In Week 11 we shall extend our discussion of radiation to include point charges moving with relativistic speeds.

There are two interactive sessions each week: in the Simon lecture theatre A (Monday) and Stopford lecture theatre 1 (Wednesday).

There are four mini-lectures, with associated small exercises and lecture notes provided.

In Mini-Lectures 21a, 21b, and 22c, we shall study the radiation by point charges moving with relativistic speeds. In Mini-Lecture 22 we shall consider two examples of the interaction of electromagnetic radiation with electrons.

N.B. The material presented in Mini-Lecture 22 will not be covered in a live lecture. Therefore you should follow Mini-Lecture 22 online.

You can find here a link to the Jupyter notebooks for the various animations of potentials,fields and radiation patterns produced by point charged particles that I have used in the lectures. The specific notebooks used in the lectures are 8,9,10,11,12. There are some others that are currently in development. These notebooks were written by my PhD student Dong Qichen - thanks very much to him for his work and Jupyter notebook expertise! You are welcome to run them in-situ in this area or you can copy them to your own space and modify your own copy. Citizen science: if you come up with any interesting modifications or new ideas, please feel free to let me know about them!

In preparation for this week's lectures I strongly recommend you take another look at question 2 on the sheet Examples Class 2. This deals with the transformation of accelerations from one frame to another.

It would also be very helpful if you could review your answer to question 1 on the sheet Additional Problems 2 in anticipation of Monday's lecture of Week 11. We shall be Lorentz boosting radiation from one intertial frame to another and this question is very relevant.

⚬ Monday 15:00-16:00 - Live Lecture - Radiation from Moving Charges (first part)

This live lecture covers approximately the same material as mini-lectures 21a and 21b. (To be continued on the Wednesday session).

Lecture 21 (first part) Podcast ............. Notes written to visualiser

You can find here a link to the Jupyter notebook for the animation of the radiation pattern produced by an isotropic source that I have used in this lecture.

⚬ Wednesday 10:00-11:00 - Live Lecture - Radiation from Moving Charges (second part)

The live lecture part covers approximately the same material as mini-lecture 21c.

Lecture 21 (second part) Podcast ............. Lecture notes written to visualiser ............. Exercises from mini-lecture ............. Answers

N.B. Please think about the puzzle I presented starting at 4 minutes into the podcast! There will be a special chocolate prize for people who have contributions to a discussion on this topic in next Wednesday's "Christmas themed lecture with chocolate prizes"!

You can find here a link to the Jupyter notebooks for the animation of the radiation patterns produced by 1) bremsstrahlung and 2) synchrotron radiation that I have used in this lecture.

By clicking on the links given below you will be able to access the video of each mini-lecture, together with the associated small exercises and lecture notes.

Three mini-lectures on the radiation by point charges moving with relativistic speeds.

Mini-Lecture 21a: Radiation produced by an accelerating point charge moving with relativistic speed. Part I: Total radiated power.

Video ............. Lecture notes written to visualiser

Mini-Lecture 21b: Angular distribution of radiation produced by an accelerating point charge moving with relativistic speed.

Video ............. Lecture notes written to visualiser

Mini-Lecture 21c: Angular distributions produced by bremsstrahlung and synchrotron radiation.

Video ............. Lecture notes written to visualiser ............. Exercises from mini-lecture ............. Answers

Mini-Lecture 22: Two examples of the interaction of electromagnetic radiation with electrons

N.B. The material presented in Mini-Lecture 22 will not be covered in a live lecture. Therefore you should follow Mini-Lecture 22 online.

Video ............. Lecture notes written to visualiser

Mini-Lectures 21: The radiation produced by an accelerating point charge - relativistic case

Mini-Lecture 22: Thomson scattering

The radiation by point charges moving with relativistic speeds.

In preparation for this week's lectures I strongly recommend you take another look at question 2 on the sheet Examples Class 2. This deals with the transformation of accelerations from one frame to another.

It would also be very helpful if you could review your answer to question 1 on the sheet Additional Problems 2 in anticipation of Monday's lecture of Week 11. We shall be Lorentz boosting radiation from one intertial frame to another and this question is very relevant.

In preparing the week 11 lectures on the radiation by point charges moving with relativistic speeds I came across the book "Radiative Processes in Astrophysics" by G.B. Rybicki A.P. Lightman. Chapter 4.8 "Emission from Relativistic Partlcles" in this book describes methods similar to those used in Mini-Lectures 21. This book is available for free online using your University of Manchester account at the link https://onlinelibrary.wiley.com/doi/book/10.1002/9783527618170 .

Optional extra-curricular reading: for alternative derivations of the radiation by point charges moving with relativistic speeds that start from the full Lienard-Wiechert fields I suggest looking at:

M.A. Heald and J.B. Marion, Classical Electromagnetic Radiation (3rd edition): Chapter 8.

J.D. Jackson, Classical Electrodynamics: Chapter 12.

D.J. Griffiths, Introduction to Electrodynamics: Chapter 11.2. (N.B. if in your edition of Griffiths, chapter 11 in entitled "Electrodynamics and Relativity" then try looking in chapter 10!)

Two examples of the interaction of electromagnetic radiation with electrons.

J.D. Jackson, Classical Electrodynamics: Chapter 14.8.

D.J. Griffiths, Introduction to Electrodynamics: Chapter 12.2.3 (N.B. if in your edition of Griffiths, chapter 12 in entitled "Potentials and Fields" then try looking in chapter 11!)

M.A. Heald and J.B. Marion, Classical Electromagnetic Radiation (3rd edition): Chapter 10.1.

Revision of multipole expansions in electrostatics and magnetostatics.

In preparation for next Monday's lecture on harmonically varying sources you may wish to revise the mini-lectures on multipole expansions

Mini-Lecture 5: Multipole Expansions in Electrostatics ............. Video ............. Lecture notes written to visualiser

Mini-Lecture 7c: Multipole Expansions in Magnetostatics ............. Video ............. Lecture notes written to visualiser

Harmonically varying sources.

D.J. Griffiths, Introduction to Electrodynamics: Chapter 11.1. (N.B. if in your edition of Griffiths, chapter 11 in entitled "Electrodynamics and Relativity" then try looking in chapter 10!)

M.A. Heald and J.B. Marion, Classical Electromagnetic Radiation (3rd edition): Chapter 9.1, 9.2, 9.8

J.D. Jackson, Classical Electrodynamics: Chapter 9.1-9.3.