# Classical Prerequisites for Purcell's EM

1. Mar 26, 2016

### RubinLicht

I know for sure that being familiar with vector Calc, multivariate Calc, and special relativity is helpful. What I mean by prerequisites is anything that would be helpful to know. For example, a textbook may include an appendix, or chapter on the mathematics required, but I'd much rather learn the topic separately and with a much higher quality.

2. Mar 26, 2016

### Simon Bridge

Agreed - so what is the question?

3. Mar 26, 2016

### RubinLicht

Whether or not there is something else I missed that I'll need for purcell

I know that the wave equation is a partial differential equation, so I could just buy dovers book on pdes for a quick introduction. I will probably also need to learn a little bit more about differential equations, so far, I only know some simple methods of solving (separation of variables, and the factoring trick for second order differs for forced oscillations/damped

Last edited: Mar 26, 2016
4. Mar 26, 2016

### Simon Bridge

Your list is exhaustive - students usually struggle if their vector calc/analysis is weak.
The book is otherwise pretty well written - make sure you have one as up to date as possible since you may have trouble from it being old.
The concepts are fine - it's the teaching and learning styles that have changed.

5. Mar 26, 2016

### RubinLicht

I'll be using the third edition which has si units, Thanks for the help!

6. Mar 26, 2016

### Simon Bridge

No worries - cheers.

7. Mar 27, 2016

### vanhees71

Well, SI units make electrodynamics more complicated than necessary. Much of the beauty of the relativistic structure is hidden under conversion factors of units. Also Purcell seems to be sometimes confusing. We had long discussions about it, and there are many people who like the book very much; so maybe I'm wrong, but I'd prefer either Landau&Lifshitz vol. II which gives also a relativistic treatment of electromagnetism from the very beginning as it should be or (more in the spirit of Purcell to derive as much as possible from electrostatics + relativity but without the laborious didactics) Schwartz, Principles of Electrodynamics, Dover.

8. Mar 27, 2016

### Simon Bridge

I don't think it is more complicated so much as messier when written down, like the need for extra constants to scale things to the right units.
Physics moves into unified units soon enough - modern students are familiar with the SI system. I think the effort old texts make to reconcile students to the SI system shows that people just find the system they grew up with to be more intuitive.

I think Purcell is boring myself ... probably just the writing style conflicting with the way I read.

9. Mar 27, 2016

### TSny

When I was a student (late '60s), we used vol. 1 (Mechanics) and vol. 2 (Purcell's text) of the Berkeley Physics Course in our first course in physics. I think you are ready for Purcell if you are familiar with vector calculus, basic concepts of mechanics (e.g., Newton's laws, vectors, work, energy, angular momentum), and basic special relativity (Lorentz transformation, length contraction, time dilation, velocity addition formulas). Actually, much of the vector calculus is nicely developed from scratch in Purcell.

I really like Purcell's book. I think it provides a lot of physical insight. It did a great job preparing me for the upper-undergraduate-level course in electromagnetism.

10. Mar 27, 2016

### jasonRF

I may be in the minority, but I think having a basic understanding of elementary electromagnetism would be very helpful. I had never learned any aspect of electromagnetism before Purcell and found it to be a little too much; students in the class who had better high-school backgrounds (some had learned electromagnetism from Halliday and Resnick in high school) found it much more digestible. I think Purcell is a great book, but am not convinced it is the best for a very first exposure to this beautiful subject.

jason

11. Mar 28, 2016

### vanhees71

I don't think it's boring. It is one of the early attempts to teach electromagnetism in a modern way and not to confuse students with the usual non-relativsitic treatment of the sources and then making up puzzling paradoxa like "hidden momentum" that in fact were solved very quickly after Einstein discovered special relativity. I think at latest in 1912 von Laue came up with the correct solution to all these problems. Nevertheless it's still taught the old pre-relativistic way in even some newer textbooks. Only at the very end you find a brief chapter on "relativistic electrodynamics", which in fact is a tautology, because electrodynamics is a relativistic field theory since Maxwell discovered it, although this was hidden for almost half a century, and it was Einstein's real breakthrough to figure out that one has to change the spacetime model affecting entire physics, including the "mechanical part" and not only electromagnetism. Thus that's how electromagnetism should be taught since 1905.

However, the book by Purcell is overly complicated and sometimes confusing, as the long debates we had about it some time ago in these forums. In my opinion one should start right away with the mathematical description of special relativistic spacetime in terms of the covariant formalism a la Minkowski (of course not with the confusing introduction of imaginary times but as a real pseudo-Euclidean affine space; imaginary times are needed only in quantum statistics and they have nothing to do with relativity) and then use simple relativistic models for matter, i.e., charge-current distributions, to present electromagnetism in a manifestly covariant way.

The SI is a pest in electromagnetism. Why should electric and magnetic components of the one and only electromagnetic field be measured in different units? Of course, sometimes we are used to that. In the US distances on the road are measured in miles, and the height of mountains or bridges in feet and inches, but that seems not to be too attractive. You can even argue, why to measure distances and times in different units and not setting $c=1$ right from the beginning. I don't think that latter idea is a good one, because indeed spatical and temporal directions are dinstinguishable in Minkowski space due to the pseudo-metric's signature (1,3) (or (3,1) for the east-coast convention) arising from the necessity of establishing a causality structure of spacetime, and times are qualitatively different than spatial distances. So there's no argument for measuring $\vec{E}$ in different units than $\vec{B}$ but some justification for measuring times in a different unit than dinstances. So I think the best choice of units is the modern rationalized Gaussian system, the Heaviside-Lorentz systems, which is used in high-energy particle and nuclear physics.

12. Mar 28, 2016

### Simon Bridge

That would be nice - however, electromagnetism is started at a stage where students don't have the maths.
It makes for a headache when you have to tie everything together for the physicists though.

13. Mar 28, 2016

### vanhees71

Sure, and I had always the impression (no the least from my own struggles to understand electromagnetism in the 4th semester at the university within the theory course) that electromagnetism is taught too early in the theory curriculum. One should at least introduce the covariant description of relativistic spacetime in the mechanics lecture (usually the lecture "Theoretical Physics II", which covers analytical mechanics) and then start electromagnetism right away within this description. The trouble, however, is that you usually don't have vector calculus at hand, and usually that's done by going the old-fasioned way by starting with electro- and magnetostatics first and then at the end rushing through the real dynamics in terms of Maxwell's equations. It would be good to have non-relativistic hydrodynamics first to introduce non-relativistic vector calculus first without having conceptual problems, using non-relativistic approximations in a relativistic field theory, but unfortunately hydrodynamics is not part of the modern undergraduate curriculum anymore.

14. Mar 28, 2016

### Simon Bridge

The trouble is that people who do not get to go to college still need to have some understanding of electricity and magnetism.

15. Mar 28, 2016

### vanhees71

Fine, but they (hopefully) won't be bothered with Purcell's book ;-)).

16. Mar 28, 2016

### RubinLicht

I learned three of maxwell's equations from halliday and resnick, but haven't finished all the chapters yet. I will proceed with caution.

17. Mar 28, 2016

### RubinLicht

referring to the posts about units, I think, at my level, it doesn't really matter that much. I am currently in eleventh grade and will for sure revisit em in college, I can pick on those things once i get there and have a deeper knowledge of electromagnetism. For a second (first rigorous) exposure, a book as good as purcell should suffice for sure. Thanks for all the replies!

18. Mar 28, 2016

### Amrator

I'm currently taking introductory calculus-based E&M, and I've been using Purcell as my main textbook. So far, it's the best textbook I've ever used. I'm not even really sure what it is about the book that I like so much. Of course you should understand special relativity as taught in a standard physics textbook (like University Physics by Young and Freedman), as well as the basics of vector calculus.

Use these notes: http://physics.weber.edu/schroeder/mrr/MRR.html
Purchase both Purcell's Electricity & Magnetism and Daniel Fleisch's A Student's Guide to Maxwell's Equations.
With those notes and two books, you should be fully equipped to attack E&M.

19. Mar 28, 2016

### RubinLicht

Im planning to go through Morin and ap f each before Purcell (summer) , so I'll be solid enough in SR, i'm learning vector Calc in school so I'll have that under my belt as well. Thanks for input

Ooooh hey Schroeder, do you guys know anything about his thermal physics book, and whether or not it's suitable for ipho prep?

20. Mar 28, 2016

### Amrator

Just so you know, Morin is an upper-division mechanics book. You don't really need to go through Morin before reading Purcell.