Maxwell's Equations Visualized (Divergence & Curl)

Maxwell's equation are written in the language of vector calculus, specifically divergence and curl. Understanding how the electromagnetic field works requires we also understand that language. Unfortunately, symbols can be ugly, so let's try some dynamic visuals instead.
Advanced Theoretical Physics (Paperback):
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gumroad.com/l/ubSc
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VIDEO ANNOTATIONS/CARDS
Electrodynamics Series:
• Electricity and Magnetism
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RELATED KZbin VIDEOS
3blue1brown on Divergence and Curl:
• Divergence and curl: ...
Eugene on Divergence and Curl:
• Divergence and Curl
Khan Academy on Divergence and Curl:
• Divergence intuition, ...
• 3d curl intuition, part 2
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Code used for fluid flow animations:
anvaka.github.io/fieldplay/
github.com/anvaka/fieldplay
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LINKS TO COMMENTS
• Why Does Stuff Happen?...

[@ScienceAsylum]

*Correction:* In the third equation (Faraday's law), those "d" symbols should be curly like they are in the fourth equation (Ampere's law). My bad! It doesn't actually matter much for the video, but it bothers me that I can't seem to get through a video without a typo. 😞 *Note:* Yes, there are similarities/overlap between my video and 3blue1brown's video from last year. That's one of the hazards of making educational content... but our videos have a slightly different focus and reach slightly different audiences, so I think it's OK.

[@kbbeats3099]

Well... You're (most likely) a human. Mistakes will inevitably happen. Don't beat yourself up over it, we love the content.

[@kbbeats3099]

See? Had to edit my comment too lol

[@jlpsinde]

Don't worry, Nick. If you were perfect you would be God lol. You're perfect as a human xD

[@Lucky10279]

Partial derivatives? And don't beat yourself up over silly mistakes. I was doing linear algebra homework last night and I must've made at least _10_ different silly mistakes. At least you you only made one.

[@Lucky10279]

Are you gonna do the video about why balls roll? I want to see it. :)

[@mask3dal3xx]

Please keep making visualization videos! I know that they might be harder for you to make but they really do help everyone understand physics better.

[@janee11able]

As a physicist I can really appreciate this pictorial and fun way of explaining :) helps me stay awake and sharp with the physics

[@lelenovo6296]

My teachers think I'll be able to understand these kinds of things by just blabbering their mouths and making us to read textbooks all day, and to think that I'm paying their tuition makes me sad! I am so glad to find this channel.

[@travcollier]

The Mechanical Universe with better graphics, more snark, and marginally *fewer* puns ;)

[@TheAmbientMage]

"Should I do more videos like this?" Me: "YES. DUH. GIMME ALL THE MATHS!!!!"

[@vladimirpain3942]

Totally. Physics needs math.

[@kiip7579]

No, that's enough.

[@danielliu2819]

@@kiip7579 😡

[@sakshamsingh1778]

​@@kiip7579 😡

[@akhil6543]

I'm a Ph.D. in Physics but I've never been taught like this. During my college, these equations seem like a nightmare to me, but your videos will really help Under Grad. and Grad. students to visualize the real things happing there. Best wishes.

[@ScienceAsylum]

I'm glad I could finally help 🤓

[@Boooommerang]

​@@ScienceAsylumYou are a genious! I love your videos

[@Boooommerang]

​@@ScienceAsylumYou are a genious! I love your videos

[@AndrewDotsonvideos]

"which most people just call the maxwell equations... don't get me started" lmao!

[@Verschlungen]

Likewise lmao. (For other readers, what Heavyside did, in distilling the 4 so-CALLED "Maxwell's equations" from Maxwell's (actual) 20 equations, was both a monumental task and a gift to the world, though his name is rarely mentioned. The least one could do is show his name hyphened TO Maxwell's, as our favorite Asylum inmate first shows it, before crossing it out in a reluctant bow to convention.) This guy never misses a trick. Sheer joy to visit his Asylum.

[@goldenwarrior1186]

I found Andrew Dotson!

[@Ayshafr]

But seriously, I really appreciate videos like this. A lot of times in college I felt like I was just doing math without really understanding what it meant, and even when I was told in words, it didn't really stick. The math is essential to understanding the physics, but the physics sure helps in understanding the math. Would love to see more videos explaining equations and visualizing them.

[@nikolamilutinovic7770]

Man, we had electromagnetism 2 years ago and I couldn't get my head around these equations... But now it seems too easy 😂😂 Well done to you sir! 👏👏👏 P.S. Can you do a video on fractals?

[@maciejfratczak4136]

didactics at universities does not exits. eat sh.. or die.

[@CaravaggioRoma]

Man, I should have known you 20 years ago when studying at the college!

[@RoulDukeGonzo]

Kids these days!

[@tswellersalzer1850]

@@RoulDukeGonzo Me too, 40 years ago.

[@kish5435]

Me too 40 years ago. Even though I am MSc in physics.

[@dmullins301TWM]

You asked "should I do more like this?" My answer is a resounding "yes, please!"

[@LuisSierra42]

But you know everything already, Dr Manhattan

[@crouchingtigerhiddenadam1352]

It's math... But it's not scary. You're breaking all the rules! I love the animations!

[@crouchingtigerhiddenadam1352]

@Diego Marra you're right, I'm working through a Weyl Curvature Tensor on the train right now, just for fun!

[@crouchingtigerhiddenadam1352]

@Diego Marra good for you and Math is fun. But it can be frustraiting. I have this problem where I end up generalising any equation to death.

[@stevenbateson8217]

😂 I’m retired and spent a couple of months working through text books, teaching myself vector calculus for the express purpose of understanding Maxwell’s equations. You just condensed the fruits of all that labour into a couple of minutes 👍 All that work has had side benefits though, such as understanding Schrodinger’s equation and the Navier-Stokes equation etc. I look forward to your video on the NS equation when you’ve finish teaching yourself fluid mechanics 🙂

[@seanfeeley8412]

It's also much easier to understand knowing the terminology and equations to associate with the visuals. Your hours have granted you advancing comprehension in minutes.

[@Mickolas21928]

Where were you when I was taking electromagnetism for my EE program? Well done.

[@Private_Duck]

This is insane. Ive learned vector calculus before. but no one was perfect like you, when it comes to explanations.

[@Enrique_Osorio]

Please make more videos like this. I am a 3rd year electrical engineering major and your videos have helped me visualize concepts in a way that makes it much more satisfying than simply applying and solving equations. I truly am on the edge of my seat while viewing your videos. Thank you so much for what you do, it means a lot.

[@avikamnarwal]

And I'm studying it in 12th grade

[@IncroyablesExperiences]

Why we don't always learn this way before to use this laws in a real calculation? I mean, is someone can use properly these laws without this real understanding? These laws have been created with this understanding, that's their real message! Are they people who managed to use properly these equations without this understanding?

[@ScienceAsylum]

I think it's a practicality thing. No one needs to understand what they're doing this deeply to actually do practical work with electrodynamics. Maybe they should, but I think maybe teachers don't want to go through the trouble.

[@guilhermetorresj]

The professor who lectured me on electromagnetism did this, basically, but explained with drawings and the right hand rule. No video with animations showing things in motion. You can understand most of it that way, but this video makes your brain get a way better grip on the whole situation. And after you start using the equations on the real world to solve problems it just clicks.

[@joshuazeidner8419]

hats off to this amazing youtuber who turns stale dull scientific material into obnoxious irritating material filled with ads.

[@mariokajin]

I should really refresh the knowledge of the electrodynamics.

[@abhaysharma9317]

David J.grifiths has joined the chat.

[@zoltankurti]

Jackson has joined the chat.

[@abhaykewate__]

H

[@jimzweighaft8079]

Much better explanation than I got in Engineering school 40 years ago. The animations help a lot.

[@frankgiancola7]

I graduated from electronics in college in the 80s and couldn't visualize electron movement and magnetism until your videos helped understand what's going on. Your videos help me visualize invisible motion in my mind which is really hard to do because magnetism and electricity are invisible. Keep up the good work Mr Asylum. Your videos always get a like from me and yes please keep on making these videos.

[@zgegosaurusrho8205]

Man, the thing I love about your videos, is that you don't think of your audience as a bunch of idiots. You give us accurate informations, so we can better understand our universe. We can be kids, or uneducated ppl, you don't care and you always managed to be accessible and fun. Well as long as you keep doing videos, and curious ppl come to see them, we may be optismistic about the future of mankind. Thank you. And in conclusion: MORE! MORE! MORE! WE NEED OUR SCIENCE FIX!

[@Lucky10279]

Yes! I completely agree. He talks to us like adults, anticipates questions, and treats those questions like he's had the same ones. He's got such a gift for communication!

[@A_Saddler]

Pizza delivered the same time you upload this video. Life is great sometimes.

[@pranavflame]

:D

[@VikramGT7455]

Keep doing visualisation videos, younger generation will get interest in science.. Its a service to society.

[@tatjanagobold2810]

Perfect, just when I am learning about phase space fluid flow ;)

[@jamestheotherone742]

But... ah... um... nevermind.

[@abderrahmaneyahiabey5521]

hahaha

[@veerakuusela5005]

Good to hear you are still learning new things. Means more things you can teach us in the future. :)

[@mikepettitt]

I would LOVE to see videos explaining equations! Keep up the good work Nick.

[@kbbeats3099]

Love the vid. I always used to think math was too difficult. But now I think it's absolutely beautiful.

[@yassinesafraoui]

it's been always beautiful

[@nothinginteresting1662]

I am very grateful to all the KZbin Math and Science (especially Physics) creators for sharing their knowledge, conducting practical experiments and simplifying seemingly difficult concepts. Had it not been for you guys, the interest in such wonderful subjects like Math and Science would have been nil owing to the boring classroom lectures. You guys have kept the Spirit of Discovery alive! Thank you very much for all that you do.

[@ScienceAsylum]

I'm sure I speak for all of us when I say "I'm glad we could help."

[@shantanupatil_]

I have never seen this type of great explanation in my life.

[@hakachukai]

You are really good at taking advanced topics and making them understandable through visualizations and breaking it down into simple language! I learn a LOT from these videos! Keep up the good work!

[@pritishjain674]

Just like always , making physics processable

[@ShadowZZZ]

This is imo legit one of the best but underrated videos in your channel. I'm currently studying physics major as undergrad and in my 2nd semester we're learning about the Maxwell equations, and your video helps me a lot to understand this concept. Thank you very much

[@rc5989]

It is amazing how much knowledge you can pack into an 8 minute video. You teach so much so well and keep it entertaining all the while! I fully intend to buy your book in the very near future.

[@declanwk1]

This is the best summary explanation of the Maxwell (Heaviside) equations I have ever see, Thank you

[@Ayshafr]

Wow, if only this existed at the beginning of this year when I was taking electromagnetism 😭

[@ScienceAsylum]

😞

[@johnroberts7529]

Thanks once again for an engaging and clear presentation. I've always wondered about Maxwell's equations; now of course, I know a lot more. Yes please ... more videos like this.

[@mixpick138]

Great video! Going waaaay back, my high school physics teacher always had a great sense of humor and made the topics not only fun but accessible --you are cut from the same type of cloth so don't ever stop making these videos!

[@rockapedra1130]

Very nice. I'm an electrical engineer and I must admit I usually think of electricity as a fluid as much as I can. It's easy to visualize. Changing between "actual" and "analogy" becomes automatic on a as-needed basis. Works for me.

[@LacenWolk]

I wouldn't mind understanding schrodingers equasions a bit more

[@WigantX]

Let's think of a cat...

[@danarrow]

... and Dirac’s. Best of luck with that one.

[@Adraria8]

danarrow Still nothing compared to the Einstein field equations

[@jamestheotherone742]

Its all an approximation.

[@mrich4510]

After watching all those videos for years, i have to admit you're genius.

[@SuperVstech]

a

[@nazlone]

Plz don't stop ur videos. They r crazily interesting.

[@PeterMatisko]

Nick, this is really cool! I was struggling at my university physics classes to visualize these math operations. I asked my physics teacher to sit down with me and explain the math in a style a 6 year old could understand :) He used a very similar explanation style as you did in the video. The physics at our university was too mathematical. They just threw integrals and derivatives at us and "here you go, this is it". But what I like about physics is that there is always a good way to visualize the math laws. They always mean something practical. Please, keep making these vieos! I see there are already 9 frustrated dislikers who cannot understand the math :)

[@aloksahoo1383]

This is exactly what students need. Keep up the good work :)

[@tomasbdepaula]

Awesome. I'll definitely watch all videos you do like this one. Granted, I always watch your videos. They are among the best out there.

[@kaptensains1711]

This is probably the best video to visualize curl and divergence

[@ultravidz]

Magnificent, you’re severely underrated dude.

[@feynstein1004]

Yes, please. More videos like this. I really can't get enough lol

[@xgozulx]

this might be the best explanation of maxwell ecuations i have ever watched

[@markampatsidis8853]

You are an amazing "online" teacher: both from a scientific-teaching point of view and from a pedagogical point of view!!!

[@userBBB]

maybe you can do tutorial of how to make these animation it's so beautiful

[@CHAS1422]

Wish I had your lectures when I took physics.

[@engr.irfansultan]

Never knew that learning Maxwell's equations could be this much fun. Keep up the good work bro.

[@jlpsinde]

Go on Nick, please do more videos like this. Maths, equations, I'll show this video to my students of electromagnetism. Good work!

[@3SPR1T]

"constants are just there that the units work out" WHY HASN'T SOMEONE TOLD ME THIS EARLIER?!?!

[@guilhermetorresj]

That's how most constants work, when you get to derive your own formulas.

[@alphagt62]

Great stuff! A magnetic field cannot create current flow, unless it is moving. To get electron flow, we must move the magnets, or the wire. So this visualization explains exactly why that is!

[@adi331]

I don't think so, at least i don't understand which Visualization / which combination of Visualizations would explain that . Can you please elaborate ?

[@Arboldenrocks]

and actually what creates current flow is the moving current that generated the magnetic field, acting on other charges. the field is only the messenger between electric charge. the lines people draw are just a bookkeeping tool.

[@sjoerdwiesmeijer7231]

This is something I’ve been looking for a long time. I don’t know how you keep suprising me, Nick!

[@7654782l]

I got Maxwell"s equations! I never would have by looking at the math symbols as I am a Non-mathematician. Good Job and Thank You!

[@hyronvalkinson1749]

As an electrical engineer who knows everything you're talking about in this video like the back of my hand, I still am amazed at how much better you help me to understand everything. Where do you get these ideas from?

[@ScienceAsylum]

I'm always trying to think up new ways to explain things. Education is my thing 🤓

[@vasilischatzipanagiotou9051]

"nabla" feels ugly to Greek aesthetics. "Ανάδελτα" is a beautiful word

[@binita4672]

I watched so many videos on curl and div, yours is the one that helped me understand just perfectly in 8 mins. Thank you!

[@hankosaurus]

This is terrific. Anyone setting about to study the underlying math might benefit from having this presentation as an orientation into what the math is talking about. Yes, you should make more videos of this sort about electrodynamics, radiation/radio and so on. Splendid!

[@harishthethird]

Recommending 3Blue1Brown's divergence and curl video for a bit more of the 'math' part.

[@ScienceAsylum]

Link is in the description 🙂

[@joeserdynski1045]

Visualization of Heisenberg uncertainty principle would be great (how to measure velocity of a particle would be great (two positions ? ? ?))

[@Lucky10279]

Ted-ed did an excellent video visualizing this if you don't want to wait for Nick to do one.

[@tusharmergu2520]

This is the best video explaining maxwell's equation on youtube... THANKS ALOTTTTT!!!!!!

[@sash4all]

Truly the best channel of all, that's exactly how I've imagined this.

[@technicallittlemaster8793]

Do you even need to ask that??? Sure you have to make more videos on various physics topics to keep us enlightened

[@wingflanagan]

I like this kind of video. I've always had a trouble with math, because it is almost NEVER taught visually, and my learning modality is primarily visual. Once I have a visual metaphor, I can "get" it. I can attach the numbers. But without that, it's like pulling teeth to get it to stick in my noggin.

[@EduardodaSilva00]

This is one of the best videos I've ever seen. Please do more like this about quantum mechanics equations, like Schrodinger equation!

[@colmwhateveryoulike3240]

Brilliant video! You are so good at what you do. Very excited to buy your book asap!

[@henrymarckisotto9025]

A glimpse inside your head? Isn't that why we need the asylum in the first place? Edit: Thank you everyone for the likes! And thank you for the heart! I love these videos and have been trying to support the channel for a long time now. I think this is a great community of fans especially with all the younger kids and trolls on KZbin nowadays and how they act.

[@Jared7873]

🤪

[@subscribefornoreason7390]

Science is logical ,yet sometimes unintuitive. It isn't actually crazy at all.

[@guytheincognito4186]

@@subscribefornoreason7390 Yup. Unfortunately though flerfers don't understand this and it scares them.)

[@moebiusfan9545]

That was my thought! When he said "take you inside my head" I had to pause and think about whether or not to continue watching!

[@Markle2k]

Note for the future that you lose the heart when you edit your comment. Consider putting thanks in a reply to yourself if you care about that.

[@jamesmnguyen]

Ahh, yes, applying my Calc 3 class to real life.

[@PanPuszekMechanik]

Amazing video, straight to the point, with funny parts. Love it!

[@asif.a15]

I have exam tomorrow, and I'm crying out of gratefulness towards you ,thank you so much for these lesson.

[@ScienceAsylum]

Good luck!

[@PirateOnYoutube]

I was here when U had 3000subs, I will be here when U be over 6mln 👌🚀🍻

[@david21686]

Remember when Ampere actually said that curl(B) = J, and Maxwell was like, "Hold up, that's missing something!"? Edit: also, I'd be interested in seeing you explain magnetohydrodynamics and how stellarators will create fusion.

[@Ni999]

The Wendelstein 7-X stellarator (a magnetic plasma-confinement reactor) accomplished fusion in 2018. Stellarators are heralded as possibly being able to get to sustained plasma confinement before tokamaks but on the surface don't seem to have a path for cost-effective maintenance and that's crucial for getting from an experimental reactor to commercial power production. The SPARC tokamak is giving significant focus on that aspect. For anyone confused about the difference, a tokamak has a cavity in the general shape of a regular donut, a stellarator is like a cruller donut. The plasma flow and fusion happens in the donut-shaped cavity. The outside of the donut is surrounded by electromagnets - basically just like the LHC, in that regard (but not in operation). Take hydrogen and deuterium, strip away electrons to get a plasma, accelerate it in a circular magnetic bottle and increase pressure until the plasma fuses into heavier elements - stellarators and tokamaks. Keep it up until the fusion reactions (already accomplished for both types) produces more energy out than you put in (we're not there yet). After that, capture the energy so as to make it usable to run electric generators, after that provide a path for maintenance and upkeep, after that make them cost-effective, and after that, profitable. The press keeps insisting that we've always been promised fusion in 20 years. I have no idea who they think promised that but they're the same people who print the same story every year about how surprised they are about yet another experiment showing that Einstein was right about gravity but they're keeping an eye on it because you never know. (Yes. Yes I do hate them.)

[@shayanmoosavi9139]

Yes you absolutely should do more videos like this one. The visual intuition is very important to me and I always appreciate it. Thanks for this video :)

[@cjddavis84]

Nick, you are a brilliant and amazing public educator, and you have one of the best KZbin channels. I want to say thank you for all the work you do, and I hope more people support you by buying your merch and donating. Keep up the great work!

[@ScienceAsylum]

Thanks 😊

[@mask3dal3xx]

Can you make a video visualizing gravity? Gravity is not like other fields in the sense that there's close to no negative energy density. It would be very interesting.

[@ScienceAsylum]

I will be doing Einstein's equation if this video performs well.

[@txe9113]

2sec in, good video :D

[@ahvavee]

That curl stuck to the hand bit...so silly! I love it! 4:12

[@kushphus]

This guy is crazy! Love his explanations through visualisations. Plz continue making such videos.

[@JDLuke]

I put this on and wondered just what kind of drugs you were on. Then I realized I still had playback speed set to 0.75.

[@ScienceAsylum]

😂😂😂😂😂😂😂😂

[@hansisbrucker813]

Lol I bought the ebook this Sunday 🤣

[@deeprecce9852]

Absolutely love this presentation format!! Very Well Done!!! 👍👍👏👏👏

[@crewrangergaming9582]

This channel is very underrated.

[@John_Fx]

"I want to give you a glimpse inside my head" - I'm very afraid

[@ScienceAsylum]

Fair.

[@0x0404]

Awkward observer clone was putting in work.

[@mateuszkucharczyk2399]

Great video! Helped me in visualizing and understanding more Divergance and Curl. Thanks!

[@swapnilshrivastava6889]

The very first thing that got me excited about physics or science for that matter is that it's very interesting, expressed in a correct manner! Your visual explanations do just that! They are indeed very insightful. Thanks for the video.

[@mask3dal3xx]

Never clicked so fast. (Third comment)

[@andrewballr]

Definitely more videos. That was very instructive.

[@nachobalasch]

Awesome video! Thank you very much - it really helped me understand the equations a lot better.

[@alexdagios28]

please keep IT up with us Nick! GREAT video! simple as that

[@PresentMindedSG]

What a great idea for a video! I would personally love more of these equation visualisations

[@pjmichaelsrocksyou]

Good way to explain these concepts. Please keep posting videos. I’ll follow you.

[@cristinaalexe7454]

This was brilliant, would absolutely want more visualization videos!

[@studion9621]

Impressive, man. That's the best explanation I've ever seen.

[@operazionetrasparenza5297]

THANK YOU FOR SHARING YOUR KNOWLEDGE AND UNDERSTANDING WITH US

[@alexandrebatalha7253]

I love your videos about Physics! I'm a high school Physics teacher from Brazil and I like to thank you a lot for all the amazing videos. It's helping me a lot. Hugs

[@demetriusjohnson5358]

Just bought your book bro. Thank you for all the hard work! God bless you bro!

[@tamass-du5dx]

thanks man, this is exactly what i need for my final exams. a whole topic is about electromagnetism. although i'm quite familiar with the equations themselves, some good visualization (which i'm not good at by myself) truly supports me. keep it up!

[@edmatzenik9858]

Great way to visualise the equations. Keep 'em coming, please.