Rigorous introductory books on Electromagnetism

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I need some rigorous introductory books on Electromagnetism, by rigorous I mean detailed and mathematical.

Many books that I have found don’t actually work out the field produced by current carrying toroid, solenoid or even some other simple electrostatic situations. They just write “by symmetry” and then they do something and puts out the result. I need something like Griffiths, he works out the derivation rigorously.

So, what are some other books which fulfills my need other than Griffiths?
 

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  • #2
vanhees71
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The standard textbook is of course Jackson, and he is pretty mathematical. Whether you can consider any physics book "rigorous" depends on which level you expect. I'm not aware of a pure-mathematician's textbook on electromagnetism. Maybe you can consider books on fiber bundles as a modern rigorous treatment of among many more things also electromagnetism, which is the most simple gauge theory one can think of, and the modern mathematical expression for gauge theories is fiber-bundle theory.
 
  • #3
PeroK
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I need some rigorous introductory books on Electromagnetism, by rigorous I mean detailed and mathematical.

Many books that I have found don’t actually work out the field produced by current carrying toroid, solenoid or even some other simple electrostatic situations. They just write “by symmetry” and then they do something and puts out the result. I need something like Griffiths, he works out the derivation rigorously.

So, what are some other books which fulfills my need other than Griffiths?
Having helped you on a few homework problems, I'd say you need to be careful not to go off in the wrong direction here. I'm not sure that EM can be particularly enlightened at your level by further mathematical rigour. On the contrary, an ability to cut through the mathematical difficulties as much as possible and think physically would be a better objective.
 
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Purcell can be good to start with
 
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  • #5
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The standard textbook is of course Jackson, and he is pretty mathematical. Whether you can consider any physics book "rigorous" depends on which level you expect. I'm not aware of a pure-mathematician's textbook on electromagnetism. Maybe you can consider books on fiber bundles as a modern rigorous treatment of among many more things also electromagnetism, which is the most simple gauge theory one can think of, and the modern mathematical expression for gauge theories is fiber-bundle theory.
"Rigorous" means (the way I intended to use it) a book where the actual mathematical derivations are carried out in detail. I want an introductory level text, something like using Multivariable Calculus, Curvilinear coordinates, and all for deriving Electrostatics and Magnetostatics results.

Some books are indeed available but their derivations seems to involve things which are not obvious but they consider it obvious. For example: In Electromagnetism by Slater and Frank we find this

Next we consider the field of a circular wire carrying a current, at points along the axis of the wire. The contribution to the field produced by an element ##ds## of wire at a point whose distance from the plane is ##x##, will be $$ \mu_0 /4\pi ~ i ds/(x^2 + R^2)$$ as we see in Fig 14. This field points at an angle to the perpendicular of the plane, however and only the component along that direction contributes to the resultant field. Thus we must multiply by the factor of ##R /(x^2 + R^2)^1/2##.

I really found it not obvious when he wrote "however, and only the component along that direction contributes to the resultant field"
 
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Having helped you on a few homework problems, I'd say you need to be careful not to go off in the wrong direction here. I'm not sure that EM can be particularly enlightened at your level by further mathematical rigour. On the contrary, an ability to cut through the mathematical difficulties as much as possible and think physically would be a better objective.
I would certainly follow that advice. But sometimes I don't get things which are "obvious" and Griffiths very well provided a way out of that but some of his proofs (see his proof of Magnetic field by solenoid and toroid) are quite too personal.
 
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Electromagnetic Fields and Waves by Lorrain is at about the level of Griffiths. There's also a book by Dover, The Electromagnetic Field by Shadowitz, which is at around the same level.
 
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  • #8
vanhees71
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Then another good one is the book by Greiner or my all-time favorite for everything concerning classical physics, Sommerfeld's Lectures on Theoretical physics (for E&M it's vol. 3 for optics vol. 4). Then have a look at the Feynman lectures as an additional read. It's done in a very deep Feynmanian way emphasizing the physics. I'd not recommend Purcell (Berkeley physics course), because it's my paradigmatic example for a text which overcomplicates things in an attempt to be didactical. A much better choice for a text emphasizing the "relativity first approach" (which in my opinion is pretty much what one should do, provided the student has some previous knowledge about E&M) is Melvin Schwartz, Principles of Electrodynamics. Of course also Griffiths is a great book from this point of view (it's particularly lucid on the sometimes difficult topic what's called "hidden momentum" though there's no momentum hidden but just momentum, and it's to be treated relativistically in all these cases to be consistent).

On the same level but partially with much more mathematical detail and also more elegance in the mathematical treatment as Jackson is J. Schwinger, Classical Electrodynamics.
 
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  • #9
jasonRF
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I would certainly follow that advice. But sometimes I don't get things which are "obvious" and Griffiths very well provided a way out of that but some of his proofs (see his proof of Magnetic field by solenoid and toroid) are quite too personal.
I don't know what it means to be "too personal.” What exactly is it about that isn’t working for you? Or is it working fine and you just want intro books to supplement it?

By the way, I think PeroK has good advice. Understanding the physics is key the first time through this material, and sometimes the math can obscure the physics. Standard intro books such as Halliday and Resnick can do this pretty well.

Anyway, besides the already mentioned Purcell, and the Feynman Lectures (online at https://www.feynmanlectures.caltech.edu/ ) the only other intro book I am familiar with that really uses the tools of vector calculus is “Electromagnetism” by Lorraine and Corson
https://www.amazon.com/dp/0716720965/?tag=pfamazon01-20&tag=pfamazon01-20
This is a different book than their upper division book recommended by Mondayman (which is also a good book). Some parts are excellent, and some parts are just okay. Perhaps the best part of the book is that it has a good set of interesting problems to solve.

jason
 
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  • #10
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I don't know what it means to be "too personal.” What exactly is it about that isn’t working for you? Or is it working fine and you just want intro books to supplement it?

By the way, I think PeroK has good advice. Understanding the physics is key the first time through this material, and sometimes the math can obscure the physics. Standard intro books such as Halliday and Resnick can do this pretty well.

Anyway, besides the already mentioned Purcell, and the Feynman Lectures (online at https://www.feynmanlectures.caltech.edu/ ) the only other intro book I am familiar with that really uses the tools of vector calculus is “Electromagnetism” by Lorraine and Corson
https://www.amazon.com/dp/0716720965/?tag=pfamazon01-20&tag=pfamazon01-20
This is a different book than their upper division book recommended by Mondayman (which is also a good book). Some parts are excellent, and some parts are just okay. Perhaps the best part of the book is that it has a good set of interesting problems to solve.

jason
Look at this proof of Griffiths:

Solenoid 1
Solenoid 2
Solenoid 3
Solenoid 4

Aren’t they “too personal” ? I mean they seem to be very informal (there are only very few instances where Griffiths get into informal proofs).
 
  • #11
vanhees71
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Hm, I like Griffiths electrodynamics book and I don't see where it is "too informal" in any sense. The language is perhaps a bit more personal than other textbooks, but that doesn't mean it's less rigorous.
 
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  • #12
jasonRF
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Look at this proof of Griffiths:

Solenoid 1
Solenoid 2
Solenoid 3
Solenoid 4

Aren’t they “too personal” ? I mean they seem to be very informal (there are only very few instances where Griffiths get into informal proofs).
Does this effect your ability to learn the material? I suspect not, and that it is just a matter of taste.

If this is the worst thing you can say about the book, then I think you have found a very good book for you to learn from.
 
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  • #13
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Does this effect your ability to learn the material? I suspect not, and that it is just a matter of taste.
Hmm... yeah! That proof and the next (that of toroid) are, of course, quite hard to comprehend.
 
  • #14
marcusl
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I read that section and think it’s explained very well. Doing physics requires understanding enough of the problem to know how to set it up for solution, what can be approximated, what the symmetries are, etc. Otherwise you’ll be reduced to solving problems with an EM simulation package like so many engineers who can’t tell when they have a good or a ridiculous solution (I work with a number of them).
 
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  • #15
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Otherwise you’ll be reduced to solving problems with an EM simulation package like so many engineers who can’t tell when they have a good or a ridiculous solution (I work with a number of them).
Ugh, you're working with bad engineers then
 
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  • #16
Vanadium 50
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But sometimes I don't get things which are "obvious"
That is a sign of insufficient background. A textbook that is more advanced mathematically is unlikely to be the solution.
 
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marcusl
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I find that many young microwave engineers have been educated in computer use without a focus on critical thinking.
 
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There many books from Mir publishers by different authors on the subject, have a look at this one:
https://mirtitles.org/2014/01/15/electricity-and-magnetism-matveev/
Matveev has done an excellent job with this book, you'll have both physics and mathematics derivations.
Here's a snapshot of how he introduces the divergence:
abc-1.png

abc-2.png

abc-3.png

abc-4.png
Another great book is the second volume of Savelyev's General physics:
https://mirtitles.org/2017/01/18/physics-a-general-course-savelyev/

Flip through both of them to see whether you have feeling for them.
 
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  • #19
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That is a sign of insufficient background. A textbook that is more advanced mathematically is unlikely to be the solution.
Yes, that may be the issue. I’m getting some strange problems in what is called symmetry. Although, my general physics is fine, Calculus is nice, Vector Calculus is okay but then also when books write “by symmetry....” I couldn’t get how they can skip such a numerous steps with so much of intricacies in them. What background do I actually lack?
 
  • #20
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I have received so many great replies, I’m just taking some time to go through all the suggested readings (I mean I’m skimming over every thing that is suggested). Thank you all, really thank you so much.
 
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  • #21
PeroK
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Yes, that may be the issue. I’m getting some strange problems in what is called symmetry. Although, my general physics is fine, Calculus is nice, Vector Calculus is okay but then also when books write “by symmetry....” I couldn’t get how they can skip such a numerous steps with so much of intricacies in them. What background do I actually lack?
First, using physical symmetry can greatly simplify the mathematics. You could try proving Newton's Shell Theorem without using symmetry. Or, try to prove that planetary motion remains in a plane without using symmetry.

Second, there are often physically spurious mathematical solutions that nothing in the mathematics forbids, but can only be discounted by appealing to symmetry or other physical principles.

Part of mathematical physics (and applied maths) is using the physical nature of the problem to simplify the problem and focus on physical solutions. You can't make physics a branch of pure mathematics.
 
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  • #22
marcusl
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Thank you, PeroK, for expressing with clarity what I was trying to say.
 
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  • #23
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Thank you, PeroK, for expressing with clarity what I was trying to say.
I found spherical symmetry, cylindrical symmetry and line symmetry in “Center of Mass” things, but this solenoid and toroid are quite exclusive to Electromagnetism. What you suggest to do for solenoid and Toroid?
 
  • #24
marcusl
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Do you have access to a professor or tutor? Difficulties in understanding concepts are best handled in a realtime give and take conversation. (Email or forums such as this one are poorly suited to the job.) You are already using a text that explains things well, but Purcell (already mentioned above) is another. Also bolster any weaknesses in math, especially vector calculus, and return to freshman-level physics books (Halliday and Resnik) or even high-school if you aren’t absolutely solid. Going forward to more advanced and mathematical books is never viable when you are struggling with basic concepts.
 
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  • #25
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Do you have access to a professor or tutor?
No.
Going forward to more advanced and mathematical books is never viable when you are struggling with basic concepts.
I’m not struggling with basic concepts, it’s just that I don’t understand them.
 

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