Divergence and Curl

[@EugeneKhutoryansky]

To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.

[@cool9930]

Hello do you need Arabic translation? im a math and statistics student from Montreal and speak Arabic fluently

[@EugeneKhutoryansky]

Although many of my videos already have Arabic subtitles available, many others still need them. If you would like to help provide Arabic subtitles, please send me an email. My email address is available in the "about" tab of my KZbin home page. I will email you the subtitle file in English (which includes the timings). You will then be able to edit the file to replace the English with the translation, and email the file back to me. I will then upload it to my channel. Thanks.

[@GauravSingh-sf3uu]

Please provide hindi subtitle.

[@achalbhoir1359]

19:23 if inner 4 particles are rotating anticlockwiz then what will be the sum? 2+2+2+2+2+2+2+2=16 + inside 4= 20 or 2+2+2+2+2+2+2+2= 16 - inside 4= 12?

[@georgehobbs5052]

After nearly 40 years of pondering vector calculus,I think you have explained line integrals,volume integrals and surface integrals and how they are all tied together,thanks.

[@EugeneKhutoryansky]

I have updated my KZbin User name and picture, to help people immediately recognize what this channel is about. As always, for each video that you like, you can help more people find it in their KZbin search engine by clicking the like button, and writing a comment. Lots more videos are coming very soon. Thanks.

[@MrCmagik]

+Physics Videos by Eugene Khutoryansky where's the puppy :(

[@EugeneKhutoryansky]

+ヌリシルヴァン, The puppy can still be seen on my Patreon page. :)

[@guitarheroprince123]

Thanks :D

[@El-ne3ln]

ɷɷɷɷ Heeyy Friendsssss I Have F0unddd Workingg Online Hacck visitttt : - t.co/bZI4TtjdlL

[@PrinceUchih25709]

How old r u ? ,i am 14 years old

[@VeganSemihCyprus33]

Best visual physics demonstration channel so far :)

[@EugeneKhutoryansky]

Thanks for the compliment.

[@tarifsiam9585]

Physics Videos by Eugene Khutoryansky

[@tarifsiam9585]

Physics Videos by Eugene Khutoryansky

[@seandafny]

+Physics Videos by Eugene Khutoryansky we love you

[@ergot1803]

Physics Videos by Eugene Khutoryansky

[@gurjindersingh8820]

Spend lots of time to understand actual meaning of divergence and curl and not succeeded , then found your video and understood in 25 minutes. Thanks you so much for these amazing videos. Best channel for Physics and mathematics.

[@EugeneKhutoryansky]

I am glad my video was helpful. Thanks for the compliments about my videos.

[@gurjindersingh8820]

@@EugeneKhutoryansky 🔥 Make more and more videos , I can spend hours and hours learning from your channel.

[@EugeneKhutoryansky]

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: kzbin.info_video?v=qOcFJKQPZfo&ref=share You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.

[@keset_startup]

is it possible to make not only subtitles but also a new voice in other languages?

[@cyberchamps2024]

I want to translate your voice into Urdu Language. Will you allow me to do so?

[@EugeneKhutoryansky]

The only way people can add a translation is by adding subtitles through the link above. Ifran, I just received subtitles in Urdu, which I assume are from you. Thank you very much. These subtitles are now available to people watching the video on my channel. People can see the subtitles by clicking on the gear symbol under the video, then clicking on "subtitles", then selecting the language.

[@nirmalaliyanaarachchi8724]

Hours of misunderstandings cleared up in 25 minutes. Thank you!

[@EugeneKhutoryansky]

+Nirmala Liyanaarachchi, glad I was able to help.

[@kakalimukherjee3297]

Remember you from a 3b1b vedio, if not I'm mistaken. Well, where are you now?

[@superstraight173]

@@kakalimukherjee3297 non of your business goddamit

[@Simply--Science]

years* of misunderstandings

[@boukharroubamediane119]

sincerely, I have just tangibly grasped the spatial meanings of the "rotational" vector and of the "divergence" scalar after having studied and manipulated them in math at the university, 45 years ago !! your videos are a blessing of rejuvenation !! I ❤️ them!

[@EugeneKhutoryansky]

Thanks. I am glad you like my videos.

[@PirateFunk]

I'm always happy to stumble on your videos when I can't get a concept through my head. So much better explained than in my engineering classes.

[@EugeneKhutoryansky]

Thanks.

[@dwnickerson]

Simple and elegant! Your videos are superb! I only wish that I would have come across them much sooner! Thank you for all your hard work Mr. Khutoryansky.

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad you like my videos.

[@eklavyachandwadkar6200]

One of the most beautiful and highly oriented educative video. The efforts given are worth praise. Thanks for the subtle visual explanation

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad you liked my video.

[@pendalink]

I can always go to a video involving the math of your topics following your newest video and follow it, thanks to how well you organize and present these. Thank you so much

[@bozo1977able]

Long ago, when I took a course on Electricity and Magnetism, the tracher didn't explain anything about curl, gradient or divergence. He only taught us the mathematical way they are calculated. Now, with this video I completely understood these terms. Thank you very much. Eugene Khutoryannky, for this and other axplanations you have given through your videos.

[@EugeneKhutoryansky]

Thanks. I am glad that my videos are helpful. The reason your teacher didn't explain it is most likely because he didn't understand it himself, and he was just repeating it the way he himself was taught. This is a very common problem.

[@fakherhalim]

I said that before, but each time I see a new one, I am forced to repeat! You are the best physics/math illustrator on this entire planet earth (known to me)!

[@EugeneKhutoryansky]

+Fakher Halim, thanks for that really great compliment.

[@Deepak-pi9xx]

These 25 minutes needed your hours of hardwork and it saved my hours of hard work to understand it so easily. I am studying engineering mathematics and wanted to understand physical meaning of Divergence and curl. Thank you, thank you, thank you. 😇

[@EugeneKhutoryansky]

Glad my video was helpful. Thanks.

[@royalromeo3156]

After completing my 1st semester I was totally disappointed to opt engineering because my love 'Physics' was continuously going far to me but thanx for your electric , magnetic field to create an attractive force between me and the Physics. 😍

[@zacharyp10]

This video was unbelievably helpful. This has shown to me that I am 100% a visual learner and that I should seek videos like this for topics I have a hard time grasping. I very much appreciate the effort that went into this!

[@EugeneKhutoryansky]

Glad my video was helpful. Thanks.

[@rodrigoappendino]

I finished an introdutory course of particle physics this semester. This video helped me a lot to visualize what I learned.

[@EugeneKhutoryansky]

+Rodrigo Appendino, Glad to hear that my video was helpful. Thanks.

[@CalebDiT]

You mean, this video helped you visualize what you didn't learn. :P

[@HassaanFareed]

ur channel is amazing and it helps me visualizing the concepts i cant before. i m from pakistan n really a fan of urs.

[@EugeneKhutoryansky]

+Cpalead Cpalead, thanks. I am glad you like my channel and that you have found it helpful.

[@hazemmmm9105]

The only time that I feel I am a physicist is the time I watch your videos. Perpendicularly thanks

[@EugeneKhutoryansky]

Thanks.

[@mohammadtarek4673]

I am really grateful that I found your channel. I thank you very much for your efforts and I really really hope that you stays interested and motivated in keeping producing such videos.

[@EugeneKhutoryansky]

Thanks. I am glad you like my videos. More videos are on their way.

[@KirkHammer-fj2of]

Holy Cow !! This is Blasphemy ,, back in my days , it took me weeks to imagine how a curl or divergence would look.

[@dc1049]

You do amazing work! Please continue to produce these videos, they are an absolutely fantastic resource for understanding these concepts better.

[@EugeneKhutoryansky]

+D C, Thanks for the compliment. Lots more videos are on their way.

[@tommarchner]

Excellent explanation and visual display. I've never really understood divergence and curl until now. Thanks much. You do a great service.

[@EugeneKhutoryansky]

Thanks.

[@johnsnow6612]

I like to watch your videos before learning more strict definitions, they help a lot.

[@quicklilac]

This visualization explains Divergence and Stokes theorems in the best way one could imagine. ❤️

[@easwareapps5191]

Excellent work. Never seen such informational videos anywhere else. No words to express my gratitude to you. Thnk you so much.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@intexclouds9607]

and this year's Nobel peace prize (for enlightening the world) goes to..... . love your work,sir.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@YWHW-y2m]

atleast it provides a ground for understanding,thumbs up for eugene and your team👍👍

[@EugeneKhutoryansky]

Thanks.

[@yoganandsoundararajan4238]

Hi Eugene Khutoryansky This video is amazing! Is it possible in future to cover topics like line and surface integrals and its applications???. Also green and stokes theorem.

[@theflaggeddragon9472]

+yoganand soundararajan For now try Khan Academy and Pauls online notes. Those are really good resources!

[@georgehobbs5052]

If you watch and think alittle that's exactly what the video goes thru,it's all there.

[@georgehobbs5052]

The orig Khan acad. video's on multivariate cal really suck,bad lots of errors,very poor,make more confusion than answer.

[@ritik84629]

Helmholtz Theorem too please.

[@federicovinelli164]

these videos are the best to develop some real math/physics intuition, every equation comes alive after watching them in these simulations, thank you so much!

[@EugeneKhutoryansky]

+Federico Vinelli Thanks for the compliment. I am glad that you like my videos that much.

[@Deepsingh-ok2eo]

Gravity is not responsible for people falling in love. But this video is responsible for falling love with you😍

[@EugeneKhutoryansky]

Thanks.

[@howmathematicianscreatemat9226]

@conacal rubdur ; nope. In the souther parts of the USA Eugene is a female Name. Listen to the voice and you will hear IT

[@Stocksn100]

@conacal rubdur The narrator is Kira Vincent. She is a voice actress.

[@yehiaelyamani6943]

Magnificent! Best visualization I've seen for such difficult concepts. Many thanks

[@coria6231]

Just when I have a multi variable calculus exam in hours and this is precisely the topic in the exam. Thanks Mr Eugene for a great video, greetings from Mexico.

[@EugeneKhutoryansky]

Thanks. I am glad my video was helpful.

[@michailmavromatis8287]

Simply amazing presentation.It is fantastic tool for understanding the terms of divergence and curl.!!

[@EugeneKhutoryansky]

Thanks.

[@heylofellas]

just an appreciation post. your videos are one of the primary reasons of my interest sparking in physics keep up the amazing work and inspiring people! You should know what you're doing is changing people's outlooks kudos!

[@EugeneKhutoryansky]

Thanks for the compliment about my videos. I am glad to hear that they are making a difference.

[@SHIFTKICK]

This is awesomely thorough and well-done. Good timing too: My multivariable calc final is on Thursday :)

[@EugeneKhutoryansky]

+SHIFTKICK Thanks for the compliment, and I am glad to have this in time for your final.

[@vincentporras4146]

1 year later, my multivariable calc final is tommorow. :)

[@alikhademi95]

SHIFTKICK oo

[@carolinekouri8951]

5 years later and mine is today!

[@SHIFTKICK]

@@carolinekouri8951 Wow...5 years. Good luck on your final!

[@parjohansson3118]

Another wonderful video! I am deeply impressed by how Eugene (and Kara!) can manage to explain so much math without (or, mostly without) using any formulas!

[@EugeneKhutoryansky]

+Pär Johansson Thanks. What I am trying to do is give people an intuitive understanding of what the formulas mean by visualizing images of what they represent. Once someone has this visualization, they can derive the formulas from the images. However, it doesn't work it the reverse order. Knowing the formula doesn't necessarily mean that someone can derive the image of what it represents. This is why I believe that the images are far more important than the formulas, and the images also make the topic accessible to more people.

[@acho8387]

+Physics Videos by Eugene Khutoryansky This is perfect for me because I am a pure visual learner and I can't learn anything if I don't see it moving... it's kinda unfortunate, but thanks to people like you, I can learn. Forever grateful here.

[@divyadl6228]

Really really helpful your videos Amazing work Thank youuu so much for you and your team for such a great work Keep going 👍🏾👊🏾💪🏾

[@sdsa007]

finally! i understand curl completely! and i now have extra intuition about divergence / flux ! thank you!

[@EugeneKhutoryansky]

Thanks. I am glad my video was helpful.

[@agrajyadav2951]

yay

[@yanggao2102]

This video is amazingly clear and informative. Thanks a bunch Eugene!!

[@Jeff7667]

It's incredible how easy the video is to understand, even to those without a background in mathematics or physics. The timing is perfect as well as my multivariate calculus final is tomorrow. Thanks!

[@EugeneKhutoryansky]

+coustyx, I am glad that I managed to finish this video in time for your final. And thanks for the compliment.

[@BrianJones01]

Your videos are amazing! I hope you know how much you are going to help people. Thank you!

[@EugeneKhutoryansky]

+Brian Jones, thanks for the compliment about my videos.

[@xinyuli9423]

OMG, it makes so much more sense to capture the flowing particles using a box instead of a ball! This way, you can easily decompose them in the direction of xyz (and generalize to higher dimension)

[@SHONSL]

Hail to the visual teachers!

[@kogx2]

Thank you so much for this great video. I am very happy to study with this subtitled video. For non-native english learner student like me needs also subtitile. So I appreciate so much! and I hope you'll keep uploading these great videos! thanks!

[@EugeneKhutoryansky]

Thanks. Glad you liked my video. More videos are on their way.

[@aryabhatt7375]

Great teaching in 25 minutes than wasting 1 hour in classes

[@太陽ぽかぽか]

Yes😊

[@Extensors]

I love 3000 ..who is explaining such a nice explanation I have ever seen!

[@syedshafintaosif1048]

this channel needs a noble prize

[@EugeneKhutoryansky]

Thanks for the compliment.

[@-SalimRaja]

I'd donate to you soon as I get a job. Thanks a lot! Excellent visual representation.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video that much.

[@mohammadayyubkhan8541]

Beautifully explained the concept and purpose of the Divergence and Curl.

[@EugeneKhutoryansky]

Thanks.

[@anuragmittal9816]

"Billion likes" Video , superb ...thanks for putting so much effort in it .

[@DeltaAccel]

This channel is truly worth it.

[@EugeneKhutoryansky]

+DeltaAccel, thanks.

[@tpespos]

This is an awesome way to picture what's happening in my E&M class right now

[@EugeneKhutoryansky]

+tpespos, Glad my video was helpful. Thanks.

[@jcharlesbayliss]

I love you you make this SO easy - I am sharing this will my ten year old son - because its so well done that he will get this too

[@EugeneKhutoryansky]

+Charlie Bayliss, Thanks for the compliment, and I hope your son enjoys my video too.

[@saikun0293]

I just love you Eugene! Your truly the best physics teacher....your videos seriously help me a lot...

[@EugeneKhutoryansky]

Thanks for the compliment.

[@Jesus-cm6ln]

Best physics channel ever

[@EugeneKhutoryansky]

Thanks for the compliment.

[@Jesus-cm6ln]

@@EugeneKhutoryansky please try to upload concepts upto graduate level or higher . 🙏🙏

[@umeshchandramakwana806]

Very nice visual explaination of difficult concepts...Thank you for making complicated things very easy to understand.

[@physicsphilosophy2492]

This is a Masterpiece video. I must say one of the best video I've ever watched and amazed

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@wadezhou8204]

This video is amazing, i'm a visual kind of person. Explaining with animation helps me a lot to understand the concept! Thank you for making the great content! :)

[@EugeneKhutoryansky]

Glad you liked my video. Thanks.

[@jo5804]

Hi Eugene Khutoryansky. Thanks for sharing you high quality visual physics demonstrations.😃

[@EugeneKhutoryansky]

Thanks for the compliment.

[@prateekthakur1848]

The music is the coolest part of this fun video.

[@mystic3549]

You and 3b1b together make my life so simple :) lovingg these masterpieces

[@EugeneKhutoryansky]

Thanks.

[@rajaaekant]

This channel is so underrated !!!

[@Singareddy123]

This Channel is just more than amazing.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@geetgeorge9696]

Thanks a lot, Eugene! Your video helped me a lot a lot a lot. I have been grappling with these concepts for a long time now! Subscribed! :) Rarely do I subscribe to a channel after watching just one video of theirs.

[@EugeneKhutoryansky]

+Geet George, thanks. I am glad you found my video helpful, and I am glad to have you as a subscriber. I hope you enjoy all my other videos too.

[@jhanvivadher257]

This was very useful to me..as i was unable to understand the physical interpretation of curl and divergence. Thank u so much for this useful information.

[@omega7377]

Great demonstration of fundamental concept regarding Electromagnetic Field Theory! Much thanks.

[@huihui666]

Oh damn.. just when I'm about to have my exam in multi variable calculus next Tuesday, you post this :D Gonna watch it for sure!

[@EugeneKhutoryansky]

+xihai luo, I am glad that I had this video out just in time for your exam. :)

[@coria6231]

Woah how about your grade? I just have my exam of multi variable calculus too in hours and the professor said in class "just study divergence and curl of a vectorial" and I found this

[@huihui666]

@@coria6231 I got 85. The final exam was pretty easy for the most part. Only question I messed up on was the last lol

[@coria6231]

@@huihui666 Bruh I finished my exam 30 mins ago and woah this wasn't the topic lol

[@huihui666]

@@coria6231 That's good because we definitely had 1 or 2 questions about divergence and curl

[@ni4egoneponyal]

Это лучшее объяснение I ever seen. Очень недооцененное видео

[@vikramgopinath8545]

This is the best explanation I had ever seen. Thank you!!

[@EugeneKhutoryansky]

Thanks for the compliment about my explanation.

[@sdsa007]

Thanks again i think this is my favourite video! It really helped my in my understanding of Nabla notation and Green’s Theorem… explained vis curl and divergance… AMAZING! THANK YOU!

[@EugeneKhutoryansky]

Thanks!!!

[@shubhimishra2067]

Best channel for studying physics.... plz keep it up

[@EugeneKhutoryansky]

Thanks for the compliment. More videos are on their way.

[@nafeesaneelufer5023]

The world of physics is full of imagination. Thanks a lot for converting this imaginative world into real world 😊😊👌👌👏👏 The more is our imaginative power the more we can explore in physics. But unfortunately all are not blessed with this imaginative power. But if they watch these videos they can surely develop imaginative power.

[@EugeneKhutoryansky]

Thanks.

[@yusufziyadilek1506]

Thank you, very good explanation helped me a lot. However it is kind of slow so that i recommend setting the speed of the video to 1.25 or 1.5.

[@CalebDiT]

As always, an invaluable contribution for those wishing to learn about these topics. Thanks, Eugene Khutoryansky. Have you considered making an Android/iPhone app, in which these physics concepts can be used and tested?

[@RubALamp]

I never quite visualized Ampere's Law well, you helped me a lot in this video!

[@ths3100]

This is awesomely brilliant. Thank you so much.

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad you liked my video.

[@pakeezaislam2737]

Hello,your vedios are so helpfull to understand the depth of things .great job...thanks for making this vedio

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@oraange]

Poetry in motion !

[@blueshadow8022]

Best explanation that I had ever seen💯👌

[@EugeneKhutoryansky]

Thanks for the compliment.

[@FaizanJatala]

Really its a nice work again...!! Thank u so much for this beautiful sharing

[@jlpsinde]

Really amazing, you deserve Patreon support!

[@EugeneKhutoryansky]

Thanks.

[@doesntmatter9996]

ridiculously lucid! couldn't thank you enough!

[@ahmeddraz962]

Thank you, I really like the combination of music and math and the super illustration of the sciences .

[@EugeneKhutoryansky]

Thanks.

[@davidbain701]

The three dimensional representational keep the mind clear And not flattering out as it can when things are written on a blackboard, thanks I find the imaginary concept insightful It makes you think that light has its negative inbuilt speed of light component So that a curl ,and divergence dampening effect stops opposing light source's from exceeding the speed of light

[@glorglory8738]

really thank you i v been trying to understand the curl for years and i couldnt but today finally i understood it after i watched this video really thank you

[@EugeneKhutoryansky]

I am glad to hear that my video was helpful.

[@aurelienmorel2585]

incredible video to visualize vector analysis and particularly Stokes theorem, great thank you

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@Azzinoth224]

You can also have divergence if the volume is accumulating particles by increasing the particle density inside, without actually destroying particles. I think that would be important to mention.

[@EugeneKhutoryansky]

Not if the region has a volume that approaches zero, since there is no place for the extra particles to go. And divergence deals with regions which approach zero volume, so that you can specify the divergence at each point in space.

[@Azzinoth224]

@@EugeneKhutoryansky Well,in that case it can take an infinitesimal amount of particles. The point is that if density is changing you have non zero divergence, that is what the continuity equation is telling you. For example consider air flow. The total mass of the air in the room has to be conserved, so you are not actually creating or destoying any particles. But if the air density is changing in some point, the air flux has non-zero divergence in that point. See en.wikipedia.org/wiki/Continuity_equation#Differential_form.

[@Santiagu01]

thanks for the explanation !!! You made me visualize something i been using for years but didn't completly understand :o

[@EugeneKhutoryansky]

+Santiago Agudelo Montoya, glad to hear that my explanations was helpful.

[@Mystl2]

superb graphics, very informative and educational subjects, please keep up the terrific work, which I know is not easy

[@EugeneKhutoryansky]

+Mystl2, thanks for the compliment. More videos are on their way.

[@calebmitchell6870]

You are a saint Eugene! I'm going to have to donate some of my student loans to your patreon. :)

[@AnchitSrivastava]

Very lucid visual interpretation of Divergence and Curl with good animation and explanation. Lot of time and work is required for such animated videos, Kudos to you for making such videos. Hope you make videos on Maxwell's equations.

[@EugeneKhutoryansky]

Thanks for the compliment, and I already have a video on Maxwell's equations. It is at kzbin.info/www/bejne/b4XQY5Zsg697ars

[@AnchitSrivastava]

oh thanks

[@ranjeetagupta9024]

You guys just blew my mind

[@cayezara8110]

Amazing illustration, it makes mathematics a wonderful and fun! Wow!!

[@EugeneKhutoryansky]

Thanks for the compliments.

[@ankushankush4665]

its like musical mathematics. i feel relax and very calm watching them. you animate very nicely. please, if you can make videos on computation physics i would really love to watch them.

[@EugeneKhutoryansky]

Thanks for the compliments. I don't know if this is what you mean by computational physics, but I have a video on how to do physics simulations at kzbin.info/www/bejne/Y5_FhaWGrLaomtE

[@jithunniks]

You are doing a really amazing job....

[@EugeneKhutoryansky]

Thanks.

[@infinitylove2713]

Thanks for giving this wonderful video

[@EugeneKhutoryansky]

Thanks.

[@gurpreetlubana4618]

Finaly I understand divergence and curl thanks a lot dear.....

[@jollyjokress3852]

I'm like: whaat?? All the time. I have no idea for what this is purposeful but some of this is deeply exciting stuff!!