In Week 8 we shall write down more equations of electrodynamics in Lorentz-covariant notation (Lecture 16). In addition, we shall discuss local conservation laws (Mini-Lecture 17).
There are two interactive sessions each week: in the Simon lecture theatre A (Monday) and Stopford lecture theatre 6 (Wednesday).
There are two mini-lectures, with associated small exercises and lecture notes provided.
N.B. The material presented in Mini-Lecture 17 will not be covered in a live lecture. Therefore you should follow Mini-Lecture 17 online.
There are official 3rd year examples classes this week.
⚬ Monday 15:00-16:00 - Live Lecture - Lecture 16: Lorentz-Covariant Treatment of Maxwell's Equations and Interaction of Charged Particle with the Fields
This live lecture covers approximately the same material as mini-lecture 16.
Lecture 16 Podcast ............. Notes written to visualiser ............. Exercises from lecture
⚬ Wednesday 9:00-10:00 - A "Worked Example" Class, Based on a Past Exam Question Concerning the Field Tensor and Lorentz Transformations
Relativity worked example: Question sheet ............. Answers written to visualiser ............. Please try to finish the rest of the problem before looking at the Complete solution [including parts of problem for which there was not time during the session].
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 16: Lorentz-Covariant Treatment of Maxwell's Equations and Interaction of Charged Particle with the Fields
Video ............. Lecture notes written to visualiser ............. Exercises from mini-lecture ............. Answers
Mini-Lecture 17: Conservation Laws - Global vs. Local
N.B. The material presented in Mini-Lecture 17 will not be covered in a live lecture. Therefore you should follow Mini-Lecture 17 online.
Video ............. Lecture notes written to visualiser
Note: there is some overlap of material with regard to energy conservation between Mini-Lectures 16 and 17 and they can be viewed in either order. Lecture 16 is in Lorentz-covariant notation. The main function of Mini-Lecture 17 is to stress the importance of local conservation laws. The continuity equation for energy is treated in "non-4-vector" notation and includes consideration of the field energy.
Maxwell's equations for the fields in Lorentz-covariant form, etc.
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 12 in entitled "Potentials" 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.
Radiation by an accelerated point charge
In preparation for next week's lectures I recommend you revise the material covered in Lectures 14 and 15, in which we derived the potentials and fields produced by a moving charged particle.
A good intuitive description at a level similar to Lecture 18 is in Appendix B of the book: Electricity and Magnetism by E.M. Purcell (yes, those are really his initials ;-)
Unfortunately, I am not aware of any undergraduate-level text books that do the vector calculus treatment of this subject in exactly the way that I have adopted in my lectures next week. For various alternative approaches I suggest looking at:
M.A. Heald and J.B. Marion, Classical Electromagnetic Radiation (3rd edition): Chapter 8.
J.D. Jackson, Classical Electrodynamics: Chapter 14.
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!)