7 ms·

I would have killed for content like this back when I was getting my Physics degree. The diagrams are so beautiful and go straight to the heart of the key vecto

I would have killed for content like this back when I was getting my Physics degree. The diagrams are so beautiful and go straight to the heart of the key vector calculus concepts needed for E&M. I remember struggling through Jackson[1] as a rite of passage, but there's no reason future generations should have to suffer as we did. This is what the web was meant to be. [1]: https://en.wikipedia.org/wiki/Classical_Electrodynamics_(book) https://en.wikipedia.org/wiki/Classical_Electrodynamics_(boo...

lupire 2y ago
It really is a shame that in the 20th Century, the "best" math and science books were judged not for their educational power, but for how difficult and impressive they were to fellow professionals. It seems as though the professors were afraid that they'd lose their lecturer jobs if the books were too educational on their own.
- jc6 2y ago
  Subject matter experts are not experts in pedagogy. Because pedagogy is a seperate subject entirely. And teaching is not about getting people to say aha. Thats just performance or entertainment. Seen everywhere these days thanks to the Attention Econnomy. You can gets ahas out of people playing great music. But dont equate that with getting people to play great music. Cuz that requires getting people to do lot of mundane mindless work for long long periods of time.
  - archgoon 2y ago
    > And teaching is not about getting people to say aha. Thats just performance or entertainment. Thank you. Reading the article will not in fact give you an easier time at the Jackson Problem sets. I think many people who think this would have helped them back in the day have simply forgotten what the actual hard part of the degree was.
    - lupire 2y ago
      Are you sure the hard part is the most important part?
      - kaashif 2y ago
        Yes. There's a difference between thinking you understand something and having to prove it via problems. Often that's how I discover I didn't really understand something at all.
  - esafak 2y ago
    What does "aha" mean to you? To me it means understanding. And isn't that the point of teaching?
    - varjag 2y ago
      I can explain memory pointers to a layperson in terms of numbered boxes and yellow notes. They're still long long way to go from that even to reversing a single linked list successfully.
  - pezezin 2y ago
    A few years ago, I tried teaching for a couple years. Something that struck me was that to teach at the elementary or high school level you need specific degrees, but to teach at a university you don't. There is this thinking that because you have a PhD you can teach, which is very far from the truth. Being a good communicator is a skill in itself.
    - vkou 2y ago
      > Something that struck me was that to teach at the elementary or high school level you need specific degrees, but to teach at a university you don't So, the thing about elementary and high school is that everyone goes to it, but only people who are good at studying go to university. Given that the students are highly selected in the latter, you can get away with much worse instruction.
      - denton-scratch 2y ago
        > only people who are good at studying go to university. I think this is arse over elbow; the purpose of an undergraduate degree course is to teach you to study and do research. The "research" done by undergraduates isn't novel research; the student repeats "research" that has been done by generations of students before them. I.e., it's practice. For this reason, writing undergraduate essays felt to me like being an impostor; you try to write in the manner of a researcher, knowing that you're faking it.
    - cess11 2y ago
      Where I live you study pedagogy and practice it while doing your PhD. If you suck at it you can still pass, but at least they take a shot at teaching it to you. When applying for positions your record on teaching might make it harder to get to those where you're expected to do it regularly. The usual nepotism, corruption and fraud in academia will of course allow some bad teachers to advance anyway.
      - pezezin 2y ago
        That sounds good, wish more places did like that.
- physicsguy 2y ago
  I don’t think this is true at all… Jackson is a good book not because it’s an easy introduction to EM but because it exposes you to more complex problems than would typically be looked at in undergraduate courses. There’s clearly a place for advanced texts for this reason.
photon_lines 2y ago
Thanks a lot man - I'm really happy to have this kind of feedback. The reason I wrote this is because I found most of the modern explanations lacking in intuition behind the equations - along with also not explaining what the actual equations meant. If you found this useful please share and subscribe - I'm also trying to provide intuitive guides to other concepts (Schrodinger's equation, Black Holes, Quantum Mechanics, other complex topics) and eventually I'm hoping to write books on some of these topics which present math and physics in a much more clear and intuitive manner. Math shouldn't be hard to grasp. At the very bottom level it's very simple but presenting it in a clear and intuitive manner I will admit is very hard. Also full credit to a lot of the material as well goes to Grant Sanderson (3Blue1Brown) and most of the diagrams there were generated using Vexlio which I also highly promote: https://vexlio.com/ https://vexlio.com/
- WalterBright 2y ago
  This is a really good article. A minor nit - it'll read easier without the exclamation points after every sentence.
- wayoverthecloud 2y ago
  You explain concepts really well. Wish I had professors like you in college.
- cgh 2y ago
  Also check out the YouTube videos of eigenchris, especially his series on tensor calculus and relativity. Probably the clearest explanations I’ve seen on these subjects.
- deleted 2y ago
  [deleted]
- robertbarbe 2y ago
  Thanks @photon_lines! In your temperature diagram, you mention that every point will take the average of the neighboring points. However, the equation is not a constraint on the temperature but on the "change of the slope (or gradient) of the temperature". The bigger the slope (in space), the faster (in time) the temperature changes at that point!
archgoon 2y ago
The basic ideas, the pictures, the diagrams, etc, found here, typically show up in enough books if you look for them that I don't feel that this was the main limiting factor in my physics education. The difficulty of Jackson (which doesn't show up until grad school for most students) is in the problem sets, not the ideas behind the equations (which most students have a had at least two courses in already). I don't believe that having a more 'intuitive' idea of the equations really helps all that much, as the intuition needed for solving the problems isn't really physical, but mathematical. Which integrals are solvable, which order of integration will make this tractable, do I need to use properties of Bessel functions here, etc. We can argue whether getting good at this sort of thing is actually useful for physicists, but I wouldn't know. Very few of us ended up becoming researchers in the field.
- angra_mainyu 2y ago
  Jackson's the standard here in Spain (undergrad), after working through a course based off of Griffith's.
abdullahkhalids 2y ago
I am confused. 1. While the posted guide is excellently written, it's not particularly novel. I was taught EM in a very similar fashion. Diagrams similar to those in the guide were drawn on the board by my professors. 2. Jackson is a graduate EM text. It is mathematically difficult, because when you read it, you should have been familiar with EM and all this conceptual underpinning for at least 3-4 years. The goal of Jackson is to solve the equations for scenarios that undergrads would find challenging. What did you study in your undergrad?
- kjellsbells 2y ago
  Re #2: Jackson was the standard text for undergrads like me doing a Mathematics degree. It was a late second year or early third (final) year text if I recall rightly. This was 1992, so I'm still amazed to read that its still a commonly used text. Fwiw, other standard texts used in Durham (UK) back then were Spivak on Calculus, Goldstein on mechanics, and for the mathematical physics kids, landau and lifschitz on mechanics and electromagnetism, and (an absolute doorstop) Misner, Wheeler and Thorne on Gravitation (relativity).
  - abdullahkhalids 2y ago
    From the first preface (1962) of Jackson > Typically, the undergrad program in electricity and magnetism involves two or perhaps three semesters beyond elementary physics.... As a general rule, a two-semester course in electromagnetic theory is given to beginning graduate students. It is for such a course that my book is designed. So, your professors did you injustice by using an inappropriate book. Spivak, Goldstein and MWT are undergraduate books and appropriate. Landau and Lifschitz is great and accessible to smart undergraduates, but I don't see why you would use it for mathematical physics. Sure, Landau emphasized methods a lot, but there are better books for it.
    - macbr 2y ago
      As someone studying Physics (Bachelor) in Germany Jackson is what my electrodynamics professor recommended. My professor greatly shortened the chapter maxwell in matter and opted to give an intro into quantum electrodynamics instead. At my uni it's a fourth semester course with theoretical mechanics (second semester) and quantum mechanics (third semester) preceeding it.
wglb 2y ago
We used the John Kraus book on Electromagnetics for the dynamic fields course. This was preceded by a course on static fields. That course’s final had the shortest test statement I had ever encountered: “Derive Maxwell’s Equations”. I found the Kraus book satisfactory.
- richk449 2y ago
  What was an acceptable answer to “derive maxwells equations”?
  - hxriv 2y ago
    [flagged]
  - wglb 2y ago
    Show the steps such as faraday’s law and other things that led up to it.
  - wrycoder 2y ago
    Maxwell's equations are statements of experimental results in differential form, plus Maxwell's guess that there are no magnetic monopoles and that there is a displacement current to carry current through a capacitor, providing continuity. You don't really derive them (unless the professor had in mind, "Produce them from the integral forms"). A better question would be, "Derive the EM wave equation in free space from Maxwell's equation and determine the phase velocity."
    - wglb 2y ago
      > Produce them from the integral forms Pretty much what he was looking for. Keep in mind that this was at the end of a course covering pretty much all of static fields. And this course was a precursor and prerequisite for the following course which was about the application and implications of Maxwell's equations. The latter was taught by my favorite professor, who seemed to have a radar to know when the class was not following. Without request, he would erase what he had written on the board and restart. The lab was fun. Three quarters of the way through the first 2-hour lab, he said "By the way, anyone who gets the right answer loses points on this exercise. The point is to teach you how hard it is to come to the right answer." He told a story of his work during WW II. His favorite thing then was to build a little $50 piece of equipment to render million-dollar radar sets useless. Clearly his task was to help improve the radar set. "The odds are stacked in favor of the jammer." Who obviously cheer for the inverse of the distance to the fourth power.
lupire 2y ago
People often make comments like this, forgetting that want they are marvelling at was actually in the book they read or class they took the first, and then actual different is that they forgot, or they've had more time to stew on the material so it feels more familiar the second time through. Hence the adage that the best book on the subject is whatever book you read second. It seems so much more intuitive the second time through.
sanderjd 2y ago
Yeah reading this a couple decades out from my undergrad physics classes, my thought was "I remember learning all of this very painstakingly over multiple years and multiple different classes". But also, I'm not sure I would have grokked much in this article without having taken those classes already, with the benefit of lectures and graded homework and group study sessions and TAs answering questions and all that...
TheRealDunkirk 2y ago
At least it wasn't Halliday and Resnick. It's been 35 years since my BSME at Purdue, and I can still remember their names. God I hated those textbooks. If someone tells me that this Jackson book was worse, I won't believe it.
- senderista 2y ago
  What did you dislike? I went through all of HRW as an undergrad (25+ years ago) and recall generally liking the presentation.
fraserharris 2y ago
David J Griffiths' Introduction to Electrodynamics was a fantastic undergraduate-level E&M textbook https://en.wikipedia.org/wiki/Introduction_to_Electrodynamics https://en.wikipedia.org/wiki/Introduction_to_Electrodynamic...

lupire 2y ago

It really is a shame that in the 20th Century, the "best" math and science books were judged not for their educational power, but for how difficult and impressive they were to fellow professionals. It seems as though the professors were afraid that they'd lose their lecturer jobs if the books were too educational on their own.

jc6 2y ago
Subject matter experts are not experts in pedagogy. Because pedagogy is a seperate subject entirely. And teaching is not about getting people to say aha. Thats just performance or entertainment. Seen everywhere these days thanks to the Attention Econnomy. You can gets ahas out of people playing great music. But dont equate that with getting people to play great music. Cuz that requires getting people to do lot of mundane mindless work for long long periods of time.
- archgoon 2y ago
  > And teaching is not about getting people to say aha. Thats just performance or entertainment. Thank you. Reading the article will not in fact give you an easier time at the Jackson Problem sets. I think many people who think this would have helped them back in the day have simply forgotten what the actual hard part of the degree was.
  - lupire 2y ago
    Are you sure the hard part is the most important part?
    - kaashif 2y ago
      Yes. There's a difference between thinking you understand something and having to prove it via problems. Often that's how I discover I didn't really understand something at all.
- esafak 2y ago
  What does "aha" mean to you? To me it means understanding. And isn't that the point of teaching?
  - varjag 2y ago
    I can explain memory pointers to a layperson in terms of numbered boxes and yellow notes. They're still long long way to go from that even to reversing a single linked list successfully.
- pezezin 2y ago
  A few years ago, I tried teaching for a couple years. Something that struck me was that to teach at the elementary or high school level you need specific degrees, but to teach at a university you don't. There is this thinking that because you have a PhD you can teach, which is very far from the truth. Being a good communicator is a skill in itself.
  - vkou 2y ago
    > Something that struck me was that to teach at the elementary or high school level you need specific degrees, but to teach at a university you don't So, the thing about elementary and high school is that everyone goes to it, but only people who are good at studying go to university. Given that the students are highly selected in the latter, you can get away with much worse instruction.
    - denton-scratch 2y ago
      > only people who are good at studying go to university. I think this is arse over elbow; the purpose of an undergraduate degree course is to teach you to study and do research. The "research" done by undergraduates isn't novel research; the student repeats "research" that has been done by generations of students before them. I.e., it's practice. For this reason, writing undergraduate essays felt to me like being an impostor; you try to write in the manner of a researcher, knowing that you're faking it.
  - cess11 2y ago
    Where I live you study pedagogy and practice it while doing your PhD. If you suck at it you can still pass, but at least they take a shot at teaching it to you. When applying for positions your record on teaching might make it harder to get to those where you're expected to do it regularly. The usual nepotism, corruption and fraud in academia will of course allow some bad teachers to advance anyway.
    - pezezin 2y ago
      That sounds good, wish more places did like that.
physicsguy 2y ago
I don’t think this is true at all… Jackson is a good book not because it’s an easy introduction to EM but because it exposes you to more complex problems than would typically be looked at in undergraduate courses. There’s clearly a place for advanced texts for this reason.

photon_lines 2y ago

Thanks a lot man - I'm really happy to have this kind of feedback. The reason I wrote this is because I found most of the modern explanations lacking in intuition behind the equations - along with also not explaining what the actual equations meant. If you found this useful please share and subscribe - I'm also trying to provide intuitive guides to other concepts (Schrodinger's equation, Black Holes, Quantum Mechanics, other complex topics) and eventually I'm hoping to write books on some of these topics which present math and physics in a much more clear and intuitive manner. Math shouldn't be hard to grasp. At the very bottom level it's very simple but presenting it in a clear and intuitive manner I will admit is very hard. Also full credit to a lot of the material as well goes to Grant Sanderson (3Blue1Brown) and most of the diagrams there were generated using Vexlio which I also highly promote: https://vexlio.com/ https://vexlio.com/

WalterBright 2y ago
This is a really good article. A minor nit - it'll read easier without the exclamation points after every sentence.
wayoverthecloud 2y ago
You explain concepts really well. Wish I had professors like you in college.
cgh 2y ago
Also check out the YouTube videos of eigenchris, especially his series on tensor calculus and relativity. Probably the clearest explanations I’ve seen on these subjects.
deleted 2y ago
[deleted]
robertbarbe 2y ago
Thanks @photon_lines! In your temperature diagram, you mention that every point will take the average of the neighboring points. However, the equation is not a constraint on the temperature but on the "change of the slope (or gradient) of the temperature". The bigger the slope (in space), the faster (in time) the temperature changes at that point!

archgoon 2y ago

The basic ideas, the pictures, the diagrams, etc, found here, typically show up in enough books if you look for them that I don't feel that this was the main limiting factor in my physics education. The difficulty of Jackson (which doesn't show up until grad school for most students) is in the problem sets, not the ideas behind the equations (which most students have a had at least two courses in already). I don't believe that having a more 'intuitive' idea of the equations really helps all that much, as the intuition needed for solving the problems isn't really physical, but mathematical. Which integrals are solvable, which order of integration will make this tractable, do I need to use properties of Bessel functions here, etc. We can argue whether getting good at this sort of thing is actually useful for physicists, but I wouldn't know. Very few of us ended up becoming researchers in the field.

angra_mainyu 2y ago
Jackson's the standard here in Spain (undergrad), after working through a course based off of Griffith's.

abdullahkhalids 2y ago

I am confused. 1. While the posted guide is excellently written, it's not particularly novel. I was taught EM in a very similar fashion. Diagrams similar to those in the guide were drawn on the board by my professors. 2. Jackson is a graduate EM text. It is mathematically difficult, because when you read it, you should have been familiar with EM and all this conceptual underpinning for at least 3-4 years. The goal of Jackson is to solve the equations for scenarios that undergrads would find challenging. What did you study in your undergrad?

kjellsbells 2y ago
Re #2: Jackson was the standard text for undergrads like me doing a Mathematics degree. It was a late second year or early third (final) year text if I recall rightly. This was 1992, so I'm still amazed to read that its still a commonly used text. Fwiw, other standard texts used in Durham (UK) back then were Spivak on Calculus, Goldstein on mechanics, and for the mathematical physics kids, landau and lifschitz on mechanics and electromagnetism, and (an absolute doorstop) Misner, Wheeler and Thorne on Gravitation (relativity).
- abdullahkhalids 2y ago
  From the first preface (1962) of Jackson > Typically, the undergrad program in electricity and magnetism involves two or perhaps three semesters beyond elementary physics.... As a general rule, a two-semester course in electromagnetic theory is given to beginning graduate students. It is for such a course that my book is designed. So, your professors did you injustice by using an inappropriate book. Spivak, Goldstein and MWT are undergraduate books and appropriate. Landau and Lifschitz is great and accessible to smart undergraduates, but I don't see why you would use it for mathematical physics. Sure, Landau emphasized methods a lot, but there are better books for it.
  - macbr 2y ago
    As someone studying Physics (Bachelor) in Germany Jackson is what my electrodynamics professor recommended. My professor greatly shortened the chapter maxwell in matter and opted to give an intro into quantum electrodynamics instead. At my uni it's a fourth semester course with theoretical mechanics (second semester) and quantum mechanics (third semester) preceeding it.

wglb 2y ago

We used the John Kraus book on Electromagnetics for the dynamic fields course. This was preceded by a course on static fields. That course’s final had the shortest test statement I had ever encountered: “Derive Maxwell’s Equations”. I found the Kraus book satisfactory.

richk449 2y ago
What was an acceptable answer to “derive maxwells equations”?
- hxriv 2y ago
  [flagged]
- wglb 2y ago
  Show the steps such as faraday’s law and other things that led up to it.
- wrycoder 2y ago
  Maxwell's equations are statements of experimental results in differential form, plus Maxwell's guess that there are no magnetic monopoles and that there is a displacement current to carry current through a capacitor, providing continuity. You don't really derive them (unless the professor had in mind, "Produce them from the integral forms"). A better question would be, "Derive the EM wave equation in free space from Maxwell's equation and determine the phase velocity."
  - wglb 2y ago
    > Produce them from the integral forms Pretty much what he was looking for. Keep in mind that this was at the end of a course covering pretty much all of static fields. And this course was a precursor and prerequisite for the following course which was about the application and implications of Maxwell's equations. The latter was taught by my favorite professor, who seemed to have a radar to know when the class was not following. Without request, he would erase what he had written on the board and restart. The lab was fun. Three quarters of the way through the first 2-hour lab, he said "By the way, anyone who gets the right answer loses points on this exercise. The point is to teach you how hard it is to come to the right answer." He told a story of his work during WW II. His favorite thing then was to build a little $50 piece of equipment to render million-dollar radar sets useless. Clearly his task was to help improve the radar set. "The odds are stacked in favor of the jammer." Who obviously cheer for the inverse of the distance to the fourth power.

lupire 2y ago

People often make comments like this, forgetting that want they are marvelling at was actually in the book they read or class they took the first, and then actual different is that they forgot, or they've had more time to stew on the material so it feels more familiar the second time through. Hence the adage that the best book on the subject is whatever book you read second. It seems so much more intuitive the second time through.

sanderjd 2y ago

Yeah reading this a couple decades out from my undergrad physics classes, my thought was "I remember learning all of this very painstakingly over multiple years and multiple different classes". But also, I'm not sure I would have grokked much in this article without having taken those classes already, with the benefit of lectures and graded homework and group study sessions and TAs answering questions and all that...

TheRealDunkirk 2y ago

At least it wasn't Halliday and Resnick. It's been 35 years since my BSME at Purdue, and I can still remember their names. God I hated those textbooks. If someone tells me that this Jackson book was worse, I won't believe it.

senderista 2y ago
What did you dislike? I went through all of HRW as an undergrad (25+ years ago) and recall generally liking the presentation.

fraserharris 2y ago

David J Griffiths' Introduction to Electrodynamics was a fantastic undergraduate-level E&M textbook https://en.wikipedia.org/wiki/Introduction_to_Electrodynamics https://en.wikipedia.org/wiki/Introduction_to_Electrodynamic...