I have to confess that I got it wrong, indeed: the right side of the equation is a Laplacian. But, rather than describing an average in temperature, it describes the divergence of the temperature field.
That section looks at three scenarios:
1. An electrically neutral straight wire with an electron current and a test charge near the wire moving in parallel to it at the same velocity as the electrons in the electron current, observed from an observer stationary with respect to the positive charges in the wire analyzed without taking into account relativity.
The analysis shows that there is no electrostatic force on the test charge because the wire is electrically neutral, but there is a magnetic force because the test charge is moving in the magnetic field caused by the electron current.
(Nit within a nit: the drawing for this shows the positive and negative charges in the wire separated with the positive charges quite a bit closer to the test charge. That would result in an electric field from the wire that would attract the test charge. Maybe insert a short note saying that the positive and negative charges in the wire are actually mixed together so that their electric fields cancel outside the wire?)
2. Same as #1 except the observer is stationary with respect to the test charge.
The observer now sees no electron current in the wire, but does see a current from the positive charges. But the magnetic field from that positive current should not exert a force on the test charge because magnetic fields only affect moving charges and the test charge is not moving in the observer's frame.
3. The Lorentz contraction is introduced, and #2 is re-analyzed taking that into account. That Lorentz contraction applied to the positive current manifests to the observer as an increased density of positive charges. There wire now appears to the observer to no longer be electrically neutral. It has a net positive charge and the resulting electric fields attracts the electron to the wire.
What's missing is circling back and looking at scenario #1 again but including the Lorentz contraction. In scenario #1 the observer sees the negative charges moving, so should see increased negative charge density due to the Lorentz contraction, and the wire should appear to them to have a net negative charge, which would try to repel the test charge.
#1 with Lorentz included then is a fight between the magnetic attraction and the electrostatic repulsion.
Assuming objective reality and so requiring the test charge to actually feel the same force no matter who is observing we can infer that if the electrostatic force toward the wire in #3 is F then the magnetic force toward the wire in #1 must be 2F, which when opposed by the -F electrostatic force from the Lorentz contraction of the negative charges in the wire gives a net force toward the wire of F.
This isn't quite right, there are field configurations where the magnetic field doesn't vanish in any reference frame. This is actually the typical case: consider, for instance, two point charges moving relative to one another.
The right takeaway from SR isn't that the magnetic field is fake and the electric field is real, it's that both magnetic and electric fields are frame-dependent and it's the electromagnetic field tensor that's the real physical object.
Deserves to be widely used to teach Maxwell's equations.
THANK YOU.
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."
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.
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?
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).
> 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.
At my uni it's a fourth semester course with theoretical mechanics (second semester) and quantum mechanics (third semester) preceeding it.
Not necessarily: undergraduate and pre-undergraduate education differs a lot between the UK and the US.
> It supplies two tracks through the subject. The first track ... is suitable for a one-semester course at the junior or senior level or in graduate school.
As you say, it picks out bits and pieces that an undergrad can understand.
Today, there are better GR books, so use those.
I will also agree with you that many professors don't teach well. I was a physics prof for a few years, and it is difficult to distill stuff well. Not everyone has the skill, passion and the job incentives to do it well. I was lucky enough to be graced with profs who did.
I am glad that you have the passion for this. I will say this though, that once you become a formal teacher (school/university), then it becomes clear to your that your responsibility is not complete until your students have the skills to use the concepts that you are teaching them. Skill here means being able to model actual physical systems and get both the behavior and numbers out. When teaching a course, you have limited contact time with students and students have limited total time to spend on the course. You have to balance teaching conceptual understanding and modelling skills in that time. That balance is extremely difficult to attain, the reasons for which will easily fill a small book.
You can go all in on concepts, and what happens is that within a few months students have completely blanked out on everything, because you need the mathematical framework and have solved difficult problems for things to stick in your brain long term. And conversely teaching only maths is terrible because no one knows and what and why.
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.
Often that's how I discover I didn't really understand something at all.
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.
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.
The usual nepotism, corruption and fraud in academia will of course allow some bad teachers to advance anyway.
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.
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...
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_(boo...