The 4 Maxwell Equations. Get the Deepest Intuition!

[@fufaev-alexander]

Do you want to solve every physics problem? Try my book! eBook: en.fufaev.org/physics-equations-book Paperback: tinyurl.com/physics-paperback Hardcover: tinyurl.com/physics-hardcover

[@jickbalinario6300]

thank you

[@Matlockization]

By removing the arrow indicating a vector your making your explanation harder to understand by the layman. So let the equations be ugly !

[@frankdimeglio8216]

WHY AND HOW THE BALANCED, TOP DOWN, AND CLEAR MATHEMATICAL UNIFICATION OF PHYSICS/PHYSICAL EXPERIENCE IS CONSISTENT WITH F=MA AND E=MC2: The following also CLEARLY explains why the rotation of WHAT IS THE MOON matches it's revolution. c squared represents a dimension of SPACE on balance WITH the fact that the stars AND PLANETS are POINTS in the night sky. Indeed, the sky is blue; AND what is THE EARTH/ground is ALSO BLUE (on balance) !! Consider what is the speed of light (c) ON BALANCE. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light (c) (ON BALANCE); AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is (CLEARLY AND necessarily) proven to be gravity (ON/IN BALANCE). General Relativity is directly taken from Special Relativity. E=mc2 is taken directly from F=ma. CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); as the stars AND PLANETS are POINTS in the night sky. Consider TIME (AND time dilation) ON BALANCE. I have exposed Einstein. Beautiful. Note: Consider what is THE EYE ON BALANCE. Think carefully about the black “space” AS WELL. Great. It ALL CLEARLY makes perfect sense, as BALANCE AND completeness go hand in hand. THE EYE represents a two dimensional surface OR SPACE (ON BALANCE) that is consistent with F=ma AND E=mc2. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN/ON BALANCE. Consider what is THE SUN. The sky is blue, and THE EARTH/ground is ALSO BLUE. Again, the stars AND PLANETS are POINTS in the night sky. GREAT. E=mc2 IS F=ma. This explains the fourth dimension AND the term c4 from Einstein's field equations. BALANCED inertia/INERTIAL RESISTANCE is fundamental. By Frank Martin DiMeglio WHAT IS E=MC2 is taken directly from F=ma, as the rotation of WHAT IS THE MOON matches the revolution; as TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. c squared CLEARLY represents a dimension of SPACE ON BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). The stars AND PLANETS are POINTS in the night sky ON BALANCE. Great. It is proven. WHAT IS E=MC2 is taken directly from F=ma, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); as the stars AND PLANETS are POINTS in the night sky. Consider TIME (AND time dilation) ON BALANCE. Consider WHAT IS THE EYE ON BALANCE. Great. Consider what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE. WHAT IS E=MC2 is taken directly from F=ma. Great. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). By Frank Martin DiMeglio

[@frankdimeglio8216]

Maxwell's equations are fundamentally consistent WITH what is E=MC2, particle/wave duality, TIME, AND the second dimension in/of SPACE (ON BALANCE), AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Great. c squared CLEARLY represents a dimension of SPACE ON BALANCE. By Frank Martin DiMeglio

[@frankdimeglio8216]

Consider what is E=MC2. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). It is imperative to consider why and how it is that there is something instead of nothing ON BALANCE. WHAT IS GRAVITY is, ON BALANCE, an INTERACTION that cannot be shielded or blocked. Consider TIME AND time dilation ON BALANCE. Consider INSTANTaneity. Excellent. By Frank Martin DiMeglio

[@christianlibertarian5488]

40 years. That's how long I have known about, and not understood, Maxwell's equations. A 40 year quest has come to an end.

[@umeshchandramakwana806]

@@jewulo Really it is true for most of us!

[@maskedmarvyl4774]

I blame the teachers. They explain principles to their students as if they already understand the subject, all of its terms, and calculus. A professor that doesn't assume any of that and explains all of the principles, terms and math clearly is a rare gem.

[@carlospascua5902]

May I just ask (without being in any way disrespectful) how have known 40 years about it but never understood them?

[@christianlibertarian5488]

@@carlospascua5902 Sure. I know the symbols. I know how to do the math. But I didn't understand what the math implied.

[@davewilson13]

As a physics professor I’m delighted to hear you finally were lead to the understanding. I only wish it could have come sooner.

[@izelyldrm6498]

That is how everyone should explain physics. No more words needed.

[@fragilephoton]

This is what Einstein meant when he said "you understood it if you can explain it to a 6 year old". Brilliant explanation with pace slow enough to grasp everything and fast enough to explain all four law under 40 mins

[@veerajvishnu899]

I'm honestly speechless. I've never seen Maxwell's eqs explained so neatly and concisely. It's like you knew exactly what I wanted. Thank you!

[@fufaev-alexander]

Wow, thank you for the motivating comment!

[@jinshokai]

This video is Gold. I want to cherish it forever hahaha

[@frankdimeglio8216]

E=mc2 is taken directly from F=ma, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. (Accordingly, ON BALANCE, c squared CLEARLY represents a dimension of SPACE.) Consider what is a two dimensional surface OR SPACE ON BALANCE. (Consider what is THE EYE ON BALANCE.) Notice the TRANSLUCENT blue sky ON BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE). Indeed, the stars AND PLANETS are POINTS in the night sky ON BALANCE; AND consider what is the speed of light (c) ON BALANCE; AS this CLEARLY explains (or proves) the fourth dimension. Carefully consider what follows. (Notice that the Moon is ALSO BLUE.) E=mc2 is taken directly from F=ma, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches it's revolution. Accordingly, ON BALANCE, the fully illuminated (AND WHITE/SETTING) Moon IS about one quarter the size of what is the Earth. Indeed, what is the orange (AND setting) Sun IS ALSO the SAME SIZE as what is THE EYE ON BALANCE. (Lava is orange, AND it is even blood red; AND the bulk density of lava is comparable to that of basaltic lava on the Earth.) In fact, it is now explained why the crust of WHAT IS THE MOON is about TWICE as thick on it's far side. Gravity is an interaction that cannot be shielded (or blocked) ON BALANCE. Again, E=MC2 is taken directly from F=ma; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE). Notice that said Moon AND said Sun manifest (or form up) at EYE LEVEL/body height, AND the curvature or shape of said Moon DOES match that of what is THE EARTH/ground (given what is a CLEAR horizon, of course). The stars AND PLANETS are POINTS in the night sky ON BALANCE. Notice that TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Carefully consider what is THE SUN AND what is THE EYE (ON BALANCE). E=mc2 is taken directly from F=ma, AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity ON/IN BALANCE. Magnificent. I have mathematically proven what is the fourth dimension. Finally, the illumination regarding said Moon AND said Sun does appear to be (or it is basically) the same. Now, what are the tides are CLEARLY (AND NECESSARILY) electromagnetic/gravitational (ON/IN BALANCE). Indeed, the average tide IS about six feet; AND the tide in the middle of the ocean is about two feet. Magnificent. Remember what is lava ON BALANCE. GREAT. By Frank Martin DiMeglio

[@nagarajamk7026]

One of the finest form of explanation heard in my life time. Great.

[@flophy5991]

You explained maxwell's equations better in 40 minutes than my professor could in 5 hours of lectures (and saved me from failing my electromagnetism exam next week). thank you so much dude

[@breveennkukan3603]

Brilliant video. I cannot praise it enough. As the other comment said, after 20 years I finally understand Maxwell’s equations thanks to you.

[@francescaerreia8859]

Idk much about physics but I just learned about geometric algebra recently and I hear it provides an even deeper intuition into this.

[@annyali4542]

You just made me understand not Maxwell's equations only but you also explained line/surface integral in a deep way, really it is the deepest intuition!

[@whatelseison8970]

The slide whistle really helped my understanding of these topics. You have a real gift for this may friend!

[@TheToffeyman]

You are a global treasure sir. Keep doing what you're doing, soon you'll have the follow base and the recognition you deserve!

[@hanyan8106]

谢谢！

[@tycobrahe7663]

Brilliant! If this is how Maxwell’s equations are held in your mind, I wonder about all the other concepts in physics that you hold in your mind - they must be held with such tremendous clarity. This clear video is possible because you must have put in the work to understand the underlying concepts in their most fundamental simplicity. I’m eager to see other videos by you and have subscribed to your channel.

[@SabaQamar-xu9hl]

BEST VIDEO FOR MaXWELL EQUATIONS WITHOUT ANY DOUBT....

[@mathathiknai]

This is the best video I have ever found on internet explaining Maxwell equation with such an amazing clarity. After watching the whole video I took no time to subscribe this channel. :-)

[@jackmaxwell3134]

I can't imagine the level of work you must have done to do this video! Thank you so much!

[@konuljafarova4159]

This is by far the most explanatory, clear video on youtube

[@YanJiang-i8l]

谢谢！

[@kwf3068]

多謝！

[@fufaev-alexander]

谢谢你的捐赠 😍

[@kola86]

Danke!

[@fufaev-alexander]

Thank you for the donation!

[@pasixty6510]

The most comprehensive explanation of Maxwells ideas, I’ve seen yet. Thank you so much. I hope, my fellow antenna developers enjoy this as much as I did.

[@fufaev-alexander]

Thank you! #### Become a channel member 🏆 #### As a channel member you have many cool benefits: * Badge next to your name * Unique channel emojis * Your vote counts 10x! * and much more kzbin.infojoin ############### Of course, I would also appreciate a small donation: tinyurl.com/denker-donate -------- Top supporters appear here: universaldenker.org/hall-of-fame

[@frankdimeglio8216]

@@fufaev-alexander Einstein never nearly understood the mechanism of gravity. Einstein never nearly understood what is gravity. Einstein never nearly understood TIME. Einstein never nearly understood what is E=MC2. I have surpassed Einstein and Newton. FACTS. The coronal heating problem in solar physics relates to the question of why the temperature of the Sun's corona is millions of kelvins versus the thousands of kelvins of the surface. I have solved the problem. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Inertia/INERTIAL RESISTANCE is proportional to (or BALANCED with/as) GRAVITATIONAL force/ENERGY, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). This CLEARLY explains what is E=MC2 AND F=MA ON BALANCE. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !! What is E=MC2 IS dimensionally consistent. What is GRAVITY IS, ON BALANCE, AN INTERACTION that cannot be shielded or blocked. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE (ON BALANCE). Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution. “Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/AS what is BALANCED electromagnetic/gravitational force/ENERGY, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! Magnificent. Consider WHAT IS THE SUN ON BALANCE !!!! THINK. Consider why and how that there is something instead of nothing ON BALANCE. Consider what is THE EYE ON BALANCE. The first, second, AND third dimensions in/of/AS SPACE are BALANCED !!! (Consider TIME AND time dilation ON BALANCE !!!) The stars AND PLANETS are POINTS in the night sky ON BALANCE !!!! TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). I have CLEARLY explained, ON BALANCE, how and why a given PLANET (including what is THE EARTH) sweeps out equal area in equal TIME. Great. By Frank Martin DiMeglio

[@mateuschahinsantos9040]

This might be the first "understanding the maxwell equations" that I actually understood them. Great video!

[@fufaev-alexander]

Thank you! #### Become a channel member 🏆 #### As a channel member you have many cool benefits: * Badge next to your name * Unique channel emojis * Your vote counts 10x! * and much more kzbin.infojoin ############### Of course, I would also appreciate a small donation: tinyurl.com/denker-donate -------- Top supporters appear here: universaldenker.org/hall-of-fame

[@njmikeche5575]

I'm a Chemical Engineer, so although we learned these in school I never really properly got my head around them. These are sort of fluid flow equations, but we don't really use the actual vector calculus itself very much. I always wished I had a better intuitive grasp of these and now I do! Thank you.

[@cstruble2]

There should be a Nobel prize for explaining complex ideas, and Universaldenker should win it.

[@peytonfitzgerald4216]

That is the greatest explanation of the divergence and curl theorems I have ever heard.

[@nrosquist]

Thanks!

[@fufaev-alexander]

Hey Herbie! Thank you for your donation! I really appreciate it!

[@nrosquist]

@@fufaev-alexander This lesson is amazing, and the understanding priceless!

[@tominsoftware]

What a beautiful explanation. One of the best videos on scientific phenomena. Thank you so much!!

[@alexxans1154]

The video is incredible. In just 40 minutes it dissects and analyzes each aspect of the equations and comes the a conclusion about what they actually mean. It's honestly amazing

[@fufaev-alexander]

Thank you, such comments motivate me a lot! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzbin.infojoin

[@frankdimeglio8216]

@@fufaev-alexander THE CLEAR, MATHEMATICAL, INTEGRATED, EXTENSIVE, LOGICAL, BALANCED, AND IRREFUTABLE PROOF THAT ELECTROMAGNETISM/energy is gravity: One, TWO, AND three dimensional SPACE are CLEARLY and perfectly consistent with what is E=MC2, TIME, AND what is GRAVITY. Consider what is THE EYE along WITH the fact that the stars AND PLANETS are POINTS in the night sky ON BALANCE. (c squared CLEARLY represents a dimension of SPACE ON BALANCE !!!!) What is E=MC2 is taken directly from F=ma, AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE); AS the rotation of WHAT IS THE MOON matches it's revolution; AS the stars AND PLANETS are POINTS in the night sky ON BALANCE. Indeed, TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Great. By Frank Martin DiMeglio

[@zakirhussain-js9ku]

Best explanation of maxwell equations on youtube. Simple, clear and crisp.Well done.

[@fufaev-alexander]

Wow, thank you for your feedback! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzbin.infojoin

[@MusicEngineeer]

amazing! it not only explains the maxwell equations themselves but also the divergence-theorem and curl-theorem along the way. and everything in very intuitive terms. i like especially, how the equations are correlated with the visual depictions - like having the symbolic mathematical equations drawn above an "equation of pictures". thank you very much. i'm looking forward to the derivation of the wave-equation from the maxwell equations!

[@artificialharmonic3527]

This ist a stupendous didactic effort and absolutely fantastic! Thank you so much!!

[@Bernhardseckm]

This channel is a hidden gem on KZbin

[@fufaev-alexander]

And your comment is my motivation boost!

[@timurzhakeyev5149]

There are one of the best explanation what I know from more than 45 years when I had started university course of potential field. Thank you very much.

[@helmutalexanderrubiowilson6835]

I am a wireless network designer 20 years of experience And must say thank you sir.. you solved all my questions i had about what is exactly a radio wave. I know its behaviour in practices but i didnt understand all the datails about how brillant minds like maxelll could visualize all this complexity of a physical phonomena and express it in such an elegant way. THANK YOU!

[@marcoantonioalcazarperedo8846]

After watching this video, I had a profound spiritual experience, because I understood four of the most fundamental principles in our universe. I'm so grateful and I hope to see more content :) Nice Job!!

[@jorn-michaelbartels9386]

Endlich eine einfach verständliche Erklärung der Maxwell-Gleichungen. Super! Da ich ein kleines Kind habe, kann ich zwar das Video nicht in einem Rutsch gucken, aber ich bin mir sicher, dass ich zumindest eine ganze Menge mehr verstehen werde als in jedem anderen Video zu den Maxwell-Gleichungen. Bin begeistert!

[@bhuvan1036]

Damm, I learnt more in these 40 minutes than around 50 * 40 hour sessions in class. Can't thank you enough!!

[@TlouMoloko-t1p]

This guy is the future. Thank you from South Africa.

[@fredg8328]

I learned these equations 20 years ago and forgot most of their meaning. Thank for this great reminder. That's the clearest explanation I've seen so far.

[@tigrayrimey6418]

I don't think if Maxwell could have explained like this! I heard people say teaching is an art I have seen it here! So explicit and delivered in a very brilliant approach. This must be the best lecture video on Maxwell Equations otherwise equal. Keep up the great work!

[@youwillseelikethis]

This was by far the best video I watched on Maxwell equations. Thanks for your work!

[@rndtnt]

this video successfully summarized 3 weeks cours material at electromagnetism, big thanks

[@fufaev-alexander]

you're welcome, Rafi! 🤝

[@frankdimeglio8216]

@@fufaev-alexander TIME dilation ULTIMATELY proves ON BALANCE that ELECTROMAGNETISM/energy is gravity. This necessarily represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE !!! Indeed, TIME is NECESSARILY possible/potential AND actual IN BALANCE; as ELECTROMAGNETISM/energy is gravity ON BALANCE !!!! Great !!!! By Frank DiMeglio

[@vincentkaruri2393]

Best video on the internet on this topic!

[@attilauhljar3636]

Clearest explanation I've seen so far, thank you so much!

[@jmcorpuz1]

Thanks for this. This is the best explanation that I have ever watched so far

[@fufaev-alexander]

Thank you John! #### Want more videos? #### As a channel member you have many cool benefits: ✅ Unlock ALL Physics Videos ✅ Channel Badges For Your Nickname ✅ Unique Channel Emojis ✅ Your Vote Counts 10x in Polls ✅ Immortalization in the Hall of Fame ✅ And that's not all! CLICK -> kzbin.infojoin

[@Delta._]

My God! What did you just explained? I owe you something. Thank you so much from my little heart.

[@mahmoudelnaggar8630]

Keep illustrating physics like that, that's brilliant ♥️

[@christophgrauel9357]

After having studied most of the really great lectures on electrodynamics by Prof. Paul Wagner (Vienna) I ran into this video and was flashed immediately - a perfect summary of the four Maxwell laws. Thank you so much for this! Sometimes, however, you find an even more compact version for the 4th Maxwell equation, using the magnetic field strength H which even eleminates the field constants µ_0 and ε_0.

[@Cdglass]

Finally :) I found a channel that goes into the maths of it like my teacher !! (I’m a first year polytechnic student from Brussels and you have all my thanks)

[@fufaev-alexander]

Nice! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzbin.infojoin

[@edvargas3105]

One of the best explanations of Maxwell's equations. Great job!!!

[@vinceespiritu4407]

This is so enjoyable to watch. This is how learning should feel like! (not like the boring lectures in class)

[@Eldi-Kwetu]

not a Physicists by you made me understand this concept . Thank you. very very well done. I am so grateful.

[@Eric-jh5mp]

What a beautiful video. A perfect mixture of intuitive imagery and well-defined mathematics. I haven't learned electrodynamics in the last 3 years, so I'm very rusty. This was a great way to revisit it quickly and get a better intuition then I had before. Thanks for the video!

[@Idkwhattonamess]

Yes it is

[@eduardoteich5892]

The best explanation i have ever seen. Thank you very much!

[@joelwong62]

Just found out this video, and this makes my day! Amazing job sir! Looking forward to your other videos sir.

[@uceee1]

+1

[@frankdimeglio8216]

@@uceee1 Consider what is E=MC2. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). It is imperative to consider why and how it is that there is something instead of nothing ON BALANCE. WHAT IS GRAVITY is, ON BALANCE, an INTERACTION that cannot be shielded or blocked. Consider TIME AND time dilation ON BALANCE. Consider INSTANTaneity. Excellent. By Frank Martin DiMeglio

[@andreadanesi53]

On YT this is the best video about the 4 Maxwell's Equations. I've seen so many videos in order to understand them but noone's explanation made them so clear as you

[@Idkwhattonamess]

Maxwell is such a great physicist, and you are a great physics communicator

[@ravikantpatil3398]

Simply amazing explained. Thanks🙏🙏

[@junchaochang6962]

The best videos about Maxwell’s equations I have ever watched,thanks very much

[@fufaev-alexander]

Thank you for your positive feedback! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzbin.infojoin

[@valerifumero2486]

Absolutely true!! I'm a high school physics teacher and this is the best way I've ever seen to explain Maxwell's equations to the students. It's a class by itself!!

[@edvargas3105]

The most detailed and brilliantly explained Maxwells equations. Thank you

[@danielmacfarlane4575]

If you keep the vector variables bold, but put a full arrow above the vector variables, I would hands down recommend this video to all my STEM buddies. It is jam packed with good stuff and makes me feel like I am getting something out of my second physics course. The use of bolding the vector variables is justifiable in the context of this particular video, because the animations and commentary explicitly demonstrate that the bolded variables are indeed vector quantities. In some ways expressing vector variables with an arrow above them and unit vectors with a ^ hat is more beautiful compared to leaving them off and bolding the variable for several reasons: 1. Someone who has never seen multivariable vector calculus can intuitively see with almost no explanation that something is different about the variables with the arrows compared to the variables without. This is great for people who are learning the material for the first time. 2. They serve as an intuitive reminder that the variable represents a vector. Much in the same way that the circle in the integral reminds us that we are dealing with a closed shell (surface of a potato). 3. Expressed with arrows the equations can be written the same way on paper as they are viewed in the video which reduces the cognitive burned in applying the equations to solving homework problems. 4. Also those with poor eyesight might not be able to distinguish the difference between bolded and unbolded variables.

[@LaurenceRonayne]

That is the best explanation of vector calculus and Maxwell's equations ever. Awesome.

[@rd-tk6js]

Best concise yet complete explanation of Maxwell's equation on the web, thanks !

[@fufaev-alexander]

Hey rd, thank you very much!

[@frankdimeglio8216]

@@fufaev-alexander Einstein was a weasel. DiMeglio is the mastermind.  Frank Martin DiMeglio 2h Do objects fall at the SAME RATE for the same reason that planets orbit the Sun at distances that are irrespective of any given planet's "mass"? Yes. Here's the CLEAR mathematical proof. THE CLEAR AND BALANCED UNDERSTANDING OF PHYSICS/PHYSICAL EXPERIENCE AND TIME: Consider THE EYE. CLEARLY, WHAT IS E=MC2 is KEY to understanding WHAT IS GRAVITY (ON/IN BALANCE). Indeed, c squared CLEARLY (AND NECESSARILY) represents a dimension of SPACE ON BALANCE !!! Consider what is the fourth dimension. CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); as the stars AND PLANETS are POINTS in the night sky. Consider TIME AND time dilation ON BALANCE. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). A given PLANET (including WHAT IS THE EARTH) sweeps out equal area in equal TIME. The ultimate mathematical unification AND UNDERSTANDING of physics/physical experience (AND TIME) combines, BALANCES, AND includes opposites. The rotation of WHAT IS THE MOON matches the revolution !!! Consider WHAT IS THE EYE ON BALANCE !!! Consider WHAT IS E=MC2 ON BALANCE !!! It is KEY to understanding what is gravity (ON/IN BALANCE), AS the INTEGRATED EXTENSIVENESS of thought (AND description) is improved in what is the truly superior mind. Consider, ON BALANCE, WHAT IS the fully illuminated (AND setting/WHITE) MOON !!! (It IS the SAME SIZE as what is THE EYE !!!!) INDEED, consider why and how it is (ON BALANCE) that there is something instead of nothing. Magnificent !!! It ALL CLEARLY makes perfect sense ON BALANCE. (BALANCE AND completeness go hand in hand.) Think. Great. Consider what is the man (AND THE EYE ON BALANCE) who IS standing on what is THE EARTH/ground. WHAT IS GRAVITY is, ON BALANCE, an INTERACTION that cannot be shielded or blocked !!! Great. Notice what is the orange (AND setting) Sun ON BALANCE. Notice WHAT IS the TRANSLUCENT AND BLUE sky ON BALANCE !!! Again, ON BALANCE, consider what is THE EYE !!!! CLEARLY, WHAT IS E=MC2 is KEY to understanding WHAT IS GRAVITY (ON/IN BALANCE). MAGNIFICENT. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! By Frank Martin DiMeglio WHAT IS GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. WHAT IS E=MC2 IS dimensionally consistent, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! BALANCE AND completeness go hand in hand. GREAT !!! WHAT IS GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. (WHAT IS E=MC2 IS dimensionally consistent.) Consider what is the man (AND THE EYE ON BALANCE) who IS standing on WHAT IS THE EARTH/ground, AS touch AND feeling BLEND; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !!! BALANCE AND completeness go hand in hand. WHAT IS GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. WHAT IS E=MC2 IS dimensionally consistent, AS “mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/AS what is BALANCED electromagnetic/gravitational force/ENERGY; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE (ON BALANCE). INDEED, GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !!! The stars AND PLANETS are POINTS in the night sky. WHAT IS E=MC2 IS dimensionally consistent !!! Accordingly, ON BALANCE, THE PLANETS (including what is THE EARTH) sweep out equal areas in equal times. Consider TIME (AND time dilation) ON BALANCE. WHAT IS E=MC2 is taken directly from F=ma, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). WHAT IS GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. WHAT IS E=MC2 IS dimensionally consistent !!! CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); as the stars AND PLANETS are POINTS in the night sky. Consider TIME (AND time dilation) ON BALANCE. INDEED, TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! GREAT !!! ACCORDINGLY, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution. GREAT !!! WHAT IS E=MC2 IS dimensionally consistent. GREAT !!! It is a very great truth that the SELF represents, FORMS, and experiences a COMPREHENSIVE approximation of experience in general by combining conscious and unconscious experience. INDEED, the INTEGRATED EXTENSIVENESS of THOUGHT AND description is improved in the truly superior mind. BALANCE AND completeness go hand in hand. By Frank Martin DiMeglio

[@robertrogers7331]

Thank Goddess that you speak carefully and distinctly. Thank you!

[@fufaev-alexander]

Thank you for your positive feedback, Robert Rogers! #### Become a channel member 🏆 #### As a channel member you have many cool benefits: * Access to premium videos * Badge next to your name * Unique channel emojis * Your vote counts 10x! * and much more kzbin.infojoin ############### Of course, I would also appreciate a small donation: tinyurl.com/denker-donate -------- Top supporters appear here: universaldenker.org/hall-of-fame

[@sammradha7628]

Deserves more than million views..great explanation ever experienced !!!

[@fufaev-alexander]

Thank you very much! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you like my channel and like my videos, I would be happy about a small donation: tinyurl.com/denker-donate Top supporter appear in the Hall of Fame: universaldenker.org/supporter

[@roncho]

You deserve all the views and all the likes in the world. This is the clearest explanation of maxwell equations ever... I could not explain it better and i have ten years teaching this topic. I am learning a lot from you.

[@fufaev-alexander]

Hello Helmut, thank you very much for you positive feedback. I really appreciate it! 🙂

[@subuhulfatirissamawatrajab7727]

Sharp and clean explanations. Thank you.

[@fufaev-alexander]

Thank you too! 😎 Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzbin.infojoin

[@geliogene2181]

The best explanation of Max's equations I've ever seen in my entire college studies

[@natejack2292]

Starting grad school in physics this fall, researching superconductivity. This was an amazing summary! I have a feeling I'll be back

[@jackshymin7356]

This is so helpful, thank you so much for making this video!! You're saving my life and your explanations are very clear!

[@hermanfourie66]

You are the best! Thanks for helping me understand this!

[@ChrisInmanDrums]

Just excellent. What a blessing to live in these times, with videos like this at our fingertips when we so desperately need them. Without this the banging-my-head-against-the-wall currently going on around this topic would've carried on into the very distant future.

[@rubysayeed6676]

u are the teacher we need in colleges

[@herbertzeller8181]

Fantastic video! This not only helped me to finally grasp what I learned about vector fields in calculus like 2 years ago, it also allowed me to finally understand these fundamental equations I've heard much about but never really understood how they work. Thank you!

[@MissPiggyM976]

Best explanation ever seen !

[@fufaev-alexander]

Thank you! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you like my channel and like my videos, I would be happy about a small donation: tinyurl.com/denker-donate Top supporter appear in the Hall of Fame: universaldenker.org/supporter

[@sanjivoddi9268]

GREATEST EXPLANATION EVER! MAN WHAT A VIDEO, Till now in all my physics courses which I have attended they just explain Maxwell's equations in a very abstract way using very complicated phrases whereas here by explaining the stokes theorem and green theorem using effective animations the concept and getting built in front of our eyes.

[@fufaev-alexander]

Thank you very much for the positive feedback!

[@smitboraniya6752]

THE BEST VIDEO TO UNDERSTAND MAXELL'S EQUATIONS.

[@fufaev-alexander]

Thank you! #### Become a channel member 🏆 #### As a channel member you have many cool benefits: * Badge next to your name * Unique channel emojis * Your vote counts 10x! * and much more kzbin.infojoin ############### Of course, I would also appreciate a small donation: tinyurl.com/denker-donate -------- Top supporters appear here: universaldenker.org/hall-of-fame

[@marspalk7611]

Most beautyfully explained complex subject. My college professor did not explain this well because did not know any better. Job well done and every minute of this video worth it.

[@santoshkunte6642]

Brilliantly explained

[@fufaev-alexander]

Thank you! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you like my channel and like my videos, I would be happy about a small donation: tinyurl.com/denker-donate Top supporter appear in the Hall of Fame: universaldenker.org/supporter

[@MEDSNMN]

One of the best videos on understanding Maxwell's equations. Thank you for doing such a great job explaining these concepts!

[@joseclementenavarrete6982]

You have accomplised to simplified the complex - for the didactical purposes and the aimed audience, this what you have done here is extraordinaire, thanks a lot, muchas gracias desde Mexico.

[@fufaev-alexander]

Wow, thanks!

[@sergiolucas38]

Dude, i've seen a lot of videos about these subjects, but yours is by far the best, in all the aspects. Great job, indeed :)

[@fufaev-alexander]

Wow thank you for your comment! I would be happy if you subscribe to my channel :))

[@softwarephil1709]

Excellent video! I’ve watched several videos on Maxwell’s equations; this did the best job of explaining the calculus representation and the derivative vs integral forms.

[@fufaev-alexander]

Thank you, I appreciate it very much Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzbin.infojoin

[@steafanmaciarfhlatha8497]

The best video I have ever seen on this topic. makes Maxwell's Equations easily accessible to anyone with A level maths (or equivalent)

[@jonomoth2581]

This was a great video. I found it hard to follow at times but after pausing to mentally recap different parts of the video I think I got it. one part that confused me was that I didn't know what flux meant.

[@iluvyunie]

flux is sort of like the change in flow of a vector field when permeating a surface (I think), usually integrated over very small volumes

[@dasanvarathan7959]

First of all, Thanks for the video, Brother. It connected all my previously learned dots from ElectroMagnetics and gave a clear understanding and big picture on Maxwell Equations. I also realized, How great James Clerk Maxwell was deriving these equations at those early years? I respect him while thank you for this video. A true teacher is the one who inspire the students to love the subject. You are the Teacher.

[@pawelchmielniak3275]

holy shit that was a great presentation!

[@fufaev-alexander]

hehe, thank you!

[@ZoonCrypticon]

An excellent explanation ! Thank you ! So far the best tutor I had in my life !

[@DiegoKhers]

thank you! I was finally able to understand intuitively the four maxwell's equations.

[@adleneboulebtateche156]

Great job. I can't thank you enough. The best video about curls and diversions on KZbin. deserves at least a million likes.

[@fufaev-alexander]

Thank you! 😍 Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzbin.infocommunity If you like my channel and like my videos, I would be happy about a small donation: tinyurl.com/denker-donate

[@2hcobda2]

1:05 Given, for example, m = 1 metre & "the large sphere" has radius 2m & is centered at the origin ( 0. 0. 0 ) of coordinates & "the small sphere" has radius m & is centered at ( 4m, 0, 0 ). Then the distance r between these 2 spheres is m, while presumably, 4m was the intended distance. Also, presumably, uniform distribution of the electric charges Q & q was intended on the surfaces of &/or in the interiors of these 2 spheres. (A little more precisely, within/on either sphere the electric charge density is solely a function of distance from the center of that sphere. )

[@QuantumGirl24]

This is by far the best explanation, Thank's a lot

[@richardeborall5900]

So clear, thank you!

[@adityachavan6383]

hands down the best video on maxwells equation

[@mahmoudalgarhy7889]

Wow wow. The best explanation for Maxwell's equations ever.

[@fufaev-alexander]

Thank you very much Mahmoud! 🙂

[@mahmoudalgarhy7889]

@@fufaev-alexander could you please tell us the name of the software that you used to present this piece of art?

[@fufaev-alexander]

@@mahmoudalgarhy7889 sure, I use Adobe Illustrator for images and combine and animate them in Adobe Premiere

[@rktiwa]

This is by far the best utube video among its kind.

[@kylewolfe_]

"I omit the arrows because they make the equations unnecessarily ugly" HERESY

[@RyanK-100]

He didn't say he was using bold letters instead but he did.

[@logogistiks8857]

Haven't had magnetic fields in highschool yet, but i think this video is very good explained for someone who has not seen this stuff often before. I feel like now after watching, i have a good intuition for the topic!

[@pff1974]

This is amazing.