Going through Jackson's Electrodynamics as an undergad who "hates" E/M

[AndreasC]

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...

 

[vanhees71]

I think one problem of Jackson is its comprehensiveness, i.e., it is very detailed on all subjects, and you may miss the main line of arguments. Maybe it's better to first use a somewhat more introductory textbook. I always liked most the old books "Lectures on Theoretical Physics" by Sommerfeld. Particularly vol. 3 on electrodynamics is very good, though in the later chapters when it comes to the treatment as a relativistic field theory it uses the old-fashioned $\mathrm{i} c t$ formalism, which is quite confusing. Somewhat similar but more modern is the electrodynamics volume of Greiner's textbooks on theoretical physics. Another classic is Becker&Sauter and, again more modern, Griffiths electrodynamics.

Jackson is, in my opinion, more suited for an extended higher-level look at the subject like the full multipole expansion of the electromagnetic field or also some where difficult and partially unsolved subjects like the notorious radiation reaction problem. Personally, I also started to like Jackson's book only after I've learned E&M on a somewhat less ambitious level getting the physics ideas first.

Another obstacle is that you need to be "fluent" in vector calculus. For the beginning the standard Euclidean 3D vector calculus with the differential operators div, grad, and rot (or the Nabla symbol $\vec{\nabla}$) and the Cartesian Ricci calculus together with the Stokes, Gauss, and Green (which is a special case of Gauss) integral theorems for vector fields is sufficient. Here a very good introductory treatment can again be found in Sommerfeld's Lecture (vol. 2 on hydrodynamics) or Becker&Sauter.

 

[AndreasC]

Maybe it's better to first use a somewhat more introductory textbook

Well, as I mentioned earlier, I'm not doing this so much to learn, but mostly as a challenge. I have a second semester of electrodynamics coming up which uses Griffiths, so I'm going to have that one too anyways.

For the beginning the standard Euclidean 3D vector calculus with the differential operators div, grad, and rot (or the Nabla symbol ) and the Cartesian Ricci calculus together with the Stokes, Gauss, and Green (which is a special case of Gauss) integral theorems for vector fields is sufficient.

Yeah I've done a semester on that too. Although I'm not very skilled on applying the theorems and my knowledge is kinda hazy.

 

[AndreasC]

Alright, I'll try one more time to solve exercise 1.12. If I can't, I'll accept a hint.

 

[Meir Achuz]

"how far I can push my patience" Why?

 

[AndreasC]

"how far I can push my patience" Why?

Why not?

 

[Meir Achuz]

If you want to learn physics, learn physics, don't "push" your patience.

 

[AndreasC]

If you want to learn physics, learn physics, don't "push" your patience.

But I am learning physics anyways, that's why it is what I am studying in uni. The reason I am doing that is because I often have trouble disciplining myself into going through something challenging, and it is a skill that is necessary.

 

[member 587159]

But I am learning physics anyways, that's why it is what I am studying in uni. The reason I am doing that is because I often have trouble disciplining myself into going through something challenging, and it is a skill that is necessary.

While I sympathize with what you write here, isn't it better to read something that is both challenging and interesting to you?

 

[AndreasC]

While I sympathize with what you write here, isn't it better to read something that is both challenging and interesting to you?

True. But I have to learn E/M anyways, as I have to do 3 more (!) semesters of that (and I've already done 1), so I'd better get used to it. My school is a polytechnic supposedly focused on engineering, and so stuff like relativity, cosmology, astronomy etc aren't given much attention, in fact there is only one class specifically about relativity in the entire 5 year curriculum (and it's not even mandatory). It is instead replaced by tons of E/M, condensed matter, QM, applications, applied math etc. It's not my least favorite subject anyways, that would be by far statics, mechanics of materials etc. After that it would be thermo.

To be honest, after starting to work through the exercises I have actually started to kinda like the subject. The book is definitely hard but it's not as hard or as boring as I expected.

However I am just now getting into the territory that I imagine people are angry at this book for and I may need some help to clarify things, because he seems to often just jump 5 steps ahead and expect you to understand what he did to get there.

 

[Dr Transport]

If you haven't completed Griffiths, why are you doing Jackson?? Challenge?? I think stupidity, you admitted that you haven't understood Griffiths, what would cause you to believe that you'll understand Jackson.

 

[AndreasC]

If you haven't completed Griffiths,

I used a different book because that was the one my course used. I have a second more advanced semester of E/M coming up which does use Griffiths. To be fair I think I didn't understand it very well because I didn't try that much because it kind of turned me off as a subject.

what would cause you to believe that you'll understand Jackson.

It's not that bad yet. It's easier than I expected it to be. I completed most exercises from the first section and I'm reading the second section and although I get confused at parts it's nothing insurmountable.

 

[Dr Transport]

I used a different book because that was the one my course used. I have a second more advanced semester of E/M coming up which does use Griffiths. To be fair I think I didn't understand it very well because I didn't try that much because it kind of turned me off as a subject.

This forum has a multitude of threads about undergrad E&M texts, you'd be better off looking and going through some other text.

 

[AndreasC]

Nah I figured I like this one. I've skimmed Griffiths too, it's also a very nice book. I'm going to get it for free in a month so I'm going to use that if I don't understand something in Jackson.

The book my other class used was Purcell BTW oddly enough. Purcell seems closer to Jackson's spirit than Griffiths from what I've seen, but definitely a lot easier.