Please make sure you have revised basic Magnetostatics by watching Mini-Lecture 6 Video BEFORE Monday's lecture in Week 3!

Please make sure you have watched the revision lecture on the basics of Electrodynamics Mini-Lecture 8: Revision Lecture on Statics --> Electrodynamics BEFORE Wednesday's lecture in week 3!

In Week 3 we shall discuss various topics in Magnetostatics (Mini-Lectures 7a, 7b, 7c) and revise basic Electrodynamics (Mini-Lectures 8 and 9).

We shall do also some basic revision of those topics from 1st year Special Relativity that are most needed for our study of Electrodynamics (Mini-Lecture 10).

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

There are six mini-lectures, with lecture notes provided. The two live lectures this week cover the same material as four of the mini-lectures (7a, 7b, 9a, 9b), which therefore do not necessarily need to be followed online. Two of the remaining mini-lectures (8 and 10) cover basic revision material from previous courses.

N.B. The material presented in Mini-Lectures 7c, 8 and 10 will not be covered in a live lecture. Therefore you should follow Mini-Lectures 7c, 8 and 10 online.

There are official 3rd-year examples classes for Electrodynamics this week. These are designed to help you revise the topics from your previous courses in Electromagnetism and Special Relativity that are most relevant to our study of Electrodynamics.

Please make sure you have watched Mini-Lecture 10: Revision of Special Relativity BEFORE the Monday lecture in week 4!

Please make sure you have revised basic Magnetostatics by watching Mini-Lecture 6 Video BEFORE Monday's lecture in Week 3!

⚬ Monday 15:00-16:00 - Live Lecture 7: Some Topics in Magnetostatics

This live lecture covers approximately the same material as Mini-Lectures 7a and 7b.

Lecture 7 Podcast ............. Notes written to visualiser

Please make sure you have watched the revision lecture on the basics of Electrodynamics Mini-Lecture 8: Revision Lecture on Statics --> Electrodynamics BEFORE Wednesday's lecture in week 3.

⚬ Wednesday 9:00-10:00 - Live Lecture 9: The wave equations for the potentials and their solutions

This live lecture covers approximately the same material as Mini-Lecture 9a and the beginning of Mini-Lecture 9b.

Lecture 9 Podcast ............. Notes written to visualiser

For the full proof that our guesses [equations 9.8 and 9.9] are indeed solutions to the wave equations [equations 9.4 and 9.5] please see the video for Mini-Lecture 9b starting at around 9 minutes 30 seconds in.

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 7a: A general derivation of the curl of B

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

Mini-Lecture 7b: Demonstration that our definition of the vector potential A is consistent with the Coulomb gauge condition

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

Mini-Lecture 7c: Multipole Expansions in Magnetostatics

N.B. The material presented in mini-lecture 7c will not be covered in a live lecture. Therefore you should follow mini-lecture 7c online.

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

Mini-Lecture 8: Revision of Electrodynamics

N.B. The revision material presented in mini-lecture 8 will not be covered in a live lecture. Therefore you should follow mini-lecture 8 online.

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

Two Mini-Lectures 9a, 9b, covering the wave equations for the potentials and their solutions

Mini-Lecture 9a: Derivation of the Wave Equations for the Potentials

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

Mini-Lecture 9b: The Solutions to the Wave Equations for the Potentials

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

Mini-Lecture 10: Revision of Special Relativity

N.B. The revision material on basic special relativity presented in Mini-Lecture 10 will not be covered in a live lecture. Therefore you should follow Mini-Lecture 10 online. Please do this BEFORE Monday's live lecture in Week 4!

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

Remember that there is a Special Relativity Revision Exercise Sheet available ............. Solutions.

My ``One-Page'' Summaries of This Week's Mini-Lectures

Mini-Lecture 7: Topics in Magnetostatics (Mini-Lectures 7a, 7b, 7c)

Mini-Lecture 8: Revision Lecture on Statics --> Electrodynamics

Mini-Lecture 9a and 9b: The wave equations for the potentials and their solutions

Mini-Lecture 10: Revision of Special Relativity

By way of getting an idea of the basic mathematical tools we shall be using it might be useful to take a quick look at:

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

Topics in Magnetostatics

D.J. Griffiths, Introduction to Electrodynamics: Chapter 5.

In Mini-Lecture 7a, a general derivation of the curl of B is given starting from the vector potential. For the more "traditional" alternative (but rather long) general derivation of the curl of B starting from the Biot-Savart Law see, e.g.,:

- D.J. Griffiths, Introduction to Electrodynamics: Section 5.3.2.

- J.D. Jackson: Section 5.3.

Revision of the Basics in Electrodynamics

D.J. Griffiths, Introduction to Electrodynamics: Chapter 7.

The Wave Equations for the Potentials and their Solutions

D.J. Griffiths, Introduction to Electrodynamics: Section 10.1.3

Note to try to avoid a potential source of confusion: In the Cambridge University Press (CUP) version of the 4th Edition of D.J. Griffiths, Introduction to Electrodynamics, the chapter entitled "Potentials and Fields" is Chapter 10. Unfortunately, in an older (Pearson) version of the 4th Edition it is chapter 12! I shall refer to the CUP chapter numbers, but if in your edition of Griffiths, chapter 10 is entitled "Radiation" then try looking in chapter 12!

M.A. Heald and J.B. Marion, Classical Electromagnetic Radiation (3rd edition): Section 4.5

Solutions to the Wave Equations for the Potentials (Mini-Lecture 9b)

M.A. Heald and J.B. Marion, Classical Electromagnetic Radiation (3rd edition): Section 8.1 gives a proof along the lines discussed in lecture 9(b)

D.J. Griffiths, Introduction to Electrodynamics: Section 10.2.1, gives a proof that is more "straight-forward", but is more "long-winded".

Special Relativity and 4-vectors: Revision of Physics and Notation

Jeff Forshaw and Gavin Smith, Dynamics and Relativity: Chapters 5, 6, 7, 11 and 12.

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

Special Relativity and 4-vectors: Revision of Physics and Notation

Jeff Forshaw and Gavin Smith, Dynamics and Relativity: Chapters 5, 6, 7, 11 and 12.

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

Remember that there is a Special Relativity Revision Exercise Sheet available ............. Solutions.

In preparing for using index notation for 4-vectors and tensors in Special Relativity, you may want to take a look again at solving using index notation the Optional Revision Exercises on Vector Calculus ............. Answers using general index notation for vectors

In solving these problems you may find the following very brief preliminary remarks on using index notation for vector calculus useful. In addition, here is a somewhat more extensive introduction to using index notation for vector calculus by John Crimaldi of University of Colorado, Boulder.

Please make sure you have watched the revision lecture on the basics of Special Relativity Mini-Lecture 10: Revision of Special Relativity BEFORE Monday's lecture in week 4.