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.
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.
⚬ Monday 9:00 - 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 ............. Answers
⚬ Wednesday 11:00 - 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, which I'll post at the end of the week! 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]. (Please do not look until you've had a go at trying to work out the second part yourself!)
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!)