In Week 7 we shall apply our newly acquired expertise with 4-vector notation for Electrodynamics to work out the Potentials (Lecture 14) and Fields (Lecture 15) produced by a point charge moving with a constant velocity.

There are two interactive sessions each week: in the Simon lecture theatre A (Monday) and Stopford lecture theatre 6 (Wednesday).

There are three mini-lectures, with associated small exercises and lecture notes provided, but all of the core material for this week will be covered in `live lectures'.

⚬ Monday 15:00-16:00 - Live Lecture 14: The potentials produced by a point charge moving with constant velocity

This live lecture covers approximately the same material as mini-lecture 14.

Lecture 14 Podcast ............. Notes written to visualiser ............. Exercises from lecture ............. Answers

Here is the Jupyter notebook used in the lecture to illustrate the scalar potential produced by a moving point charged particle

⚬ Wednesday 9:00-10:00 - Live Lecture 15: The fields produced by a point charge moving with constant velocity

This live lecture covers approximately the same material as mini-lectures 15a and 15b.

Lecture 15 Podcast ............. Notes written to visualiser ............. Exercises from lecture ............. Answers

You may find this Reminder of the Field Tensor and Lambda Matrix useful!

Here is the Jupyter notebook used in the lecture to illustrate the scalar potential and electric field produced by a moving point charged particle

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.

Mini-Lecture 14: The potentials produced by a point charge moving with constant velocity

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

Edvard Munch is surprised that the equipotentials are centred at the current position of the point charge and not the position at the retarded time!

Two Mini-Lectures on the Fields produced by a point charge moving with constant velocity.

Mini-Lecture 15a: E and B fields for a point charge calculated from the potentials in the frame in which it is moving

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

Mini-Lecture 15b: Transformation of E and B Fields from the frame in which the point charge is stationary to the one in which it is moving

Video ............. Lecture notes written to visualiser ............. Exercises from mini-lecture ............. Answers ............. Field Tensor and Lambda Reminder

Mini-Lecture 14: The Potentials produced by a point charge moving with constant velocity

Mini-Lecture 15a and 15b: the Fields produced by a point charge moving with constant velocity

The potentials and fields produced by a point charge moving with constant velocity

The Feynman Lectures on Physics, Volume 2: Chapter 26.

For a really instructive alternative derivation of the potentials produced by a point charge moving with constant velocity from the point of view of retarded time see: The Feynman Lectures on Physics, Volume 2: Chapters 21.6.

J.D. Jackson, Classical Electrodynamics: Chapter 11.10.

N.B. Many texts treat the problem of a point charge moving with constant velocity from the perspective of the so-called "Lienard-Wiechert" potentials. We'll discuss these potentials in a few lectures' time in preparation for radiation, but if you'd like to take a look at this formulation you might try:

D.J. Griffiths, Introduction to Electrodynamics: Chapter 10.3. (N.B. if in your edition of Griffiths, chapter 10 in entitled "Radiation" then try looking in chapter 12!)

M.A. Heald and J.B. Marion, Classical Electromagnetic Radiation (3rd edition): Chapter 8.1-8.5.

Maxwell's equations for the fields in Lorentz-covariant form and interaction of charged particle with the fields.

M.A. Heald and J.B. Marion, Classical Electromagnetic Radiation (3rd edition): Chapter 14.5.

J.D. Jackson, Classical Electrodynamics: Chapter 11.19.

D.J. Griffiths, Introduction to Electrodynamics: Chapter 12.2.4. (N.B. if in your edition of Griffiths, chapter 10 in entitled "Radiation" then try looking in chapter 11!)

Continuity equation for Energy-Momentum, etc.

J.D. Jackson, Classical Electrodynamics: Chapter 6.7.

The Feynman Lectures on Physics, Volume 2: Chapter 27.