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Intuitive Guide to Maxwell's Equations

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Re: Intuitive Guide to Maxwell's Equations

#81

Post by SilasX »

ghaff wrote: post #7
chronolitus wrote: post #3

These kinds of visual, well thought out explanations of topics which are often taught with terse, obscure and uninviting methods are a gift. On a tangent: I remember asking my Calculus 101 professor what the "intuitive meaning" of divergence and curl was, outside of the formal math and equations. He was shocked that one could ask to sully these perfect mathematical concepts with dirty intuitive reductions. A guide li…

Wikipedia is probably the most obvious modern exemplar of this. The editors of most mathematics articles clearly are much fonder of playing with the equations editor than they are of actually explaining things.

lol agreed. Every Wikipedia article about math is:

is a that a 's . It is an example of a that cannot a .

Me: I learned nothing from that.

(Yes, which is partly my fault, but it's really not helpful for an intro to any math topic unless you already have mastered 99% of the topic and just want to resolve the last few things. The encyclopedia model really goes against what you need for the general population here. Arbital tried to do a more helpful model here but is defunct; Khan Academy is a generally better for this but requires more investment.)

Re: Intuitive Guide to Maxwell's Equations

#82

Post by ddxxdd »

devalgo wrote: post #74
ArubaJamaica wrote: post #56

Earlier quoted context omitted.

This statement is misguided. A lot of physical phenomena doesn't lend itself to intuitive understanding. Quantum Mechanics is a great example of this. You cannot expect subatomic particles to behave the same way that macroscopic objects do (and macroscopic behavior is what humans find intuitive because we experience it on a day to day basis). Its the same misguided thinking that leads to the popular PopSci explanatio…

Isn't this just a misunderstanding of what we mean by intuitive? It's possible to have an intuitive understanding of a thing that's not "intuitive" to humans.

Exactly. Just imagine the quantum world as a bunch of liquids floating around carrying their associated particles, and you have an intuitive grasp of (the debroglie bohm interpretation of) quantum physics.

Re: Intuitive Guide to Maxwell's Equations

#83

Post by Rayhem »

Aardwolf wrote: post #25

I'd be interested in an intuitive explanation of the units of electromagnetic quantities. E.g. the unit of magnetic flux is equivalent to volt times seconds, and inductance is volt times seconds per ampere. But I can't find intuitive explanations for this

This is phenomenally interesting to me because that very question led me to understand a lot more about the nature of units themselves. In particular, EM practitioners often use "Gaussian units" that name the math much cleaner (factors of 4pi appear and then disappear, instead of carrying around ε0 everywhere), but they have the weird side effect of perverting SI units. For example, in Gaussian units the standard unit of charge, the statcoulomb, has dimensions involving length to the 1/2 power. I think that has rather interesting implications on the nature of length; it seemd to me that the dimensions we take for granted might not be as fundamental as we think.

Re: Intuitive Guide to Maxwell's Equations

#84

Post by Daub »

reikonomusha wrote: post #16
Daub wrote: post #6

James Clark Maxwell is one of the Demi-gods of Colour science. He produced the first Colour photograph, and was the first to quantify Colour. Every time you define an RGB value, he is sitting on your shoulder.

Small nit, it’s “Clerk” not “Clark”.

Well spotted. Thanks.

Re: Intuitive Guide to Maxwell's Equations

#85

Post by mikez302 »

athinggoingon wrote: post #59
ghaff wrote: post #7

Earlier quoted context omitted.

Wikipedia is probably the most obvious modern exemplar of this. The editors of most mathematics articles clearly are much fonder of playing with the equations editor than they are of actually explaining things.

I wish there was an "intuition" wiki where you can learn the intuition first and then a link at the bottom takes you back to the Wikipedia page where you can stare at the math until you really get it.

I am not aware of such a thing. But this is arguably the closest thing I could find: https://betterexplained.com/

Re: Intuitive Guide to Maxwell's Equations

#86

Post by peter_d_sherman »

>"The Greeks were the originators of this conception. They imagined that 'things' were built out of smaller things, like atoms and molecules. When the atomic theory came about, they expected the atoms themselves to have some sort of mass, shape and size, and to be a microcosm of more things. Let's take sand as an example. To the careless eye, sand seems like a fluid, since quantities of it appear to freely merge and split, but on closer inspection, it's just a bunch of tiny objects which can be described as individual `things' interacting with each other.

The world of quantum mechanics and quantum field theory introduce a different conception of what things are though. It turns out that elementary particles can't be thought of as individual 'things' which have a volume.

In fact, if atoms did have a volume, physics wouldn't work.

We would end up with "surfaces" of electrons behaving in an impossible manner and spinning faster than the speed of light.

Well then, you say, what if atoms aren't objects with a volume, but points in space? It turns out that this notion isn't easily prone to interpretation either! No one actually knows or understands what a 'point mass' is! It also has a bizarre implication: if indeed we did have volume-less point masses, we obtain something with an infinite density!

In theory, the entire universe could be squeezed to a single point!"

Re: Intuitive Guide to Maxwell's Equations

#87

Post by jabl »

tobinfricke wrote: post #35
OscarCunningham wrote: post #12

Earlier quoted context omitted.

You can even write them in terms of the four-vector A rather than F (related by F = dA) to reduce them to d dA = J.

Discovering that the Maxwell equations can be written in this succinct form is kind of mind-blowing, but I'm wondering whether it provides any additional insight? It seems like one needs to do a significant "unpacking" to actually use the equation or gain insight from it. I would love to hear an explanation of electrodynamics starting with "star ddA = J".

Yes, I kinda agree. The underlying physics is, by definition, the same, and what you gain by reducing the number of equations you lose by having more complicated "objects" and needing more advanced maths to handle them (e.g. the electromagnetic field tensor, external calculus and whatnot vs. just vector fields and basic vector calculus).

To get an intuition of the physics, I think the traditional 4 equation form is actually more useful, as you can construct toy examples and study the equations one at a time in isolation.

Where the more advanced formulations are useful, and actually are used, is for stuff like relativistic physics where 4-vectors, curved spacetime etc. are needed and not just a gimmick.

But for more down-to-earth applications of electrodynamics like antennas, field propagation in various forms of matter etc., the classical version is fine.

Re: Intuitive Guide to Maxwell's Equations

#88

Post by C4stor »

uoaei wrote: post #40
C4stor wrote: post #28

Earlier quoted context omitted.

Well, it's not Wikipedia's fault if people producing intuitive content are not contributing to it. It's not like editors go out of their way to remove nice explanations.

There are many anecdotal reports of tyrannical Wikipedia editors doing exactly this. They claim dominion over a subset of Wikipedia articles and then manicure them exactly to their own personal tastes. I'm sure the situation you describe happens often in various corners of the website.

Well, I've personally contributed to small parts, and never encountered the problem. I don't doubt there are jerks on Wikipedia, but I would also bet that neither the author of this nice github repo or the praised youtuber mentioned in the comments even tried to commit anything into it.

Not that they should for some reason, but too often editing wikipedia is presented/thought of as something reserved to a happy few with deep social consequences, when it's in fact the simplest thing in the world.

Re: Intuitive Guide to Maxwell's Equations

#89

Post by mikorym »

I didn't have 1st year physics, so this was very informative for me.

Maxwell 1 + 2: Field per surface area. The asymmetry between magnetic fields and electrical fields is that magnetic ones have a total field of zero; that is, al magnetic lines loop back on themselves.

Maxwell 3: The principle behind power generating turbines.

Maxwell 4: The principle behind electrical motors.

To be honest, I didn't even know you can condense it into four equations. I was only exposed to the history of electromagnetism, not the latest expression thereof.

Re: Intuitive Guide to Maxwell's Equations

#90

Post by chongli »

SilasX wrote: post #81
ghaff wrote: post #7

Earlier quoted context omitted.

Wikipedia is probably the most obvious modern exemplar of this. The editors of most mathematics articles clearly are much fonder of playing with the equations editor than they are of actually explaining things.

lol agreed. Every Wikipedia article about math is: is a that a 's . It is an example of a that cannot a . Me: I learned nothing from that. (Yes, which is partly my fault, but it's really not helpful for an intro to any math topic unless you already have mastered 99% of the topic and just want to resolve the last few things. The encyclopedia model really goes against what you need for the general population here. Arbi…

The problem is that math is inherently more abstract than any other topic. It’s so abstract that the vast majority of math terms have no simple, intuitive translation into everyday English. Everything is built upon a tower of abstractions that have developed over centuries.

In this community, we’ve witnessed the difficultly first-hand with the much-maligned monad tutorials. A mathematician would have no trouble understanding monads —- they’re just a matter of reading the definition and the laws. That’s what you do every day when you’re studying math in university. Read some definitions and some theorems, play with things a bit, try to prove stuff, then move on to the next topic.

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