more detail). Method of separation of variables in cartesian coordinates (Griffiths Example 3.3). Method of separation of variables in spherical coordinates. Reading material: Griffiths 3.3 and Jackson 3.1-3.3.

Lecture #7 (23/03/2022): Multipole Expansion. Potential of a physical electric dipole (Griffiths Example 3.10). Definition of a pure dipole (in the context of Griffiths Problem 3.31). Electric field of a dipole (and solved Problem. 3.36) Reading material: Griffiths 3.4.

Lecture #8 (24/03/2022): Electric Fields in Matter. Discussed Griffiths Examples 4.1, 4.4 and 4.5. Solved Griffiths Problem 4.14. Reading material: Griffiths 4.1-4.4.2.

Lecture #9 (30/03/2022): The modern theory of polarization. Reading material: A beginner's guide to the modern theory of polarization, Nicola A. Spaldin, Journal of Solid State Chemistry 195, 2-10 (2012). Also available on arXiv. Extra reading for the ones acquainted with quantum mechanics and solid state physics: Theory of Polarization: A Modern Approach, R. Resta, D. Vanderbilt, Topics Appl. Physics 105, 31–68 (2007).

Lecture #10 (31/03/2022): Introduction to magnetostatics. Magnetic field defined from forces between current loops. Biot-Savart law and its generalizations to surface and volume current density. Local charge conservation and the continuity equation. Example: magnetic field generated by a finite or infinite wire (Griffiths example 5.5). Suggestion: check also magnetic field directly above a circular loop of current (Griffiths example 5.6). Reading material: Griffiths 5.1-5.2.

Lecture #11 (06/03/2022): Magnetic field lines. The divergence and the curl of the magnetic field ("Gauss Law for magnetic fields" and Ampere's Law). Discussion on magnetic monopoles. Reading material: Griffiths 5.3. Extra reading: The search for magnetic monopoles, A. Rajantie, Physics Today 69, 10, 40 (2016).

Lecture #12 (07/03/2022): Comment on the Dirac Delta function (Griffiths 1.5). Example: magnetic field generated by an infinite current-carrying wire using Gauss' law (Griffiths Example 5.7). Suggestion: check also examples 5.8-5.10. The magnetic vector potential and gauge symmetry. The Coulomb gauge. Example: magnetic field generated by an infinite current-carrying wire calculating first the magnetic vector potential and than the magnetic field (Griffiths Problem 5.23). Boundary conditions in magnetostatics. Introduction to the multipole expansion in magnetostatics. Reading material: Griffiths 5.4.

Lecture #13 (14/04/2022): Definition of the magnetic dipole moment. Torque on the magnetic dipole moment in presence of a homogeneous magnetic field. Semiclassical discussion of paramagnetism and diamagnetism. Ferromagnetism and the hysteresis loop. Reading material: Griffiths 5.4.3, 6.1 and 6.4.2. Extra reading material: Feynman Lectures Vol II - Chapters 34 - 37 (for an heuristic discussion of the Bohr-Van Leeuven theorem, see 34-6).

Easter Break (14 - 18/04/2022): No lectures

Lecture #14 (20/04/2022): Definition of the magnetization density and associated volume and surface bound currents. Example: Griffiths problem 6.7 (determine the magnetic field everywhere for an infinite uniformly magnetized cylinder). The auxiliary field H. Boundary conditions for H and revision of boundary conditions for B. Example: Griffiths problem 6.14 (sketch the field lines for M, B and H for a finite magnetized cylinder). Linear media. Reading material: Griffiths 6.2-6.4.

Lecture #15 (21/04/2022): Example of a solenoid with a magnetized material (Griffiths example 6.3). Introduction to Electrodynamics. Lorentz force. Ohm's law and Drude's model for conductivity. The electromotive force (EMF). Motional EMF and the flux rule for motional EMF. Discussion of exceptions: circuit with a switch and Faraday's disk. Griffiths 7.1.

Lecture #16 (27/04/2022): Faraday's law. Lenz's law. Maxwell's correction to Ampere's law. Maxwell's equations in vacuum. Maxwell's equations in matter. Reading material: Griffiths 7.2.1 and 7.3.

Lecture #17 (28/04/2022): Superconductors. Defining properties of a superconductor. The difference between a perfect conductor and a superconductor (see Figure 2.2 in Rey and Malozemoff). Londons' equations, Meissner effect, screening currents and the penetration depth. For the discussion of London's equations, see Section 5.1 from C. Timm's (TU Dresden) lecture notes.

Lecture #18 (04/05/2022): Conservation Laws. Conservation of energy and Poynting's theorem. Conservation of momentum and the Maxwell stress tensor. Reading material: Griffiths Chapter 8. Extra reading (overlapping with Griffiths content): Feynman lectures Volume II, Chapter 27. Suggestion: read section 9.1 from Griffiths about waves in one dimension for next lecture.

Lecture #19 (05/05/2022): Brief review of waves. Electromagnetic waves in vacuum. Fundamental properties of electromagnetic waves. Reading material: Griffiths 9.1 and 9.2.

Lecture #20 (11/05/2022): Waves in linear media in the absence of free charges and currents (insulators). Reflection and Transmission at oblique incidence (normal incidence as a special case). The three laws of optics. Plane of incidence. Fresnel's equations for polarizarion parallel to the plane of incidence. Brewster angle. Reflection and Transmission coefficients. Reading material: Griffiths 9.3. Notes available in ADAM.

Lecture #21 (12/05/2022): Electromagnetic waves in conductors. Reflection in metallic surfaces. Dispersive media and the frequency dependence of the permittivity. Reading material Griffiths 9.4. Notes available in ADAM.

Lecture #22 (18/05/2022): Waveguides. Boundary conditions. Solution for TE waves in rectangular waveguide. Cutoff frequency. Wave velocity and group velocity (to be discussed further in the exercise session). Reading material: Griffiths 9.5.

Lecture #23 (19/05/2022): Radiation. The retarded time and retarded potentials. Radiation from an arbitrary source. Electric dipole radiation and the rudimentary antenna. Why is the sky blue? (see discussion in Example 11.1 in Griffiths). Reading material: Griffiths 11.1.

Lecture #24 (25/05/2022): Radiation of moving point charges. The Lienard-Wiechert potentials and fields. Bremsstrahlung radiation. Synchrotron radiation. Reading material: Griffiths 10.2.1, 10.3 and 11.2.1. Notes available in ADAM.

Ascension Day (26/05/2022): No lecture

Lecture #25 (01/06/2022): Introduction to the special theory of relativity. Einstein's postulates. The breakdown of simultaneity. Time dilation. Lorentz contraction. Lorentz transformation. The 4-vector notation and the Lorentz transformation matrix. The dot product of 4-vectors. Reading material: Griffiths 12.1. Suggested extra reading: Griffiths 12.2, on relativistic mechanics (not covered in the lecture and exam).

Lecture #26 (02/06/2022): Relativistic electrodynamics. How electric and magnetic fields transform under a change of reference frame. The electromagnetic field tensor and its dual. Maxwell's equations in terms of electromagnetic field tensors. Relativistic potentials. The most elegant (and manifetedly Lorentz invariant) formulation of Maxwell's equations in terms of a single equation for the potentials. Reading material: Griffiths 12.3.