History of Maxwell's Equations #1: Gauss' Law
Вставка
- Опубліковано 6 чер 2024
- The experiments, theories and math behind Maxwell's Equations. From Charles Coulomb in 1780s to Michael Faraday in 1837 to Maxwell in 1855, 1861, and 1864 and how they led to Gauss' Law.
To read the script (with citations) and download the pdf of first 3 chapters of "Lightning Tamers" please visit:
www.KathyLovesPhysics.com
Pre-order my book:
amzn.to/3I7N4mq
Patreon: www.patreon.com/user?u=15291200
A few extra links:
Woman in Faraday Cage (very good BTW): • Prelude To Power: 1931...
Feynman Lectures: www.feynmanlectures.caltech.edu/
0:00 Feynman Lectures
3:30 Coulomb (1784-86)
7:15 Faraday (1837)
15:44 Maxwell's "On Faraday's Lines of Force" (1855-6)
23:42 Maxwell's "On Physical Lines of Force" (1861-2)
30:00 Maxwell's "electric elasticity" (1864) vs. Heaviside's permittivity (1880s)
This woman is a total unicorn.
She understands history, she understands mathematics, she understands the science, she reveals the true scientific process, and she’s able to teach it.
you don’t need many people like this to absolutely change the world and my God she’s doing it basically for free
Thank you.
Incredible.
Why thank you that was lovely 😊
Agree. The channel gives new meaning and credibility to "I learned it on the internet".
This channel is full of gems that I would love to tell my students in order to get them motivated.
She is a national treasure!!! Not many like her in the world!
@@julian65886 international*
Having done my honours degree at Edinburgh University 1991 995 and studied in the JCBM (James Clerk Maxwell building) and covered electromagnetism as part of my engineering degree , I was never happy with my comprehension of electric voltage ( potential difference). Years later I went back to source and read the same papers you are quoting and had my eureka moments. It still remains sad to me that coming from the home of JCM I had to figure all this out by myself years later. I reckon I'm probably the only one in a class of 100 students who ever did this ? I always intended to explain Maxwells ele tromagnetics in the way Maxwell first formulated it as it is brilliantly 'simple'. Glad to see that you have done this so well. Thank you.
I had a similar epiphany contemplating why the neutral wire did not electrocute me while installing an outlet. I thought how could charge flow through this circuit if the neutral doesn’t carry a charge. Took a while but bam…… a clear understanding of what a potential is became clear. Mind you, when this occurred I already had a masters degree in chemistry, was an engineer in the semiconductor industry, etc. Impressive how the fundamentals do not get comprehended through all that schooling.
Chemical engineer here. You pick the subject (thermo, almost all the math, etc.) and the professors never taught the historical context, for good reasons I suppose. EM was never my subject at all! I took the standard one-year physics sequence plus two quarters of EE [plus undergrad electrodynamics several years ago (PHYS 330 Griffiths, 4th ed.)]. A lot of it went over my head (OK, so I'm not the sharpest pencil - LOL). I am learning so much from Kathy's lectures. It's starting to make sense... at age 62!
@@rightousray2 - - - - Depressing how the fundamentals do not get comprehended - - - - -
Hi Kathy,
I am an EE.
I have never seen this concise and accurate history ever presented by anyone.
Thanks!
Heaviside is the only reason we understand Maxwell now - before Heaviside, there were 20-21 equations with as many unknowns. Heaviside reformulated these into the 4 recognized equations we use today.
Heaviside was treated very unfairly, and from my recollection, this was due to his Operational Calculus. His response to their accusation that he didn't prove, mathematically rigorously, that this method worked, was along the lines of: "Just because I don't know understand how my body digests my breakfast, doesn't mean I shouldn't eat it.". BTW - it works. His efforts, along with Charles Proteus Steinmetz (almost not allowed into the USA b/c of his dwarfism), are the sole reason electricity is engineerable.
Heaviside eventually go so fed up with the criticism from the British establishment, that he stopped writing. He did something like painted his fingernails and removed all the furniture from his house, and gave up...
Vector calculus was born embedded deep in Hamilton’s quaternions, and Maxwell was so excellent a mathematician that he could express novel physical and geometrical intuitions using them. Heaviside and Gibbs then crystallized vector divergence and curl, etc. as the practical, useful concepts within quaternions. When Heaviside showed that del could be an operator, quaternions began to shuffle off the stage.
Feynman's lectures are great for people who already know physics. Seeing it for the first time? Depends on the student.
One really important part of this history is the complementarity of Maxwell and Faraday. Both were geniuses but in their own ways. Faraday was a genius of experimentation and Maxwell of theory. These two were the perfect compliment of each other.
And Joseph Henry?
Faraday was unfortunately from a poor family and lacked the mathematical knowledge Maxwell had
@@johnfitzgerald8879 😊❤😂❤a😅
My wife gave the three-volume set to me for Christmas several years ago. She gave me "Feynman's Tips on Physics" a couple of Christmases later. They are my most cherished Physics books, even more than all my textbooks.
You are the person who makes history an interesting subject because other historians focus more on politics and wars, but you focus more on physics. ❤
I appreciate this video. I am writing this note from the steps of maxwells home in Aberdeen Scotland at 129 union street in Aberdeen Scotland ..as a coincidence!
You are phenomenal Kathy, the research you put into your work is astounding. Thanks for putting this all together and presenting it in a fun and comprehendible way.
Have you seen her regular website? She has all the scripts with citations there. It is also astounding.
I am an electrical engineer so of course I studied electrodynamics and Maxwell's equations. The video was very detailed and and exact. The graphics were very helpful. But I found that the discussions and derivations went by a bit too quickly. This is a subject that really needs a slower step by step derivation plus seeing and deriving it by writing the equations. But I know that you really don't want to stretch this out into too many videos so I understand why you went at the pace you did.
For me as a young undergrad, the epiphany was realizing that based on these equations the speed of light through a vacuum is a function of mu-zero and epsilon-zero ie physical constants based on static measurements!!! A group of us made T Shirts with Maxwell's Equations with the words "Let there be light!" a the bottom!
I understand what you mean, and I am going to go through the math in much more detail in the next video because I wanted to focus more on the concepts in this video and I felt like that if I went into much detail in the concepts and in the math in one video I would lose a lot of people. Sorry if you found that frustrating.
@@Kathy_Loves_Physics I'm looking forward to watching this.
I agree especially being a non native English speaker
@@Kathy_Loves_Physics I am a biochemist, but I love to learn about physics. I just want to say that your videos are amazing! I thoroughly enjoy learning about the history of breakthrough scientific advancements. You do a great job summarizing and explaining the context behind these important equations. Thanks so much!
@@frankdimeglio8216 - What you just wrote is gibberish, no offense. There are some good online introductions to physics, I think you could benefit from reading them.
Whasnt Farady and spectacular mind. Such insgight. I love your direct delivery. No circumlocution or repetition. Very clear and focused.
Never before have I had such dry equations be brought to life with such nail-biting drama and cliff-hanging excitement. Thanks so much for this!
Hey, you don't need a REASON to mention Feynman - it's always a good thing. The man is a top hero of mine.
I bet the comment section is all STEM professionals. I’m Petroleum and I can’t thank Kathy enough. Your presentation is addictive. Thank you!
Round 2: I am watching this video again. It is an amazing synthesis of the why and how Maxwell came to his equations. Keep going Kathy. You have a very special gift in the way your explain physics. Thank you,.
Thanks again!
This is great - I just taught an intro class in E&M and leaned in a bit on the historical aspects, but there are many here I was not aware of! Great work here.
Thank you for bringing O. Heavyside into discussion of Maxwell's Equations.
It's a good introduction to a long tradition in physics, taking someone else's brilliant idea, and turning it into brilliant math. Minkowski is another classic example. I've heard Einstein quited as saying that by the time Minkowski got done with it, he barely understood his own theory.
I read somewhere (I don't recall where) that Maxwell didn't right or saw the "Maxwell Equations". It was four of his twenty propositions that were deemed as such and a result of the efforts of Hertz and Heaviside. Since the formulations were still in a primitive form they were set in stone before the formulations could develop into a mature into electrical theory.
@@Nojack71 3 of them are other people's ideas. He completed the set and figured out how they work together.
Fascinating to this old physicist. It seems I have used the equations for 40 years without knowing their real origins.
It is an absolute necessity to go through the history to understand the development, if included in syllabus it will really put colours in the repulsive textbooks, we all have gone through hours of memorization before truly convincing ourselves through understanding, that process might be more forgiving and seeing the leaders of the fields to fumble and try and fail might give courage.
Another masterpiece, thank you.
My sentiments entirely.
true but thats why IQ is required in scientific fields : if you're in an environment where no one knows how to justify concepts with logical historical reasons, you need to be able to understand the pattern through sheer logic and brain power. A lot of the math language is arbitrary and I dont think science education will solve that anytime soon.
Ever heard of pick lock boy ? If you know Science like we all should his name should leap to your mind.
I would so love to make that man a coffee.
Kathy, I have said it before but I can't say it enough; thank you a million times for all the wonderful videos you produce and all the time and energy you put into your work. Everyone enjoys your channel and it is so needed. As you say science needs context and you are filling that void. God thank you sooo much.
Thank you Ross. That was lovely.
@@Kathy_Loves_Physics Please do a video on Oliver Heaviside , he deserves your careful attention, slowly his name is becoming more prominent, in particular his use of the Heaviside step, and its relationship to the Laplace transformation and Fourier transformation. Thank you for all your contributions
Yes I agree with what Ross says!!!
Her new video is her best ever! It was just posted for Patrions. The rest of us will see it very shortly.
Crazy, my home tutor was just telling me about it. I'm gonna finish high school in a month (high school is 9th and 10th grade here) and he was just letting me know about some stuff I'm gonna learn in 11th and 12th grade starting from next month and this was the first thing he talked about. Basically, he went:
"At present, you know Coulomb's Law right? You can solve problems with it as well. But what if, I had a metal plate, which is obviously a conductor, and insert 4 positive charges into it? The same charges would repel each other so each charge would try to maintain the best distance it can from the other three within the allotted space inside the metal plate.
Now, what if I bring a point of negative charge near the plate? Of course, it will be attracted to the positive charge of the plate. But can you, at your level, measure the force it will be attracted with?"
I replied, "Well, I can measure the force for each positive charge according to their distance from the negative charge and then add up the vectors." But he said, "Good idea, but in reality the number of charges won't be 4, but in the millions. What will you do then?"
I could not answer. Then he said, "This is when Coulomb's Law stops working, and this is the point from where your new grade will start. This is the the point when physics has to advance, and we have to hand it over to the hands of a new boss. Do you know his name?"
"No, I don't think so."
"Gauss. Remember it, because when you'll understand Gauss' Law, you'll stop depending on good ol' Coulomb."
Then he proceeded to show me the equation and say some stuff about loop integrals that flew over my head but nevertheless, I was very excited to learn about it. It all just happened an hour ago too lol. What a coincidence that my favorite physics UA-camr would talk about it so soon! Thanks!
That is crazy! Are you feeling paranoid? (Maybe your tutor is a subscriber). Congrats on graduating high school and good luck with some pretty intense sounding upper high school (or whatever you call it).
Yup, although I don't think you will be taught the differential form though. The integral form is more commonly used where I live in highschool
Thank you for your excelleant work again on history of the Physics/Maths for important discoveries/inventions in these areas. Maxwell equations for fluid-dynamics/heat-transfer/electricity/magentism/etc are one of the least understood by majority of engineering students (as most of them are not exactly aware about the equations that are used in textbooks).
Your excellent series on these topics gives students/learners about how these equations are derived in first place and amounts R&D was being done in non-internet-era (with limited sources of information/equipments) and still those pioneer scientists have succeeded in their discoveries/inventions despite all odds in those times with so many iterations(that sometimes span over couple of years). It also reminds how lucky we are in this modern internet-era to get these information at finger-tips.
Wish you great success in your endeavours and your book sales.
Also I wish that most of the universities and colleges also teach the history/stories behind these discoveries/inventions (so that students/learners can understand better )
Thank you! I am on a mission to try to convince the colleges and universities to teach physics this way too. It is so profoundly useful in my opinion.
@@Kathy_Loves_Physics - It is! Studies have proven that the more context you can give for something, the easier it is to memorize. So, giving the history and the reasoning behind these important topics helps create more connections in the brain, making it easier to remember. Please keep it up! You are awesome!
Thank you Kathy! I am a high school Physics teacher and have longed for videos like this to give my students to understand the historical developments in Physics. Great videos!
After Newton and Einstein, Maxwell should be regarded as one of the greatest scientists. I really enjoyed your chronological history of Maxwell's equations that now a day are integral part of technology.
Possibly more important, as Maxwell was Eisenstein’s hero,
Hard to grade them in importance as each one produced thinking that became big stepping-stones in physics. Maxwell remained more obscure perhaps because his mathematics was the primary means of communication.
Maxwell was one of the brightest minds of the 19th century for sure. But, if first place has to go to someone, my choice is Gauss.
You can not compare apples and oranges. Scientific work is build over contribution of their predecessor. Every work is important. People get carried over who was the greatest scientist of all time and all the scrap. Just look at quantum mechanics, lots of people contributed towards the advancements and still we did understand it completely.
@@marspalk7611 Who said anything about apples or oranges? The 19th century has been over for a while. We can easily compare the contributions of its exponents in terms of the output, impact, innovation, etc. And let's not forget, one of the four Maxwell's Laws is known as Gauss's Law. So my statement is hardly controversial. In fact, it merely reflects what many have said about Gauss, that he is not only one of the brightest minds of the 19th century, but in the same league as as Newton and Archimedes.
Thank you Kathy for presenting this historic physics lesson. Very well done!
Kathy, you have done an outstanding job transporting our imagination back to 19th century and allowing our minds to grapple along with Maxwell the scientific questions about electricity as viewed through glimpses of primary publications and contemporaneous discourse. Viewers should not expect to learn Maxwell's equations from the lecture or use it as a substitute for a textbook. Instead the lecture delights, enriches, and deepens, our appreciation of the Maxwell equations. Feynman recommended that , and you have done a marvelous job taking up Feynman's challenge, which reflects truly your deep love for both physics & history. Well done!
Thank you Kathy for another wonderful video. As an EE grad (1981) we were taught Maxwell's equations. But digging in, and understanding them deeply were graduate courses. Your videos have brought me a much deeper understanding of them. It's great to see how they grew and changed over time and its much easier to see what they mean when seen from this historical context.
What a simpathy and pleasure in teaching physics. Wish you were a professor of Mine. Congratulations.
Well you did it again, you have blown me a way. I love the lucidity with which you present the subject.
Kathy has given us a wealth of knowledge worthy of any college course for FREE! A masterful job to say the least.
Thank you.
Great video Kathy! Am looking forward to the rest of this series!
Kathy, that is an amazing tour de force of scientific virtuosity. You have done all the heavy lifting. I sense much love in this. Love for the subject and love for the students. This is really great work!
Had to pause at 2:47. You are truly a gem Kathy. I have Feynman's lectures and consider them to be the best material there is. Throughout your videos, I know that you are the most suitable person to take this challenge of doing a series of videos and succeed. Best wishes, Erik. I wish I had a teacher like you. I had to find out all the beauty by myself years after "formal education" age. Anyway, I am humbly grateful and hope that your channel, your excellent videos, will be the source (among other) for people in their curious "young" years, to find here. I wish all this was available during my years of University, and I mean other channels on YT, not just yours. EDIT: I am grateful for understanding the English language, for having access to the Internet and living a care-free life in peace, freedom and prosperity in central Europe. I am pretty privileged, I know.
- One of the things that needs to be mentioned is that the differential equations are a condensed (shorthand) form of the integral equations. If one misses that fact, one might find the equations difficult to relate to real problems.
- I've heard people describe Maxwell's writing as equivalent to vector equations, but in a more awkward notation. I now see why that was said. I've never been told about Heavyside's contribution! This was a wonderful lecture.
Faraday and Maxwell, the experimentalist and the mathematician, bound together over their love of electricity, changed the world forever.
I really like the way this shows how the thinking evolved and, in particular, how the meaning of the equations and constants gradually became more closely linked to the phenomenon being modelled.
This was really good! I wish we had more of this historical motivation in my physics degree. Looking forward to future parts!
I’ve been waiting for a UA-cam video on the history of Maxwell’s equations. We are lacking the historical basic measurements driving most of physics. So much missing from physics textbooks.
Kathy, thank you for your video. Being an EE DSc, I cannot help being less than passionate about Maxwell's equations
Amazing! I'm very excited for this series!
I loved watching those lectures. His style of teaching was amazing, just like yours.
If only every lecturer had Kathy's articulate, charismatic and enthusiastic delivery, along with her brilliantly organised and researched unfolding of events, then physics would be more popular than reality TV.
Thank you Kathy!!
She was on TV today!
Not gonna lie. When I saw your slide listing the 5 parts, I got hopeful for a 5-video series on this. Excellent work!
Wonderful to see you back Ms. Kathy with a fascinating subject. Congrats on the 100k subs too.
Thank you kindly!
A brilliant exposition, but as a non-mathematician there was some heavy going and much scrolling back. How lucky we are to have someone who knows the subject inside out and can also express it so lucidly and with such enthusiasm.
Thank you so much for doing these videos. Most of us have studied these things from the theory side but it is so much fun and I think important to learn the history also and you do a great job presenting that.
Very nice. I look forward to the rest of this series! Heaviside is one of my intellectual heroes, so it is always exciting to see him get some credit for his work on Maxwell's equations 🙂
I have acquired a fondness for Faraday and Maxwell since we have initiated a TMS program (Transcranial magnetic stimulation). Your teaching has illuminated an amazing time. It is remarkable that these men just intuited these relationships. Keep it up!
Thank you Kathy, this was great, I enjoyed every minute of it. Really looking forward to the next one, Quaternions, Heaviside etc.
During world war 2 ships had to be de goused to prevent magnetic mines. they had coils of. wire around their hull.
Fascinating video again Kathy
Based on this video lecture, I purchased the kindle version of the book: "Lightning Tamers". This lecture was, to me, worth the purchase price of the book.
- ANOTHER FANTASTIC VIDEO - as always :)
- Having a formal education in electrical engineering, and being a self-taught math teacher (by nature/profession), and a lover of history, your subject matter, and presentation are richly appreciated.
- Now, as for quaternions, I've also been a 3D animator, where me initial exposure to quaternions arose (for rotations). And, I've heard that Maxwell's Equations were originally written in the form of quaternions - so, I was excited to get the details of exactly why/how... only to find I will have to wait for your next heroic effort! So, I await in giddy antici...pation :) ...
excellent video, anxious for the next of the serie :)
Congrats on getting to 100k! My wife and I love your videos! I studied physics in undergrad, but my professors never spent much time putting discoveries into context or explaining how many failed hypotheses are explored on the road to each great discovery. Your videos humanize the great scientists as well as the process of science, which makes a career in science seem much more attainable.
Anyways, thanks and congrats.
Thanks
@@Kathy_Loves_Physics - Hey Kathy, I have a quick question. Are you a physicist or do you work in the scientific field? Or is this purely a passion for you? Either way, you make great content, I am thankful you put out these videos.
I’m really enjoying your videos; I especially like the way you (for want of a better word) often “deconstruct” abstruse concepts and the degree to which you contextualize STEM subjects historically! Great stuff 👍
Honestly its how science should be taught in general. I know its not easy but giving historical background on the discoveries that lead to what we have will better help students to understand how things developed. Its first principles essentially.
thanks, I like the term "deconstruct"
Reading his actual text (26:33) cleared up my understanding of his displacement current. It is a transient! I had assumed it was a steady state current. Thank You for a GREAT video!!
What a wonderful video. I appreciate the energy and intelligence you bring to the table. Subscribed.
Can't wait to devour this series ... thanks a lot !!
I'm so looking forward to the next video already!!!
So glad i got this channel recommended
My grandmother was born in 1868. Just three years after the American Civil War. The war that Fiineman thought was insignificant compared to Maxwells equations. That hasn’t been all that long ago. Look at what has been discovered. My mother, her youngest daughter, told me she was offered a scholarship to the University of Arkansas. That just didn’t happen to women back then. Her father refused it. He didn’t think women needed an education. A lot has changed since then.
I will likely never get a tattoo, but if I do, 100% chance it will be Maxwell's equations. Beautiful timeless perfection. Celebrate genius and mental effort.
Thank you so much for this incredible video. it is so well thought out, clear and captures your attention from start to finish!
The torsion balance is really a marvellous invention. It's so simple, but yet precise enough to measure even the very weak gravitational constant (this was first done by Cavendish in 1798) and even the yet most precise measurement of the gravitational constant was done with a torsion balance.
Just started watching the video and I already love it!
Absolutly brilliant😀😀 I’m an economist with interest in innovation. The creative process that you describe have far reach beyond physics.
This was great because there's SO much to get our teeth into - (I actually don't have any teeth but that won't stop me trying) - There are questions I've always wanted to ask but never dared - and STILL daren't - even though I've seen other people ask the same question and get rather, err, unusual answers that sounded rather like they didn't know either but merely did their best to pacify the enquirer. Well this video, if I watch it a FEW times more, sounded like it probably contained the answer to our question, if only I can stay focused when it gets more involved. In the meantime I thank you for painting a really good picture of how all these discoveries came about - the nearest thing to being there. Thank you.
I'm pretty old now, but back in my twenties, it was a primary goal of mine to develop an appreciation of Maxwell's genius. Now I have a place to start. Thank you!
way back in the 70´s as a Physics teacher's assistant I came by I guess one of the first books compiling Feynman's lectures now I see there is a collection of them. I wish I had that chronological way of studying physic as you do in your outstanding lectures, would love to hear from you how did Lord Kelvin came up with his "thunderstorm" machine, same with mr wimshurt´s high tech contraptions even to our times
I have been a fan for a while! So I love all the videos. I love this one especially! So good to learn about the history of all this beatifull physics
Great video. I love how you explain everything.
Glad you liked it
Just wonderful Kathy!
Thanks
I think your videos are amazing. Thank you for what you do.
She is a treasure ! Thank you Kathy!
15 minutes in, I’ve already spent almost three hours within this video - thanks to rewinding mercilessly, pausing and reading nearly all the text attached to the video, the normal Internet rabbit hole tangents, and my favorite - cracking open my Ohanian Physics text from 1989! Incidentally, with not a little help from Kathy, the Ohanian makes considerably more sense now as to when I was 19. This channel is bad for my sleep hygiene.
Scripts and citations on her website also...
Your work is gold! Thank you
hey Kathy just stumbled upon this video and learned about your channel. God bless you, great work
Wow you done such an amazing job 👏 waiting for the next parts eagerly
It's amazing how Faraday thought of light related to electromagnetic lines of force.
Impressive video as always
Great job!
Thanks for sharing your content with all of us 🙂
I Can't wait for the next episode !!!
I fully support your deep-drive in E&M history. Go for it. Let's Go ! ! !
Kathy, I love your videos, they are so good!!!, you put all your heart to share this wonderful physic world. thanks so much for your work, you are absolutely AMAZING!!
This video was amazing. Keep up the good work!
Thanks.
Thank you. Another well researched and well presenrted video. We respect and appreciate you. You bring to life things that have confused me for years.
Thank you 😊 I am a little nervous/excited about this video in particular as it is a different style for me. I’m glad you liked it
As a non engineer, I find this breathtakig. It helps us understand how simple the really complex can be when viewed through the prism of those that developed the equations. Thank you,
I love your videos, Kathy
Thank you for the video Ms. Kathy!
Maxwell was a genius on the par of Einstein. His equations were too difficult to be grasped by any scientist at the time, and Heaviside provided a viable description accessible to many. You can learn Maxwell equations, but understanding the real meaning of how energy propagate thru empty space - is quite a task, which requires some dedication at the beginning.
If you haven’t seen it already, please read “Oliver Heaviside: Sage in Solitude” by Dr. Paul J. Nahin. It is a wonderful historical account of Heaviside. I was fortunate to be able to take classes from Dr. Nahin when I was in undergraduate engineering at UNH. He’s a fantastic story teller and gifted author…
Excellent Presentation!
Maxwell is also a top hero of mine - maybe even above Feynman. The degree to which Maxwell's work has impacted the world we live in is just impossible to overstate. Just look around you, and electromagnetic phenomena, under our mastery, is EVERYWHERE. It's hard to even imagine life without it now.
Great video ! I love how you bring to life the human motivations of the great physicists.
I can’t agree more with Feynamn quote on Maxwell equations.
In the 20th century, they led to De Rham cohomology theory which is deeply linked with the topological aspects of space-time. A subject which has been further generalised in Homological Algebra with deep implications in modern mathematical physics…
On these matters, I recommend Friedrich Hehl’s « Foundations of classical electrodynamics ».
Happy to elaborate on this exciting topic…
Hi Kathy. Have been looking forward to these videos.
I hope you get the time to tie the four Maxwell equations together at the end of this series by talking about the electromagnetic tensor. Specifically how to get the Maxwell equations from the EM tensor always seems to me a lot like pulling a rabbit from a hat using only first derivatives.
This rabbit/ hat way of writing the Maxwell laws in an unbelievably compact form was never covered in my own undergraduate physics course. I suspect they decided that the unit already had too high of a failure rate and adding in even more mathematics would not have worked out so well. I do not share that particular view, I think it is absolutely beautiful and I wish more students had the pleasure of seeing what looks like an empty hat and then seeing the rabbit emerge.
This is undoubtedly a lot to ask of you. For one thing, history aside, for the most compact form of writing out the derivatives would require a discussion of Einstein notation and possibly a discussion on the geometric meaning of the Bianchi identity (and what an identity even is) but I think the payoff might be worthwhile if only because it demonstrates just how compactly Maxwell's equations can be written when you get them into another form and, moreover, how the four Maxwell equations can be doubly paired and in a way you might never suspect, by a complementary set of operations involving only first derivatives of *E* and *B* field terms, in Cartesian coordinate form, with respect to space and time.
Either way, thanks. Your work is wonderful and, as always, your passion is infectious.
I love these videos. Thank you!
Excellent breakdown.
14:19 - the slickest edit I've ever seen. :) Thank you so much for this fantastic video Kathy, you're a treasure!
🤣 thanks, I accidentally said the wrong year so I had to sort of cheat.
@@Kathy_Loves_Physics We don't mind - 1853, 1854, it does not take anything away from the story. But I'm impressed you are so meticulous that you felt the need to correct the year :)
Before I did this, I never considered myself OCD. In fact, I consider myself the opposite of OCD. Now with my videos I might have a twinge. Also, if you read the comments if I got the year wrong people would tell me. A lot of people.
one of best channels
Wow !! I am so loving this. When I was studying Electronics back in the 80s I could structure my understanding of the theory by putting it in the context of the historical emergence of said knowledge. It gave me a structure to weave the theory around. A filing system if you will. BTW I can hear the influence of Feynman in your voice and presentation. You are clearly an admirer of his as am I.
Thank you for this fascinating video.