- #1

AndreasC

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**Summary::**Not entirely sure if this is the appropriate board, if I'm mistaken feel free to move it somewhere better. I decided to slowly go through Jackson's infamous Classical Electrodynamics book as a challenge to myself, solving as many exercises as possible. I will document my progress here, make questions, and anyone interested can also talk about their experience with the book and participate.

So as I stated in the summary, I challenged myself to go through this infamously difficult book. I've only taken one semester of basic electrodynamics and to be honest, I didn't really like or feel like I understood the subject well. I understand that going through Jackson is not the best method if you want to understand it, however I am mostly doing this to see if I can do it and how far I can push my patience and understanding. As I mentioned, I will try to solve as many exercises as possible.

I skimmed through the introduction, to be honest I didn't understand very much. A few things piqued my interest, but most of it was talking about things that I had no exposure to so I didn't take much out of it.

I moved on to the 1st chapter, which was about electrostatics. I have taken a semester on PDEs (as well as that other basic E/M course I talked about) so most of the things in that chapter I was familiar with, and it didn't seem hard. There were a couple of points that puzzled me but nothing too bad. One thing I DON'T feel like I understand very well though is section 1.11, the one about electrostatic potential energy, energy density and capacitance. It talks about self energy which I still don't quite understand what it is supposed to be and what its physical significance is, and I also got a bit confused by the description of the method of calculating forces with changes in energy by displacing elemental areas etc. But overall it wasn't nearly as bad as I was expecting.

I've done the exercises up to 1.10. Again, not as hard as I expected, although I did require hints from peaking at solutions online 2-3 times. Some exercises were very interesting, I really liked the one about the potential of the hydrogen atom. Now I am stuck at 1.12. I skipped 1.11 because I don't even know what the "principal radii of the surface" means. Now I am trying to figure out what the correct way to include what I know about fields on surfaces and volumes and Green's identities in such a way that I can make a connection between two different fields. If someone doesn't know what I'm talking about, you're supposed to prove Green's reciprocation theorem, and it seems pretty challenging to me. Maybe it isn't, and I just haven't found the "trick" yet.

Another thing I found interesting was proving the mean value theorem for fields in 3d space. I already know it is also true in 2d space, from complex analysis (you can use Cauchy's integral formulas to prove it for harmonic functions). I'm wondering if there is a generalization for higher dimensions for harmonic functions...