Electrodynamics PHYS30441 (M)

Prof Terry Wyatt FRS


News Posted Since the End of term

16/12/19: I have updated the Course Summary to include the section of the course on radiation from accelerating charges and to include a few notes on the exam.

21/12/19: Here is a `extra' example sheet. These problems are intended to be relevant to helping you understand and practice using the core material of the lectures, as part of your revision for the January exam.

Bonus Example Sheet ...... Solutions.

Please fill in the Unit Survey for this course! Thanks for your feedback!


My ``One-Page'' Summaries of the Lectures

Will appear here after each lecture.

Lectures 1 and 2: Introduction to Electrostatics

Lecture 3: Solutions to Laplace's Equation (general results)

Lecture 4: Solutions to Laplace's Equation (example in spherical polar coordinates)

Lecture 5: Multipole Expansions in Electrostatics

Lecture 6: Magnetostatics

Lecture 7: Magnetostatics (continued)

Lecture 8: Introduducing Time Dependence -> Electrodynamics

Lecture 9: The Wave Equations for the Potentials and Their Solutions

Lecture 10: Special Relativity and 4-Vectors: Physics and Notation

Lecture 11: Special Relativity in the Minkowski Representation

Lecture 12: 4-Vectors for Electrodynamics: the 4-velocity, 4-momentum and 4-current

Lecture 13: The 4-Potential and the Wave Equation in Lorentz-Covariant Form

Lecture 14: E and B Fields for a Point Charge Moving with Constant Velocity (Method 1)

Lecture 15: E and B Fields for a Point Charge Moving with Constant Velocity (Method 2)

Lecture 16: Lorentz-Covariant Treatment of Maxwells Equations and Interaction of Charged Particle with the Fields

Lecture 17: Local Conservation Laws and an Alternative Approach to the Potentials for a Moving Point Charge

Lecture 18: The Lienard-Wiechert Potentials and Fields: Radiation from an Accelerating Point Charge (introduction)

Lecture 19: Radiation from an Accelerating Point Charge ("non-relativistic" and Bremsstrahlung)

Lecture 20: Synchrotron Radiation and Thomson Scattering

Lecture 21: Magnetic Dipole Radiation

Lecture 22: An Alternative Approach to Radiation from an Accelerating Point Charge


Scanned Copies of What I Wrote on the Visualiser For Each Lecture

Will appear here after each lecture.

Lecture 0: General Course Introduction/Overview, including material not written to Visualiser

Lecture 1: Course Introduction + Start Electrostatics

Lecture 2: Electrostatics (continued)

Lecture 3: Solutions to Laplace's Equation (general results)

Lecture 4: Solutions to Laplace's Equation (example in spherical polar coordinates)

Lecture 5: Multipole Expansions in Electrostatics

Lecture 6: Magnetostatics

Lecture 7: Magnetostatics (continued) . . . . . Pictures of some accelerator magnets

Lecture 8: Introduducing Time Dependence -> Electrodynamics

Lecture 9: The Wave Equations for the Potentials and Their Solutions

Spread over Lectures 9 and 10: Proof that the Retarded Potentials are Indeed Solutions to the Wave Equations

Lecture 10: Special Relativity and 4-Vectors: Physics and Notation

Lecture 11: Special Relativity in the Minkowski Representation

Lecture 12: 4-Vectors for Electrodynamics: the 4-velocity, 4-momentum and 4-current

Lecture 13: The 4-Potential and the Wave Equation in Lorentz-Covariant Form

Lecture 14: E and B Fields for a Point Charge Moving with Constant Velocity (Method 1) ............ Handout: Pictures of the electric and magnetic fields produced by a point charge moving with constant velocity

Lecture 15: E and B Fields for a Point Charge Moving with Constant Velocity (Method 2)

Lecture 16: Lorentz-Covariant Treatment of Maxwells Equations and Interaction of Charged Particle with the Fields

Lecture 17: Local Conservation Laws and an Alternative Approach to the Potentials for a Moving Point Charge ............ Some extra-curricular reading: Local gauge symmetry and its consquences for the Schroedinger equation

Lecture 18: The Lienard-Wiechert Potentials and Fields: Radiation from an Accelerating Point Charge (introduction) ............ Handout: Proof of Lienard-Wiechert Fields for a moving point charge

Lecture 19: Radiation from an Accelerating Point Charge ("non-relativistic" and Bremsstrahlung) ............ Handout: Patterns of radiation produced by an accelerating point charge

Lecture 20: Synchrotron Radiation and Thomson Scattering

Lecture 21: Magnetic Dipole Radiation

Lecture 22: An Alternative Approach to Radiation from an Accelerating Point Charge


Podcasts of Each Lecture will become available shortly after the lecture finishes.


Question Sheets For the "Official" Examples Classes

The question sheets for the examples classes will be posted here as we progress through the course. Answers will be posted here at the end of the week of the associated examples class.

Background Revision Example Sheet ...... Solutions.

Example Sheet 2 ...... Solutions.

Example Sheet 3 ...... Solutions.

Example Sheet 4 ...... Solutions

Example Sheet 5 ...... Solutions.

Here is a `bonus' example sheet to provide some extra practice at solving problems.

Bonus Example Sheet ...... Solutions.


OPTIONAL Bonus Electrodynamics Sessions

I shall organize some OPTIONAL bonus Electrodynamics sessions throughout the term. They will occur on some Wednesdays at 12:00-13:00.

There will be a few extra-curricular lectures and some sessions will take the form of a small bonus `Examples Class', in which we'll work on a new problem that I'll bring along to the session.

These sessions are also an opportunity for you to ask questions about lectures so far.

I'm happy to adapt the format and frequency of these sessions to the requests/needs of the students that turn up!

I currently foresee these being at the following days/locations:

2nd October: Bonus Revision Lecture: Solutions to Laplaces Equation (example in cartesian coordinates)

16th October: Question For Optional Examples Class 1 ...... Solutions.

6th November: Bonus Session 3 - The Lorenz Gauge Condidtion and Cosmic Ray Muons

20th November: Bonus Session 4 - The appearance of objects moving at close to the speed of light. The website containing the animations used in the lecture can be found at: https://www.spacetimetravel.org/bewegung/

4th December: Questions For Optional Examples Class 2 ...... Solutions. -->


Supplementary Material

Here is the complete Course Summary and Notes on the Exam ..... Please let me know if you find any typos or other mistakes!

A summary of useful formulae concerning vector calculus, coordinate systems, etc

Example Sheet on Vector Calculus

Pictures of the electric and magnetic fields produced by a point charge moving with constant velocity

Proof of Lienard-Wiechert Fields for a moving point charge

Patterns of radiation produced by an accelerating point charge

Local gauge invariance and the Schroedinger Equation: R. Barlow Eur. J. Phys. 11 (1990) 45.

The syllabus for the course as given in the Blue Book


Material relating to past exams may be found on Blackboard. Please look at the "Course Summary" for some notes on exams before January 2019, which is the first year I taught the course.


Your Questions, Feedback, etc

Do you have any questions about the physics, the lecturs, or the example sheets? Do you have any feedback on the lectures or other aspects of the course? Did you find any mistakes anywhere? I'd be very interested to hear from you! Please come and find me in Room 6.22 (Schuster) or:

Send email to userid: twyatt at the mailserver: fnal.gov