Maxwell's equations explained logically! (Ep: 1 - Power of Gauss's Law)

[@rajanvenkatesh]

43 years ago I struggled with Gauss' Theorem and have stayed trapped in it.. I feel somewhat liberated now, thank you Mahesh.

[@Mahesh_Shenoy]

Such a wholesome comment, Rajan. Thank you!

[@NewCalculus]

You don't even have a clue what is the fundamental theorem of calculus, never mind Gauss' Theorem.

[@niks660097]

@@NewCalculus there is no " fundamental theorem of calculus", there is "First principle" but it doesn't work for higher order differential equations, calculus is just a mathematical tool to solve a class of math problems, it has nothing to do with physics, you can even remove the differentiation and integration and it'll still be calculus e.g hilbert space..

[@NiteshYadav-ve5cj]

@@Mahesh_Shenoy HSAs theewuuupà

[@Afrinn]

this is easily the best explanation of gauss's law that i've ever seen. cant believe you managed to make it all so intuitive

[@Mahesh_Shenoy]

That’s very encouraging! Thanks :)

[@adityan3208]

​@@Mahesh_Shenoy please can we get a video on quantum mechanics explaining what problems the physicists were trying to solve and about the schrodinger cat experiment? Albeit with or without maths, I see no one on KZbin explaining it well enough.

[@robertsala8031]

⁠@@adityan3208That one example - “schrödinger’s cat” - has been so misinterpreted that, in some cases, it no longer makes sense, nor does justice to the point Schrödinger was trying to make. Schrödinger himself was said to have become entirely frustrated at the misinterpretation and misuse of his words.

[@adityan3208]

@@robertsala8031 yup I checked all channels and podcasts that I could, still can't wrap my head around it. It's not that I don't understand what they are saying, it's just that it does not make complete sense to me. How they jump from it being superimposed to parallel worlds.

[@catnipaddict126]

I was so shocked throughout this entire video that my gf mentioned that my mouth was wide open for the past 20 minutes. Like wow, I am speechless. This is the best explanation I have ever seen.

[@Epoch11]

You might be giving the best explanations that exist on KZbin. I think even Richard Feynman would be impressed

[@tyapca7]

If only I had such lecturer when I was young. I do not say they were bad. They *were* masters. However, sometimes, they were boring. I'm sorry. So, thank you very much, Sir! You're a talented man, IMHO. This lecture was a wonderful experience for me. So simple, and so clean. A big thank you.

[@ottrovgeisha2150]

Well, he more or less reports what R. Feynman wrote: if anything, Feynman was (is) a talented man.

[@ffggddss]

Wonderful transmission of Feynman's explanation of Gauss' Law! As a mathematician and a physicist, I especially admire how much math you *didn't* use! The wise view is that the math flows from the concepts, which you relayed so well. This video is excellent preparation for moving into vector calculus. And I've always admired the approach Prof. Feynman used in explaining physics. The Feynman Lecture series (3 vols.) is essential for anyone who wants not just to know, but to *understand* physics. Fred

[@Mahesh_Shenoy]

Wow, that’s encouraging! Thanks

[@solotekle2999]

@ffggddss it's been so long since I saw you in the comment section

[@dip-tree]

I had the fortune to read the Feynman Lectures - all three volumes - cover to cover - several (four to be precise) times throughout my life as a physicist for the past four decades. Each time (separated by roughly 5-7 years apart) I read them, the logic seemed so fluid and convincing, and yet every new time I could see new insights that my earlier reading had missed ! Feynman has been my hero since my high-school days (and I am actually no hero-worshiper ) !

[@ganapathysenthilkumar2655]

SIMPLY Brilliant Brother!!!

[@alexandrekassiantchouk1632]

Try then deriving new momentum conservation from recent correction of Newton's inverse square law and his 3rd law: Final Reality Check: Space Curvature vs. Time Dilation - story on Medium.

[@thepandaman6756]

When I learned Maxwell's equations before I saw them as no more than some random equations, but your explanations allowed me to get a new understanding of them and see the beauty of Physics. Thank you for the effort.

[@D_dusze]

Why are you so good at explaining?!?!? You make me feel like im good at physics😭😭

[@mickwilson99]

Mahesh, I am so glad you have Feynman's daemon on your shoulder, along with Maxwell's. Oh, the conversations you must have!

[@Mahesh_Shenoy]

haha :D

[@garrett3640]

Great presentation as always! Another consequence of gausses law that no one talks about is the fact polarized light is not physically realizable. Only quasipolarized light can exist since em waves must always form closed loops. Plane waves are only mathematically polarized be becauae they extend infinitely. Real light cannot be polarized in a single direction. There are so many interesting consequences of gaussses law!

[@Mahesh_Shenoy]

Very interesting. I need to look it up!

[@douginorlando6260]

Yeah. Start with a point source and radiating out in every direction in phase. Polarized plane waves can work in a 2D horizontal x,y plane (for a circle wavefront in the plane, E is always vertical to the plane while H is always tangential to the circle). But this can not work in a sphere. Consider a vertical slice through the center of the same sphere. A new 2D circle is formed in the x,z plane. Now at Z=0 the H field is in opposite directions for the 2 points of intersection (X,0,0) and (-X,0,0). Now consider what happens as you approach (0,0,Z) on that circle. the 2 H fields are in opposite directions and cancel out.

[@Mahesh_Shenoy]

@@douginorlando6260That’s a lot to unpack 😅 Added it to my list though

[@garrett3640]

It's also true in less obvious light sources such as a "polarized" laser beams. Another interesting consequence off gauses law is that it shows that all light must diverge. (Laser cannot stay collimated forever) Starting from the fact a beam cannot be polarized in a single direction across it's entire width, we can predict the propagation direction of each section of the wavefront from Kdirection= E x B. Depending on the phase of the wavefront you can show that the laser is either diverging or converging(then ultimately diverging again). And this argument all came originating from gauses law

[@simpleprogrammer9552]

I really enjoy your videos. I could not have hoped for a better elucidation of charge flux while taking physics in college. I love the joy and the excitement you express at each of the 'lo and behold moments along the way, and your respect for Feynman's beautifully revealing inferences and approaches to finding answers. You're a good teacher: this is good teaching. Love it.

[@Familyproud-e9h]

I really like your videos and appreciate the time you take to explain physics. These days it has become so common to judge the work of previous scientists and say they were wrong, they didn't know this, they struggled to solve this or that problem, etc as if we found out by ourselves all the flaws in their theories oe equations. Scientists build their work on the works of the previous ones. Their struggles laid the foundation for the future scientists. I hope one day we appreciate the efforts s of all who contributed to our modern understanding of the world. Thank you so much for the great contents you create on this channel

[@romanburtnyk]

That's so cool. Everything I was feeling somewhere inside about electromagnetism has been extracted here is this video. I'm happy I found this channel

[@jlpsinde]

This was pure genius! I’m a physics teacher, and I found your video to be amazing, the idea of the water was incredible.

[@gazsibb]

Oh I loved that. The clearest explanation ever. Thank you so much for posting. What a teacher you are.

[@nigelmansfield3011]

Beautifully described. After a lifetime I now understand Gauss' Law

[@manoochehrtakrimi]

The dot is not fancy way of dealing with surface. It is ruling the effect of angle between da and direction of the E field. Also, putting all the charges at the center is ONLY valid if charge distribution inside the sphere is symmetric. Otherwise E can not be factored out. Regards.

[@Mahesh_Shenoy]

True!

[@alejrandom6592]

So it is a fance way of dealing with surface. Bivectors are more intuitive tho

[@jamesraymond1158]

I love your sense of amazement. That's what drives the best physicists.

[@denkid4478]

The discussion also motivates why we define Electric flux the way it is! Amazing Sir.

[@dominicestebanrice7460]

The entire video is excellent but the final five minutes is a tour de force!

[@autismuskaefer]

I really like how you explain everything here in a easy-to-follow way and simultaneously making it exciting to understand. It helps so well to get an intuitive understanding for these physical phenomena and the relationship to their equations. Well done, keep it up👍

[@timkin4190]

Definitely one of the best expositions of Feynman's explanation of Maxwell's first two equations I have seen... definitely better than my undergrade physics lecturer 30 years ago! I wish I'd had the internet available when studying back then... student's definitely have it easier now! ;)

[@mayurkalsekar524]

This channel is going to blow with such quality videos

[@jamieoglethorpe]

A nice demonstration. This is similar, in its way, to Penrose's generalization of Openheimer's proof that a mass can collapse to a black hole. Openheimer required spherical symmetry, and Penrose generalized it to any shape.

[@paulg444]

God bless this young man!.. he is delivering !

[@ACuriousChild]

If one has the imagination and creativity one can easily see how all of this is SIMPLE GEOMETRY ... packaged in calculus. THANK YOU FOR LAYING IT OUT IN SUCH A DIGESTIBLE FORMAT!

[@timd3000]

Best 20 minutes I've spent this month! Great video!

[@ericrawson2909]

This is an astonishingly good video. I first encountered these laws fifty years ago, and it was hard work. You make it seem so simple.

[@emeraldist]

Hi! I've been always interested in trying to understand the equations and text printed in my textbook more intuitively. Not gonna lie, it is a tedious job- going through forums, blogs, videos, etc etc, which is why others around me advise me to always focus on the sums, save time, prepare for board exams and blah blah. But you- you've made everything more interesting and simpler to understand! I used to dislike electrostatics- mostly because I used to find it plain and not so intuitive as the chapters in our pt. 2 physics textbook (wave optics, light's duality- all the quantum stuff). I've started to go through your videos here, beyond the content posted in the khan academy channel, and oh! am I blessed! I love your explanations, sir! Now having my board exams almost two months away, you've kindled my passion in otherwise very tedious chapters in physics. You are great, sir! Thank you so much for getting me through one of the toughest years of my life. I'd possibly have to thank you again if I actually choose physics as my major! I'm so glad that I found you :)

[@SultanInStem-t3i]

The dedication of Sir Isaac is insane.

[@rajanne2947]

In college 36 years before I couldn't understand Gauss and Maxwell! Now I do! It was never explained well but still the flux lines flowing from the charge should remain the same whatever the radius of the sphere we keep drawing bigger and bigger around it, I reasoned! Hence the area of a sphere. And epsilon being the permeability to the flux. This could be applied to any type of flux like the radiation coming off the sun! To calculate how much the earth could capture that solar energy in a year! This could be used in all kinds of situations for all kinds of energies.

[@justicewillprevail1106]

I love the way you explain things. Unlike other channels all I hear is complicated terminologies after terminologies which can be so confusing. You explain them with so much clarity any none physics person like me can understand. So glad I found your channel. Great job!!!!

[@erroroflife187]

Even after learning Physics C E&M ur videos make understand this even more. I was always confused on why u have to make a Gaussian sphere around a charge, it makes so much sense now. Thank You

[@edsharman7037]

Your enthusiasm and passion made this not only amazingly informative (and I really mean that) but a pure joy to watch. Wonderful, thank you.

[@TashiRogo]

The way you lay out your explanations is very clear.

[@Mahesh_Shenoy]

Thanks :)

[@Kosmiceggburst]

VERY NICE. That's exactly right: There's beauty finding the presence of a symmetry that's being sensed by the mathematician in exploring a problem resolution. In a round about way, what Newton didn't come up with on several of his direct attempts at a resolution, Maxwell satisfied the demand of Pii being THE RELATION OF A PERFECT CIRCLE, in the situation of when it's applied to wicked shapes, in this workaround to get at the sensed underlying symmetry. Nice presentation.

[@syedshadmansakib]

This channel is truly underrated.

[@lowbudgetmaths]

Very enjoyable and informative video! I would like to emphasize that only for spherically symmetric masses is F/m = GM/R^2 (and E = Q/(4piR^2). For example an ellipsoid or cube of mass will not obey the inverse square law. The TOTAL flux through any surface only depends on what's inside the surface, but if the ball of mass is not symmetric, then on a spherical surface enclosing the mass (or charge), there will be different contributions to F dot dA (E dot dA) at different places on the enclosing spherical surface. So you wouldn't be able to factor F (or E) out and solve for it. But if the ball of mass (charge) is spherically symmetric, every point of the enclosing spherical surface is like every other point, and the contributions to F dot dA (E dot dA) at different places on the enclosing spherical surface are identical, so F (E) can be factored out.

[@raviramanathan5565]

Your passion is electric. Such a good lecture around Feynman's explanation (already beautiful) of Maxwell's Eqns! This is the way it must be taught in schools (these are very important eqns)

[@roberttrask6826]

These videos are really great expositions of clear intuitive thinking. I’d recommend them highly to anyone seeking better understanding. Thanks very much for bringing physics to life!

[@xjuhox]

It's not obvious that we can infer the non-spherical flux integral in this way. But we do know that to every closed surface in R^3 that does not go through the origin we can associate the flux integral "int E*dA" of the vector field E = x/Ixl^3 through that surface. E can be interpreted as the strength of the electric field arising from a point charge placed at the origin. In particular, div(E) = 0 for x ≠ 0, and by divergence theorem the flux integral does not change if the closed surface undergoes a continuous deformation, so long as it never crosses the origin. This is a topological property of the flux integral, just like the closed path Cauchy integral of 1/z has the same topological homotopy invariance property in complex analysis. Here the type of the vector field is of paramount importance.

[@kaustubhpandey1395]

Gauss was a genius of his time Truly He contributed a lot to even mathematics!

[@prulikowski]

nice explanation, although following reasoning from most of introductory EM textbooks, one comment - around 16:30 - that integral does not "vanishes" it is just that E is uniform around the sphere (does not vary with r on the surface of that sphere) and can be put in front of the integral BUT integral when calculated resolves to the surface of the sphere

[@sudiptoatutube]

This is one of your brilliant explanation. I already found you explaning this in one of the Khan Academy videos. From that day I am your fan!

[@iamdino0]

Every video from this channel is a treasure. Incredible explanations and enthusiasm. Keep it up man

[@PieterPrinsloo]

Mind blown. You are really good at this! Wish I had your vids back in university

[@peterhall6656]

You are doing a really good job with these explanations. First rate.

[@SpotterVideo]

Conservation of Spatial Curvature: Both Matter and Energy described as "Quanta" of Spatial Curvature. (A string is revealed to be a twisted cord when viewed up close.) Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree. String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension? What did some of the old clockmakers use to store the energy to power the clock? Was it a string or was it a spring? What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine. Quantum Entangled Twisted Tubules: “We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr (lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957-8, in Scientific American vol. 199, no. 3, 1958) The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with some aspects of the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”, and the work of Dr. Lisa Randall on the possibility of one extra spatial dimension? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics? When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if Quark/Gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks where the tubes are entangled? (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry. Modern physicists say the Strong Force is mediated by a constant exchange of Gluons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other. Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change. ===================== Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons? Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension? Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons . Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase. Gamma photons are produced when a tube unwinds producing electromagnetic waves. ( Mass=1/Length ) The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge. Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms. In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137. 1= Hypertubule diameter at 4D interface 137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted. The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.) How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter? Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles? I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. This topological Soliton model grew out of that simple idea. I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles. -----------------

[@phoenixmistertwo8815]

I wish I can peek inside your mind when visualizing all that you have written here. I keep re-reading it to form my own visual models, but my understanding for the bigger picture is lacking in knowledge of the components that make it up. Yet....If one stays too long studying and working with the components they could lose sight of the bigger picture.

[@SpotterVideo]

@@phoenixmistertwo8815 A twisted soliton is formed when the stopper is removed from a sink full of water. Take a flexible rubber hose and start twisting it until it collapses upon itself. These are the best analogies I have.

[@phoenixmistertwo8815]

@@SpotterVideo , Its difficult to move away from a more pointalistic model of our tangible reality, and a more vector based mindset on the interactions on both macro and micro realms, among the standard particles. One of my first breakthroughs from that legacy mental model was a 3d modeling of gravity's effect that was unlike the more commonly used trampoline model. This was an eye opener that led me to research the concepts and modeling of 5 dimensions, where the 4th is duration, and the 5th is probability. Then I was introducing to the infamous double slit experiment that to this day, if I am not mistaken, cannot detemine exactly why the introduction of an observer forces the waveform to collapse and position itself from probability into a particle. Of course we are stuck in the weeds, analyzing the effects and interactions with something we cannot grasp with regard to photons. I would also say that most likely, gravity is larger than we can see from its' observable interactions, so, the Higgs field is a theory that indeed got my attention, with its interactions with mass that made sense in scaled proportions. I have seen some good models of String Theory and M Theory, but it is still difficult to imagine the quark and proton connection you mention, however, it makes more sense than how I learned about quarks in class as an independent particle that comes to a 'strong' existance. It makes more sense the way you describe it as being just a spring like spatial stricture connected into the proton union or entanglement. I think that we, as Earthlings, need to move past our affinity and inclination to visualize our world as a composition of particles to a sheet or fabric, and start embracing what these particles really are, in wave form and visual probability clouds to represent orientation and even potential charge. I have seen some decent models that are now out there, but I was more formely educated with the particle model that I think becomes a buden as you learn more about the quantum world, and I have much to learn and understand, well beyond the confines of my old University textbooks. I dont know you that well, but from your post and explanations, I get the impression that you are on a higher level that many with your understanding on this subject matter. I bet they call you either a genius, or a bullshitter. I'll go with the genius level ranking by the evidence, as it's hard to bullshit what you have written here. 😉 If anything, you have indeed inspired me to learn more.

[@SpotterVideo]

@@phoenixmistertwo8815 I made some models out of twisted wires in an effort to understand "String Theory" and that led to this model. The wire can have either a Right-hand twist or a Left-hand twist analogous to particles and anti-particles. Each twist cycle is a cycle of curvature, which is "Quantized". If electrons have properties of both particles and waves, then they must be something else. Instead of trying to invent a particle called the "graviton" to explain gravity, this model uses the spatial curvature often used to help explain gravity to produce a cyclic curvature model to help explain subatomic particles. My university degree is in Biology. However, I did take several Physics classes and one of them was a Nuclear Physics class. As a part of that class, we heard a lecture given by the guy who was then the head of the laser fusion lab which built the "Shiva" machine in an attempt to produce nuclear fusion in a small fuel pellet. During my science instruction in the public schools of my state I did teach a unit on Nuclear Energy. One of my former students eventually became a Nuclear Engineer. I remember the day I told his class almost all nuclear reactions are reversible, and he asked a question about it. I am amazed at the men like Feynman and others who were willing to admit they did not understand Quantum Mechanics, even though they had made incredibly accurate predictions of how particles interact. Unfortunately, I do not have the math skills required to complete this model. It is intended to be a framework for others to confirm as correct or discard as one more failed attempt to explain particles.

[@user-pj1wv1ns9x]

Gonna watch this after chem exam tmrw. Can already tell its another banger.

[@Mahesh_Shenoy]

All the best :)

[@zhh174]

I don't have words to thank you enough. But a real appreciation from heart for your efforts. Thank you so much for making the hardest concept the easiest.

[@debasishnath7079]

Newton never struggled with the integrals. Agreed that they are a bit tedious to solve but not that hard, definitely not for Newton to struggle for "YEARS". Indeed, Newton was already aware of what the final result was going to look like, when he began this work. Newton was adamant to not use Calculus, which he had invented, in any of the proofs in his Principia. Therefore, he furnished the above result, in a sequence of Propositions and if I remember right, those were Propositions 70-76. These propositions showcased every bit of the glittering genius that he was. He did not have Gauss's law and yet, came up with sublime and insightful proofs which helps us gain insight into the physics of the problem. He even provided proofs for non homogenous densities and attractions between spheres right after this. Newton was a genius of the highest order.

[@lancediduck6278]

The way I first saw this, was in vector calc class. The professor drew the irregular shaped objects that surrounded the charge. The one sphere inside the object, then one outside surrounding both. The total flux of course is the same for both spheres, so easy to see it's the same flux going through the irregular shape.

[@jayakrishna6635]

Just wish I have seen this video 15-20 years ago😅.. great work man!!

[@mlmichel98]

man this guy is such a good teacher

[@JasonAStillman]

Was anyone else 'screaming' the whole time, the area and E are dotted! :D You are great Mahesh, love the way you teach!

[@douginorlando6260]

Intuitive understanding provides the context that makes it all logical. Sometimes the intuitive understanding is based on an oversimplification that works but not perfectly.

[@Mahesh_Shenoy]

True. Did you find anything ‘not perfect’, here? Curious!

[@douginorlando6260]

My favorite example is how Schrödinger derived his wave equation based on several established equations that described measured relationships such as Energy= h* frequency. Very successful in describing spectral atomic emissions … but not perfect. Dirac added the complexity of special relativity and was able to derive hyperfine spectral lines of the hydrogen atom that Schrödinger wave equations did not … and the existence of positrons.

[@jspanyer]

Okay you got me now, and I just subscribed. Even though I'm an electrical engineer I've always struggled with Maxwell's equations, but now they're more intuitive and you gave me a "no duh?" moment. 😂 Ty

[@AdithyaRajkumar]

Hello sir, I came from your lectures from Khan Academy for class 10 and I wanted to thank you because I was able to *top* in my school's half yearly (I have never topped in my entire life) with your fun way of teaching. Thank you so much❤

[@AdithyaRajkumar]

oh I was talking about topping in science, not overall. I still have a long way to go

[@Mahesh_Shenoy]

Wow! Congrats. But it’s mostly you! :)

[@LeoH3L1]

Makes sense if you think about it like a surface tension with a fixed value, the field gets locally weaker or stronger depending on the distance, which depends on the shape and the location on the surface of that shape, but the surface area grows or shrinks with it, so it makes sense it would be a constant.

[@alejrandom6592]

We do not deserve you sir. Your classes are amazing

[@arthurwatson8973]

An elegant and simple explanation. Remarkably clear.

[@kartheekpattigilli2759]

Now i can feel physics with my heart, Thank you sir

[@adb012]

I already understood all this and had the intuition, but it took me a lot of time and effort. This explanation and presentation was just brilliant. Congratulation and thank you, Mahesh and Feynman.

[@jadioj]

Dude thanks for becoming a content creator. You are helping so many of us understand the most fascinating things!

[@youtube_fantastic]

Mahesh main to apka fan ho gaya hun! You make the best explanations and you infectious love for science just bleeds through so authentically! Thank you

[@Mahesh_Shenoy]

Thanks, buddy :)

[@sohambhattacharya_xc1685]

Feynman is the greatest teacher we never had...but we DO have someone like you😊

[@DrDeuteron]

speak for yourself!

[@northdallashs1]

Mahesh, great videos; you're a natural teacher, a rare ability! One small suggestion on this one. I think you should point out that the electric FIELD of the distributed charge is only the same as the FIELD for the same total charge concentrated at a single point if the charge distribution is spherically symmetric around the same point where single point charge was. Newton had to make this assumption for the density of the earth in order to find the gravitational field outside a spherical mass. As you very nicely showed, the flux INTEGRALS are independent of the distribution, but not the fields.

[@krishnan447]

You just nailed it. One of the best explaination i came across.

[@fancuboid2712]

I love the way of teaching and your energy ❤❤

[@joan4jays]

Again! 👌 The difference is in 1. you are willing to explain fundamentals. against in school 2. hiding fundamentals for show off. and/or more likely 3. no funda teachers. I don't blame them though 😅

[@politicalfoolishness7491]

Ending - you are doing great and I love your style of presenting - A+ and I haven't seen any better.

[@paaabl0.]

You're really good at this! I will share this with all my friends. Real modern preaching.

[@johnniefujita]

Ten minutes of standing ovation for triste vídeo! Congrats!

[@buteforce]

Richard Feynman,. No ordinary genius!

[@Enfieldic]

Sir what do you think When current moves in a particular direction it creates magnetic field Because of length contraction ( concept from theory of relativity) So when length contraction takes place it takes place in the direction of its motion right? 0 0 0 0 0 0 - - - - - - Its a wire when no current flows here 0 represent protons - are the electrons When current starts 0 0 0 0 0 0 - - - - - Length contraction Generates magnetic field So here you can see there are some protons which don't have any corresponding protons So does electric current produces dipole magnetic field ? I hope that you will answer this question Thankyou

[@boardndude]

The visual explanation was cool. But if you look at the right side of the equation, it tells you the left side is always going to give the same result regardless of shape or distance.

[@Achrononmaster]

@17:00 that is interesting, and fascinating though. It implies Newton did not have the concept of charge as a source of photons, even though he understood light was particulate. A bit harsh to criticize him though, since Faraday was born 65 years after Newton died. Even Faraday probably did not understand the charge as a source until Maxwell tidied things up. Even Maxwell did not understand charge as a source until Einstein explained Maxwell for good. It's a photon nerds, not a wave. ψ functions are statistical, not ontological.

[@GodSahil]

Your story telling is just on next level!

[@MichaelJones-ek3vx]

4:28 In the 1970s, a friend of mine was studying physics at UC Berkeley. Richard Feynman lectures on physics were what they used. He's a professor, emeritus in physics now. If it was good enough for Berkeley, good enough for me. I'm going to buy the lectures myself.

[@paolomonti8027]

Very interesting content. Only, at 11:05, that's not really a 'fancy way' mathematicians like to write 'things'. That's a vector scalar product, using the Electric field vector E (written as a E with an arrow on top) and the infinitesimal area dA multiplied with the unitary vector normal to the dA surface (written as dA with an arrow on top). By using a scalar product of vector, the result is that you are actually considering the portion of dA perpendicular to E.

[@davidhenry7946]

watched this video, the first pf yours i have ever watched and fully...you earned a subscription

[@bergmanfan]

What an incredible job explaining this concept. Thanks so much Mahesh!

[@qualquan]

E = #Field Lines/Area = #FL/A Then E*A = #FL (FL also called Flux). E*4pir^2 =Total #FL (Flux). E*4pir^2 - Total FL (Flux) = Q/Eo. If O/Eo is Constant then E and 4pir^2 are inversely related but Total Flux is constant and remains constant for ALL CLOSED Surface Areas and not just spherical.. Finally Eo = Q/Total FL which is a constant MAHESH instead of worrying about size of areas focus on TOTAL FL(Flux) =Q/Eo Total Flux is independent of size and shape of ENCLOSING SURFACE and ONLY depends on Q/Eo

[@gmnahin]

I think Mahesh sir is one of the most underrated physics teachers in today’s era. Respect and ❤ from🇧🇩..

[@Mahesh_Shenoy]

Awwww…. 🥺

[@Puzzlephil4]

I loved your explanation, still watching but this is very edutaining!

[@Mahesh_Shenoy]

Glad to hear that :) :)

[@tapashnandy3594]

We solved many problems in Resnick Halliday without a good physical understanding...thanks!

[@dansatMaryland]

This is fantastic! I never understood this concept well but you did it! Thank you!

[@AbirSheikh-p8r]

You are a blessing from the lord to me.

[@clashenriksen961]

Thank you for explaining Maxwell's law. Suddenly become easy. Love your enthusiasm! It is a beautiful equation!!!

[@berniv7375]

Thank you for the video. Subscribed.

[@lahunakbal4277]

It is so much easy when the teacher understands what he is explainig. Excelente job brother.

[@itsiwhatitsi]

One of the best physics channel 💯

[@rubenoteiza9261]

Wow. Excellent explanation.

[@philipoakley5498]

Nice. Even more fun is to add in the 'units / dimensions' to the terms so as to get steradians (solid angle), and then later, to decide how to determine the "volumes" in 4d space time. A lot of optics and EM is greatly 'confused' by the omission of the solid angle units (which represent the cancellation of non coherent lengths in the equations)

[@pieterhuman8049]

Great explanation! Also your enthusiasm is contagious.

[@lake4ishikawa]

This is genuinely the first time I understand wtf those Maxwell equations are about

[@kingplunger1]

Thank you for this glimpse of hope

[@rkalle66]

Two side facts ... The inverse square law (= surface area of a sphere in relation to the radius) is proofing that we have three dimensions. Because what does the hypersurface of a 4D sphere in relation to the radius? Gauss's law is interesting on gravitation, too. Think of a hollow earth. What would be the gravitation inside? Answer: zero, because there is no mass inside the sphere.

[@alikaperdue]

I don't fully understand. Still I am fully impressed.

[@varsha_1703]

Whenever the floathead physics notification pops up ...ok mahesh is cook something interesting 😂run...run🏃🏃💨💨

[@Mahesh_Shenoy]

Woah!!! Love the support!!!

[@vinnycrism]

So happy just to listen to this.