The Long Road to Maxwell’s Equations | Hacker News Reader

The Long Road to Maxwell’s Equations

spectrum.ieee.org

96 pointssohkamyung12 comments

To this day, I still think derivation of the speed of light in a vacuum from the Maxwell equations is one of the most elegant and beautiful things in Physics.

Not only that, but if you change the permittivity and permeability to that of any material, you get the speed of light in that material. And for all this to happen, you get the fact that light is an electromagnetic wave from Maxwell's equations.

Agreed. I went to college in the US and got a EE degree and along the way almost switched to Applied Physics because of a really awesome professor I had and during which the physics I was taking was making use of the EE courses I went through. I was introduced to Elctro-mag theory from a physics class that was again used in some of my EE classes. I still remember physics experiments of passing current through two conductors each placed on balanced aparatus and watching the repel and attract due to current direction.

I had (still have) a knack for math and science but I'm just so amazed by guys like Maxwell.

The one thing that strikes me over and over is how insightful guys like Maxwell were. At such a young age and time he was piecing together I guess what others living at the same time might call phenomenon. Same for Einstein and Tesla. I mean he literally devised the mathematical model that foretold what we would discover in the future. And some 20 years later, Hans Christian Ørsted obtained the first evidence of a link between electricity and magnetism is quite amazing to me.

I recall reading an article some time ago about Tesla and how it was described that Tesla literally envisioned and saw AC current and then struggled to write it all down. I write software and I can see a similar pattern in myself. I often know and see, in my head, how something should work is so hard to explain. Of course at a much more basic level than these guys. It's as if Maxwell just saw and imagine how things were connected.

I keep waiting for the link that adds gravity to the mix.

Very nice article.

I really enjoyed this book on the discovery and definition of electromagnetism.

Faraday, Maxwell, and the Electromagnetic Field: How Two Men Revolutionized Physics (http://www.amazon.com/Faraday-Maxwell-Electromagnetic-Field-...)

When I read these stories, it always amazes me how the ordinary terms we use everyday are simply the names of the people who discovered them. That and how difficult it was to make discoveries back then when even the math wasn't fully formed. Today we just ask Google for anything we don't know.

when even the math wasn't fully formed

You'd be surprised by how much of today's used mathematics is actually "old". I mean most of it (even the mathematics of electromagnetism) hasn't changed since the 19th century and before, we are using the same theorems they used at the time.

It depends on what you mean by fully formed. For example the idea of vectors and quaternions, which seem so natural, is quite new (~250 years old) [1]

When maxwell derived and unified electromagnetic theory, he didn't use constructs like the gradient and divergence of vector fields (those concepts didn't exist), instead performing those operations 'just' partial derivatives [2]. Sure, the math is explicitly identical, but the modern concepts of operators on vector fields that is so powerful just didn't exist which, to me, is rather telling about the evolution mathematical thinking: we are all doing the same thing (and have been for a long time) but way we think about it evolves with our notation. And notation that we are used to is actually quite new

[1] https://www.math.ucdavis.edu/~temple/MAT21D/SUPPLEMENTARY-AR...

[2] http://rstl.royalsocietypublishing.org/content/155/459.full....

Languages are so weird when deconstructed. My observation is that English in particular seems to have a big lead on eponyms.

What a coincidence, earlier today we studied these equations in class, only we used different names:

Maxwell-Faraday equation.

Maxwell-Gauss equation.

Maxwell-flux equation.

Maxwell-Ampère equation.

Interesting! Are you studying in the US? I went to high school and university in the States and never learned individual names for those equations.

But now you say this it's kind of odd -- we have Ohm's law (and pythagoras' theorem and the Riemann function etc). What's different about these four?

(and it seems the name "Maxwell's Flux Equation" would really be simply the description of that one rather than a name).

Are you studying in the US?

No, Tunisia, 2nd year of CPGE (Maths/Physics), French curriculum.

What's different about these four?

It's just the names, what matters is the equations themselves I believe, the names only reflect their history (except for that third one indeed, it seems like a description but that's the actual name used[0] )

0.http://fr.wikiversity.org/wiki/%C3%89lectromagn%C3%A9tisme_d...

I thought it was interesting that they felt the need to briefly explain "del".

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