Maxwell's Equations Explained: Supplement to the History of Maxwell's Eq.

I start with the basics (vectors, dot & cross product) and then give an overview of where all 4 Maxwell's equations came from, what they mean, and why they are important!

To read the script (with citations) and download the pdf of first 3 chapters of "Lightning Tamers" please visit:

order my book:

A few extra links:

Sand Castle of William Rowan Hamilton and Helen Hamilton carving quaternions on a bridge by Daniel Doyle 2002. Used with permission. Check it out!

0:00 Introduction
0:38 Vectors & Vector Multiplication
5:02 Del, Divergence and Gauss's Laws
13:25 Maxwell's Equations with Curl
25:35 Maxwell's Equations and Magnets
27:14 Maxwell's Equations and Light

[Micetticat]

I'm a seasoned electrical engineer, and during my studies I've seen the Maxwell equations in a lot of courses. First in high school, then in the physics course on electromagnetism, then in a dedicated course on antennas and radio wave propagation, then in a course on lasers, then in fundamentals of quantum mechanics and in many other courses. This is the best lecure about he topic that I have ever seen!

[cluelessinky]

My regret is that at 74 years of age I am now finding these wonderful lectures from an enthusiastic, vibrant and delightful teacher . Would I were 20 again.

tThank you Kathy.

[Raphael_NYC]

Kathy takes all the tension away from learning physics and math in a way I have never ever seen before. Showing us why and helping understand how Maxwell's equations came to be, all with an honest love of the subject matter sounds impossible but that is what Kathy does. It is an amazing gift. Thank you.

[thomasmerritt]

Fabulous presentation of Maxwell's equations. It brought back memories of deriving them from first principles as an electrical engineering major 40 years ago. I particularly liked how you included images from his papers that do not use vector notation.

[erikziak]

This is by far the best explanation of this that I have ever seen. You managed to get so much into only 34 minutes, I am truly amazed. Especially how you linked all the discoveries.

[juanantoniocarrascomojica]

I am a recently retired electrical engineer and I would like to say that this is on of the best explanations on the subjet I have ever seen.
My congratulations from Spain for your excellent work on your YouTube channel.
By the way, I'm looking forward to reading your book "The Lightning Tamers" which will no doubt be just as fascinating as the videos.

[randyshoquist]

That was excellent. I wish this had been available when I was studying this stuff 45 years ago. I knew several bits and pieces, and you've assembled them into a consistent story, which triggers more insights. I can re-watch this several times, and pick up a little more each time. Wouldn't it be fun to bring these fellows back in a time machine (especially Hertz, who foresaw no practical uses) and show them what we do with their discoveries today.

[cakgun]

I have a Ph.D in EE. My specialty is Telecommunication. I am retired now. Of course, I took grduate courses in EM and antenna theories in one of the good EE Deparment in the US (Polytechnic/NYU). I did not have a textbook that went into the background of these 4 equations, and the professors who lectured in this subject to teach as simplified as Kathy did. It was always bogged down with heavy math without touching the Physical aspects of the phenomena. Students are forced to memorize them even in fine instutions without capturing the essence of them. I do not know your background, Kathy. I wish I had someone like you then to simplify that genius work.

[keyurjoshi]

Wonderfully explained! Studied these equation in first year physics during under graduation and always had these unsettling feeling of not grasping them fully. Over a period of time, have tried to understand from different literatures and physics videos like this in leisure, but so far have found it just mathematical jugglery. This is the first video that I could relate to and ties everything that I know about magnetism and electricity seamlessly. Thank you very much!

[lcmiguezYT]

Your vision of showing the history of each one of the ideas that finally were mature enough to bring Maxwell to write them with math equations is really brilliant and very powerful to give us a better understanding of this subject. Congratulations for your work. All of these famous developers would be proud of you. From Brazil, a great hug!! Miguez

[GoCoyote]

Your enthusiasm is infectious! While I enjoy math, I am not very gifted or fast at it. Most of the math in my electrical apprenticeship was above my full understanding, but I found that treating it like a language really helped. I have forgotten most of it, but so much enjoy your putting together the historical development of the people and the math that have given us so much in our ability to understand our world.

[willisfouts]

I must say, you really know how to keep a viewer’s interest in a subject, Miss Kathy.
Great job on your latest effort. Thanks so much.

[SocratesAlexander]

Your videos always make me want to learn more, even when I think I know the subject well.

[mingshey]

I have bought your book by preorder and a few minutes ago it is delivered to me! Live long and prosper, ma’am!

[dougieh]

Thank you for the wonderful content. I’m 57 and still enjoy learning. Your videos are accurate and not dumbed down. You keep me thinking. Thanks again.

[CheeseAlarm]

I studied physics 40 years ago at King's College London, Maxwell's Alma mater. I remember having such a hard time of it with vector analysis. That green Schaum textbook haunts my memories. I never really understood it - I just memorised it all. No such thing as YouTube and teachers like Kathy and 3blue1brown. I'm really enjoying this series.

[buidelrat]

I've seen many videos on vector multiplication and the divergence and curl operations, but yours finally made it "click." Thanks for being such a good teacher, Kathy.

[TheMemesofDestruction]

Your balance of the history behind and not, “dumbing down, ” the maths is beautifully unique! Thank you.

[billcook]

I know you’ve done at least one video on the class and background differences between Faraday and Maxwell, and the general resistance of the aristocratic scientists of the day to properly credit Faraday. So it was nice to see Hertz fully crediting “Faraday-Maxwell” in that paper. Yeah, the science is always cool. But sometimes the personal stories behind the science are equally interesting.

[nashaut]

This thing remained sort of a mystery to me for about three decades. Now I believe I've seen the light.

Thank.
You.