Maxwell's Equations - The Ultimate Beginner's Guide

[@upandatom]

Hi everyone :) Visit brilliant.org/upandatom to try everything Brilliant has to offer for FREE for a full 30 days. You’ll also get 20% off the annual premium subscription if you sign up!

[@NewYoutubeisstupid]

First!

[@juiceman110]

Cool I'll maybe try it :)

[@user-yz5fr1iw7h]

Personally i haven't clue whts going on with scientific stuff or bio, but u r Hot🥵oops lol wink. Anyhoo aren't we part of atom status vast of all things tht can be control? Just imagine a certain person who can harness or focus on particular connection with all matters. WHt if we use 50% of our brain electrification to control. Why we haven't evolve yet lol...Meow

[@pingnick]

@@juiceman110 I definitely would have been happier in my school days in the 90 I presume almost certainly had I had 2024’s Brilliant Jade and all - no pressure BUT do even more please Jade etc!🎬🫶🤪♾️🤩

[@nneeerrrd]

28:45 that's not Maxwell's photo

[@steve23063]

I wish my college professors had explained these concepts in such an easily understandable way instead of focusing so much on the math. Your content is amazing!

[@joshuaychung]

I feel like I was lucky that I was able to take this class in high school rather than in college. I feel like the high school teacher want to teach you and help you understand. I feel like the college professors are there to research and, begrudgingly, teach because the kids pay the tuition.

[@jakeroper1096]

Agreed! This would have been so helpful❤

[@vaibhavgarg1982]

Unfortunately, there is a chasm in the goals of the presentations by the college professors and KZbin content creators. The YT videos are targeted towards you understanding the equation, akin to you picking up an object and having you look at it from all directions and appreciate its beauty. The college curriculum is aimed at you being able to solve problems using that information. That obviously becomes dry, tiring and gets bogged down in formalism too fast. Different goals, different approaches. I bet, a person can’t analyse the simplest of situations after watching a KZbin video; while a typical college student will be able to solve but not tell you what they just did.

[@jakeroper1096]

@@vaibhavgarg1982 Hence, the “introductory” adjective on her lesson. Try taking an English class for once!

[@varunv2584]

She focuses on the Maths too. Just it's relatively simple equations.

[@keithweiss229]

I wish I would have had this video 40 years ago when I studied EE. Your explanation of the math is simply elegant! Thank you for making physics fun.

[@bastiandoen2583]

Same wish, just 25 years ago :D

[@lesalmin]

Hear, hear!

[@daleforrester8701]

Ditto

[@alvaro_ch]

me 2

[@BulentBasaran]

Almost 35 here, 1990.

[@EduardoLauandeTeixeiradeSouza]

I think this video represents one of the most comprehensive in scope, simplest to understand, and most straightforward classes on Maxwell's equations that I have ever watched before. If not the best in all these aspects. At this more accessible level of complexity, it may even be the most perfect class in these aspects.

[@shortiewaswo]

Agreed! and a great refresher for those that learnt at uni but don't deal with it every day as well. really quite... brilliant!

[@civwar64bob77]

To me the most amazing thing is that after this, Maxwell used these equations to figure out that moving B generates moving E generates B generates E which is an electromagnetic wave, and that it travels at the then measured speed of light, so light was an electromagnetic wave that travels at speed c = 1/Sqrt(permittivity times permeability). Brilliant!

[@davidthane9002]

Which was a part I thought was missing. The whole "and in sum this means electromagnetic waves" Or how generators/electric motors arise from the behaviour. That might make it even easier to understand the fundamental nature of those laws.

[@clemensvorbauer1183]

Maxwell was a professor at Kings College in London, not a telegraph operator! He found his famous equations as a student in Cambridge in the 1850s.

[@edkideys8953]

that is the classical explanation. Quantum mechanics shows that electromagnetic waves, of which visible light is a subset, are actually particles (photons) which exhibit wavelike and stochastic behavior. At the quantum world scale we have to append to the definition of 'particle' from the traditional localized billiiard ball to one that includes traditionally wavelike properties of frequency, wavelength, interferance, non-locality, etc

[@DumbledoreMcCracken]

@@edkideys8953 particles are an idea, and a word, but not a reality. We don't have better vocabulary for it / them. Even mass, momentum, energy, and power are dubious words when you jump into a nonspatial quantum realm?

[@edkideys8953]

@@DumbledoreMcCracken You are right. These are all ideas, and abstractions in our minds to model reality. Quantum mechanics is a model that reflects reality very accurately. While mass, momentum, energy, and power are part and parcel from the conservation laws of classical and quantum physics (conservation of mass/energy, momentum, angular momentum, and charge) the word particle needs to be redefined to steer the mind away from the billiard ball image that is incompatible with the quantum realm. We may be better off just not using the word particle anymore altogether and replace with a novel word. Definitions and postulates based on the definitions are crucial for theories and modeling. Euclid's definitions, postulates, and axioms were so clear and concise from over 2000 years ago that we still use them in geometry today. The current definition and mental image of 'particle' just doesn't fit reality and causes more confusion than clarity.

[@666shemhamforash93]

Please do more visual math explainers like this! This was so helpful and intuitive and clear!

[@TheDeadStyx]

My respect for even bringing such a thing to youtube

[@garrettstambaugh6271]

This was a great introduction for physics "fans" like myself who have a good layman's understanding of things but are put off by the maths. I've found there are usually two types of content on this: either so vague and afraid of the math that you only learn the idea and not the mechanics, or so deep into the maths that, without a really, really strong mathematical background it makes zero sense. This was a refreshing and uncommon middle ground. The explanation of the terms without going into solving them made the whole thing make a lot more sense, and now, as I'm studying how to solve some basic examples, it makes sense rather than looking like a bunch of gibberish. Maybe I'm a mathematically inept person, or maybe teachers have really let me down on the basics, but I found this really helpful. It might even be nice to see a follow-up where we can see a few examples with values and units to gently step into the mathematical waters.

[@chadwagoner7056]

Yep! I often think about what the greatest minds have in common from pre-computational eras. My overriding assumption is that they all had the ability to visualize abstractions more clearly than "normal" humans. Einstein imagined what the train and clock were doing, how they looked and felt; he didn't write it out first and then think about the reality of his theories. That's pretty impressive. However, look at how much further this can be taken when gifting the world with examples of what these theories actually mean and how they look when in action. Pretty cool!

[@nidhi4079]

This was sooo sooo well explained!! Never had an intuitive sense of what these equations represented before!! Thank you, i’m glad I stumbled across you a few years ago, you make a great teacher :)

[@GSBarlev]

There's a lot of interesting history around Maxwell and "his" equations, which are beyond the scope of this excellent video. For anyone who's interested: As you point out: all of the equations were previously attributed to others (Gauss, Gauss, Ampère and Faraday). Maxwell's original treatise actually outlined *20* equations, and it was *Heaviside* who reduced them to just the four that we all know and love. Maxwell's breakthrough was to tie them all together and describe them in a single coherent "field theory." And at the same time, Maxwell's contributions to physics were numerous and broad, including the rings of Saturn, color theory, thermodynamics and what would one day become chaos theory-I wish I could remember the exact quote (and who said it) but it goes like: _If Maxwell had never set his sights on E&M, he would still be one of the history's greatest scientists._ Plenty of physicists idolize Newton, Einstein or Feynman, but for me, the one true will always be JC Maxwell.

[@tomkerruish2982]

Didn't Maxwell modify Ampère's Law to include the @E/@t term ("displacement current")?

[@hyperduality2838]

Electro is dual to magnetic -- the electro-magnetic field is dual. Positive is dual to negative -- electric charge. North poles are dual to south poles -- magnetic fields. Real is dual to imaginary -- complex numbers are dual. Photons are modelled using complex numbers -- probability. Light, photons or pure energy is dual. "Always two there are" -- Yoda.

[@GSBarlev]

@@tomkerruish2982 Yep. He introduced the concept of displacement current in his 1861 paper "On Physical Lines of Force, Part III," four years before _A Dynamical Theory of the Electromagnetic Field_ and twelve before his seminal _Treatise on Electricity and Magnetism._

[@FulgenceMalvenue]

@@GSBarlev But before Heaviside reduced them to 4 equations in 1884, Maxwell had already reduced them to 8 equations in 1873, right?

[@musicman53]

Back in the '70s I was a young Telecom engineer grappling with the new problem of the latest 5000 volt pulsed electric fences used by New Zealand farmers causing loud clicks in the adjacent aerial phone lines serving those same farmers. If their fence (sometimes 5 km long and 5000v) had any grass or shrub touching it, then a current pulse would flow along the fence and Maxwell's 3rd law would cause a large longitudinal current pulse down the nearby pair of telephone wires. If the pair of wires (often decades old) was even slightly imbalanced from the exchange to the rural customer then a net current pulse would loop through the circuit, creating a very loud click. It took a huge effort to convince farmers throughout NZ to keep their fences clean, and to convince Telecom to spend money keeping their old phone lines up to spec.

[@chadwagoner7056]

Far out!

[@anullhandle]

What about time creates imbalance? I assume twisted pairs but do you know what is physically happening to the line or is it just corrosion etc. at terminations?

[@LupusMobile]

Your growth as a content creator, educator, and overall character has been incredible to witness over the years. This is by far your best. Absolutely astounding job with conveying the information in a way that really solidifies one's understanding of the material. Thank you so much for this, and all your wonderful videos. Wishing you the best with all your future endeavors.

[@RichMitch]

Can you do a pre-beginners guide? Like a single celled amoeba focused course for me, please

[@marcelob.5300]

You sure you're not being a little lazy, perhaps? I don't think it can be done simpler or clearer!

[@Thomas-gk42]

Hihi😅

[@katarinatill4713]

Yes, please! 😮

[@ryanfriedrich6634]

Yeah this is more a review for people who have already taken courses related to Maxwell's equations. In order to go slower, she would have to do one equation per video, and show experiments. And that's getting into Khan academy/tutor territory, which isn't what was intended here I'm guessing.

[@michaelsommers2356]

I doubt it. You need to use vectors and vector calculus to have a hope of understanding this stuff. Note that this video is not asking you to use thee equaitons to solve problems, just to read and understand what the equations are saying.

[@ChevroN7]

I really wish I had access to such an incredible explanation back when I was taking physics in university. I always found it easy enough to grasp the concepts, but when it came to the equations I often struggled. I can't tell you how much I appreciate the work of going over each term in the equations (along with such helpful animations). These types of detailed explanations will be invaluable for students 👍🏻

[@ed.puckett]

Your video presents such a clear and accessible explanation while still maintaining a good depth! Thank you for all the care and effort that must have gone into making it!

[@martincastillo5401]

A good teacher is one who explains concepts that are difficult to understand through an easily accessible manner. You are that kind of a teacher. Clearly, you have truly mastered these concepts that now you are able to explain them so well. Thank you so much.

[@MachiningandMicrowaves]

I was very lucky to have a great teacher who made sure I had an intuitive grasp of Maxwell's Equations in differential and integral forms before I went to Uni in the 1970s. Your clarity in explanations reminded me of them. I'm going to recommend this video to the folks with zero maths background who ask me about how electromagnetic FDTD solvers work using the equations iteratively across meshes of Yee cells. Might make the transition to nonlinear dielectric media and ferrimagnetics and all the special-relativistic business a lot less painful. Excellent stuff.

[@greysponge66]

I have never come across a presentation that presented Maxwell s equations so clearly as to almost appear self evident and yet so eloquently. Outstandingly excellent.

[@bobthecomputerguy]

"Permeability" refers to a material's ability to allow magnetic fields to pass through it, while "permittivity" measures how easily a material allows electric fields to form within it. By measuring the permeability and permittivity of free space, these equations will give you the speed of light. That always fascinated me.

[@XEinstein]

Why does that fascinate you? Permeability and permittivity can be viewed as the resistance of the vacuum against magnetic and electric fields. Since light is an electromagnetic wave it stands to reason (at least it does to me) that permeability and permittivity define the speed of light.

[@ijabbott63]

@@XEinstein The coincidence that the speed calculated from Maxwell's equations matched the measured speed of light is what provided the clue that light is an electromagnetic wave in the first place.

[@ENGRAINING]

photons possess both magnetic and electric fields so it's obvious

[@ijabbott63]

@@ENGRAINING But they didn't know that at the time. They didn't even know about photons.

[@XEinstein]

@@ijabbott63 yes that is right. The work of Maxwell indeed lead to the finding that the measured and calculated speed of light match and thus to the conclusion that light is an electromagnetic wave. Something that at the time certainly was not obvious. But I studied physics two centuries after Maxwell compiled his equations and thus when I was studying it was simply thought to me that light was an electromagnetic wave. And therefore it was very obvious to me that permeability and permittivity must lead to the speed of light.

[@newhampshirelifestyle4233]

I earned my BSEE from NorthEastern in 1991. I had to take 3 courses in Electromagnetic Fields. When my professor who taught me E-Fields 1, he explained how Maxwell's equations were one of the greatest discoveries in Physics. As I studied and studied, I used Maxwell's equations in nearly ever problem with static fields, time-varying fields and finally antennae design. Eventually, I was astounded by how fundamental these equations were to all modern electronics, power generation and communications, antenna design, etc. And how did James Clerk Maxwell determine these equations? THAT is pure genius. He is one of the unsung hero's of physicals. Great documentary.

[@pboston6RR]

WELL Done! You have defined the difference between College Physics and University Physics. I studied College physics 70 years go, when Calculus was optional. The ideas within this presentation were presented as changes but WITHOUT examining the math necessary to sharply define the effects. Your presentation was Calculus without the need to take the Calculus course. WELL Done. Thanks a bunch.

[@transponderings]

Thanks for this nice refresher of something I studied as an undergraduate about 40 years ago (yikes!).

[@civwar64bob77]

Me too! (But in my case, 53 years ago)

[@alihms]

I sort of noticed the age of the audience for this type of videos (ie, a bit math heavy) are either old (50+, like myself) or young adults (18 ~ 25). Those in the 30s and 40s are very-very few.

[@markonar140]

An Amazing Overview of the Maxwell Equations!!! And a Great Reminder and Refresher too!!! Thanks for Sharing!!! 👍😎

[@kgriffin1032]

An excellent summary, and a great resource for reviewing the concept. Thank you!

[@matthewmuscheid]

These are the kinds of videos we need more of! The depth and quality of information that is usually behind the paywall of a textbook, made available to everyone. Thank you for doing what you do!

[@spencerwenzel7381]

This is the first time in my life I can look at Maxwell's equation and I understand them on an intuitive level. Thanks for the excellent video!

[@kindlin]

Basically all I knew before this video was the first little table she showed, with produce/change, electric/magnetic, making it 4 equations, and I thought I was hot shit. Now I actually understand the equations.

[@apprentiz2186]

I think there's a slight correction at 28:45 when the picture was shown of Faraday instead of Maxwell. Otherwise, superb video and your animation deserves high praise!!

[@marcelob.5300]

I strongly support the "little difference" in this video compared to your usual videos. So, keep up the great job!

[@GTI099]

I spent hours trying to understand this 4 mathemathically pompous equations during my studies. With correct explanation everything is simple. Thanks so much. Great job 🎉

[@CC--qn4gf]

I love how you made sure to summarise each law at the end of each segment to make the concepts more memorable and easier to grasp.

[@DenilsonSa]

My only nitpick or suggestion would be to use double-squiggles to denote area integrals, leaving a single squiggle to linear integrals. ∯ instead of ∮ₛ ∬ instead of ∫ₛ Because then it's clearer that ∮ is a contour integral (1 dimension) and ∯ is a surface integral (2 dimensions). In my humble opinion, that's clearer than just using the subscript letters ∮c and ∮ₛ (sidenote: there is no Unicode glyph for subscript c) But I understand this was a conscious choice from the video creator, and I admire how well everything was explained.

I'd love to see a 4 video series focused on each equation and comparing the integral and differential versions for each. Great video!

[@johnbonnett5746]

Well Jade you have certainly outdone yourself with this one! You have made some great videos over the years but this one takes the cake. A serious Physics topic presented in a really clear way. It has been many years since I studied this sort of thing, being off in software engineering for 51 years so far, but I wish I had see this back then. Having such a charming presenter would have helped too.

[@georgesos]

No,this episode was made possible because you are brilliant!.❤

[@over_score4033]

This is the first time I've seen Maxwell's equations explained so clearly and comprehensibly! Even in my native French, I never really understood! A huge THANK YOU.

[@capitalist88]

Jade is just awesome at making this stuff accessible as usual. One small bit I would have added at the end to make the whole thing more relevant to everyday experience is that Maxwell's 3rd and 4th laws are the key to how generators and electric motors work. These two things are opposites: Spin a magnetic field around a wire and you get a current (Maxwell's 3rd law). That's a generator. You can spin the thing by hand, by pedaling a bike, or using a gas powered engine or whatever. Send a current through a wire and you get a spinning magnetic field (4th law) which can create rotary motion. If you have a ring with magnets on it, the ring will spin when you send the current through its axis. That's an electric motor. The current can come from a battery or the power grid, or whatever. This is probably overly simplified, and based on my vague recollections from getting an engineering degree way back in the eighties, lol, but I think it's generally correct.

[@carlosalbertogonzval121]

I remember seeing only the electric field at school, the rest I had to study on my own. This video was very educational and made very entertaining.

[@2smoulder]

Jade's explanations of Maxwells equations is rather too simple for words, unless that word is BRILLIANT.

[@ceo1OO]

so her name is Jade... you just taught me something i didn't know... 🟢 that name always reminds me of Mortal Kombat... the ninja girl with the green outfit... 🥷🏻

[@2smoulder]

@@ceo1OO Also a very interesting mineral from the pyroxine group.

[@DenariusHaveNarius]

Her magnetic personality is very attractive, though her accent is quite shocking. Yeah, lame but someone had to do it.🙂

[@2smoulder]

@ Nothing wrong with a good Aussie accent 👍🇦🇺

[@ScienceTalkwithJimMassa]

This is simply a brilliant video!! Well explained and presented!! Often professors get hung up on the math without explaining what the math is communicating to us. You did this brilliantly! Thank you)) BTW, cool shirt))

[@rjstone98]

Super video, Jade! Very well done! One small suggestion: for this and future videos of its type, add the units of measure to the equations and constants. (This might even be a worthy of a video unto itself!) As a young student studying math and science, I was fortunate to have a few teachers who were sticklers for indicating UOM in the answers to quiz/exam problems and I found it very helpful in ensuring that my calculations made sense and included all the elements required to get to the correct answer. If you’ve already done this, I missed it and apologize.

[@rangerBlu]

Yes, and please explain the units of each quantity with some intuition of the meaning. Many of these terms are similar and easily confused so understanding the units is helpful to understanding the meaning. It would also be nice to hear the reason why Faraday's Law and Ampère-Maxwell's Law differ in sign. Otherwise a very nice video and I thank you for making it.

[@jimromanowski6966]

Thanks!

[@RobardoHughes]

Always be aware of the special case of the vector calculus theorem which dictates that a circulating vector field with amplitude which declines as 1/r, even though it is rotating, has curl = zero. This is of fundamental importance to implications of Green's theorem, Kelvin-Stokes' theorem, and the divergence theorem, as well as the existence of the magnetic Aharonov-Bohm effect.

[@alans172]

Do you think this is what might have led to the inappropriate application of the Kelvin-Stokes' theorem of electromagnetic fields to "flow fields" in fluid dynamics?

[@RobardoHughes]

@@alans172 @alans172 On one level, Green's thm and its more generalized cousin, Kelvin-Stokes (and its even more generalized version, the divergence thm) have to do only with potentials. The application of the potentials interpretation to fluid dynamics would be inappropriate. But on a simpler level, there is an interpretation of Green and K-S which can be interpreted only as "conservation of circulation." I.e. the total rotational circulation at the perimeter is the sum of the "swirls" (rotation) within the surface (integral). There is always the possibility that you are referring to yet another interpretation or application of the thms, but I feel this "conservation of circulation" equivalence of line and surface integrals is applicable to objects with mass, and therefore can be correctly applied to finite element analysis of fluid dynamics. But I feel the quantum interpretation of exclusively potentials and/or probability amplitude cannot be applied to massive particles such as atoms or molecules in circulation to obtain a meaningful result.

[@squared8290]

This is the course that forever changed my life. I loved electromagnetism so much and calculus too that after finishing at the music conservatory I decided to go hard-core into science. The textbook we used in high school was Sears Semanski and Young. It had this beautiful golden tsundial like pattern on a white background. A friend of mine in High School was a great artist and he painted it for me on the back of my Jean jacket. People would walk up to me all the time and ask me, “Dude, your jacket rocks! What band is that?” And I would simply reply “Sears, Semanski, and Young”…

[@PauloRenatoRodriguesprr]

Marvelous explanation! Simply amazing! You teach very precisely and at the right pace. Another nice feature of your presentation is that you stop at some points to recapitulate what was already explained. To be perfect, you could do a similar explanation of the Maxwell's equations in the differential form. The video would be way longer, but it would be among the most complete explanations on YT. Congrats!

[@camilopaz8384]

I’m a visual learner and this explanation clears up many misunderstandings I had, thanks Jade!

[@Beyondtomorrow31]

Thank you, this video was a fantastic idea. Most prof.s take months of classes to convey what you covered in one video.

[@beauthestdane]

You are a great teacher for these concepts. I know there is a lot more detail to all of this, but you were able to convey the basic principals here concisely and quickly and understandably even to those of us who have relatively little background on the subject.

[@aragamsubbarao5912]

In the college ,my teacher said that Maxwell equations are most difficult.He asked us to mug up a few lines and present it ,if they asked you in the examination.that was 50 years ago. I was very happy to understand it ,thanks to this lecture.Thank you. You are a great teacher.

[@gethnoble4316]

Thanks, this video is very clear!! Last time I studied this subject was 40 years ago, but thanks to you I understood it all again!

[@2CVCult-zl8eo]

I studied all this at Uni 40 years ago. This video is a wonderful easy way to refresh what I had learned then.

[@TejasDhuri-p8z]

Amazing video.I have never seen something such as Maxwell's equations explained in simple and understandable manner.

[@zanderrobertson5138]

This is hands down one of the best KZbin videos ever!! Thank you very much

[@iwbnwif]

This is by far the clearest explanation of Maxwell's Equations I've ever seen - thank you. I would love to see something similar for the Telegraphers Equation and the wave equation, as most videos simply repeat the derivation and skip the underlying meaning of the terms.

[@arj123sub]

Great video. It helped me get a sense for the equations. The way you walked thro' the individual parts of each equation and tied them up into an easy to understand concept, is just what my mind needed. Thanks again very much.

[@krishbatra7010]

This is an amazing video! I love the ingenious way you have explained everything here. I wish this teaching style was more common. I am very much appreciative of your efforts-this is truly awesome and unique! I wish everything were taught like this. I wish I could convey my sentiments in their full grandeur, but my writing abilities limit my doing so! Way to go, upandatom!

[@Legendsandlessons-68]

Thank you so much. I'll be doing the maxwell equation next semester, and thanks to you, I'll get the best headstart. Love your content as always.❤❤

[@stjernis]

I much appreciate how straightforward and to the point this explanation is - no extra faff whatsoever (besides the sponsorship message).

[@mog068]

This is fantastic. I’m a software engineer in astronomy and astrophysics but was not a great math student. So I tend to glaze over at the sight of equations. This is exactly the kind of explanation I need to make them useful.

[@theosky7162]

30 min better than what I remember as my Uni Electrodynamics semester ! Wow ! Subscribed, and pleased to see a whole stack of videos to dive into! Thanks !

[@Linusgump]

I’m glad I watched this video. It took me back to my struggles in university level calculus, but it also made me think. And just like chemistry and calculus, I can see further study in this topic would reform my view of the world; chemistry taught me to view the world in terms of electron exchanges and bonds, calculus taught me to view the world in terms of rates of change, and this would combine the two in terms of flux created or changed in terms of time.

[@madlarch]

Wow - you really have an amazing talent for explaining things clearly! Only discovered your channel recently, but expect to watch many more of your videos as I get the time. Many thanks!

[@bimblinghill]

This is a very clear explanation of some quite tricky stuff. Thank you.

[@punditgi]

Very well done, Jade. When I see your video, I feel like I am entering a force field generating a powerful attraction. I wonder what the equation for that would look like. ❤🎉😊

[@anurasilva3405]

.Your explanation is superb and brilliant. Even a person who has least knowledge of maths and physics could understand. You have ability to explain very complex things in physics and maths in very simple way that most of the people could understand.Thank you!

[@dtg816]

I seldom understand all of what you are speaking about - but I sure enjoy watching and listening! Up and Atom!!

[@narrotibi]

I think this video is brilliant. Forces me to concentrate. Perfect for increasing my attention span and learning something again. Also helps to make and understand connections between different scientific applications.

[@TheJohnblyth]

The most clarity I’ve ever encountered on this kind of topic. I’m closer to grasping this than I’ve ever been. The distinction of closed and open seems fundamental, and it’s neat that they can have a notation that reflects this fundamental difference. So then it’s more than a bit quixotic to go looking for magnetic monopoles, as used to be longed for half a century ago. Also the asymmetry between electric and magnetic seems to hint at other analogous asymmetries. When we bundle these two components together as the electromagnetic field, we’re actually losing a bit of clarity and elegance, even although doing so is both true and useful. I’m often daunted by this channel because I like to think I’m clever, and, no, it’s you who’s clever; but this was good. Thanks!

[@Vardaris]

Epic videos are epic. This one can be saved as the golden standard of introductory videos and the go to way to begin understanding Maxwell's equations.

[@MathewDzirutsva]

this presentation is par- excellent. Gives you very good intuition. Keep it up Jade

[@boredgrass]

This is opening a window! I see the first lecture of a course! What you have created here goes above and beyond! I',m anxiously awaiting the next lecture;.) Thank you!

[@DraxeSlash]

I've always wanted to understand Maxwell's equations and I've watched lots of youtube video but I still couldn't understand. But today, this video changed it. Great job. keep posting more of these. Thank you.

[@hyperduality2838]

Electro is dual to magnetic -- the electro-magnetic field is dual. Positive is dual to negative -- electric charge. North poles are dual to south poles -- magnetic fields. Real is dual to imaginary -- complex numbers are dual. Photons are modelled using complex numbers -- probability. Light, photons or pure energy is dual. "Always two there are" -- Yoda.

[@faisalsheikh7846]

Jade, You are amazing❤

[@shahrammakoui859]

This was an absolutely FANTASTIC video that you made with beautiful explanations … I’m just a Neurosurgeon in Los Angeles & don’t know too much of advanced physics or math, although I’m self teaching myself & enjoy it very much … Amazing work you did ❤🌺🌹👏👏👏🙌🥂

[@atharvaagarwal2489]

Thank you so much for explaining such hard equations easily!!

[@tonybalazs]

This is really excellent. I will use it with my advanced physics students!

[@robtroman7917]

This video is a revelation. While watching this I began to understand concepts that I’ve been struggling to get my head around for years. At some points in this video the experience of enlightenment that I felt almost made me pass out. 😊

[@complete1211]

Absolutely incredible explanation of Maxwell's equation. Thank you for connecting the dots between all the different components of the equations. I greatly appreciate your content you have put together... Will be sharing it with others in preparations for finals

[@bobblaine1437]

Thanks for this explanation! It's been almost 50 years since I studied this so this was a great refresher.

[@sanketsurve-u7h]

Nicely explained Ma'am. I wish I had a fantastic teacher like you in my school days. I hated physics back then. You helped me grew the intrest back into the subject. Thanks a ton.

[@rwired]

Videos like this are how you earn new patreons! Beautifully produced. You are adding something valuable to the world with these kind in explainer.

[@johnydyroy1576]

I learn so much from your videos!

[@HojaUno]

You have clear grip of this equations. You have awake my curiosity on this topic.

[@DrPG199]

What a brilliant explanation!

[@coraltown1]

This is the Mona Lisa of explanations for both the concepts and the math. Thanks for your masterpiece!

[@MemphiStig]

Very well explained. Now I want to know how this applies to everything else. Like what these teach us or allow us to understand that we couldn't without them. Context, I suppose. I've always found math to be difficult, not because of the numbers, but because of the meaning and applications of the equations involved. You've given me a great starting point in understanding how these work. Thank you. This is ready-made for classroom use btw. Well done.

[@SiddhantSharma181]

I’ve been looking forward to this video, and it absolutely exceeded my expectations-truly insightful and expertly crafted!

[@eric1138]

Excellent job. It all came back to me again, both the math and the physics.

[@RobertSmith-pw1cl]

A really clear explination. I will need to watch it several times to get a firm understanding.

[@DisasterxUs]

didn't think I would understand, but you explained it so well that I just managed to grasp it. A few more watches and I'm sure it will sink in. Thank you!

[@xBrandinOx]

this is an amazing breakdown!

[@KRISHNA-dt9kx]

Maxwell was the game changer in modern physics and it was very crystal clear explanation from you and you have also touched vectors which is heart of physics and mathematics is the language of physics

[@hanneswhittingham2683]

A truly illuminating explanation of a topic in physics I have never studied, but always wished I had. Thank you!

[@Inertia_m7y3]

I have always heard of it but knew nothing about it. but after watching your video, I finally understand the laws. Thanks a lot !

[@JaiMadhusuthan]

Thanks for this I’ve been wondering about them for a while

[@Jcactus213]

As an Indian who has coming up entrance exam for MSC physics for IIT and have to memorize 2 books of formula notes for electricity and magnetism this video helps....

[@cerealport2726]

memorising formulae is one thing, but understanding them is something else.

[@Jcactus213]

@@cerealport2726 I know bro but for entrance exam I have to memorize it 😅

[@Harald-j1e]

... the best explanation of Maxwells equations I ever saw ! Very good !

[@hightechsystem_]

This video really helped me a lot. Please keep making more training videos, your approach is good.

[@zbigniewkrupa1877]

Dear Ms. “Up and atom” you have the gift of persuasion. I procrastinated starting courses at Brilliant until today. Thank you. May you do well. Best regards Zbigniew Krupa

[@CaritasGothKaraoke]

I’m glad you’re back. You’re very charming and clear.

[@spacelem]

I work in the James Clerk Maxwell Building in Edinburgh University (I'm a mathematician, not a physicist), and they have those equations written in large letters on the floor in the 3rd floor lobby. I have to admit I've walked over those equations so many times without ever really understanding them!