Maxwell's equations explained logically! (Ep: 1 - Power of Gauss's Law)
ฝัง
- เผยแพร่เมื่อ 17 ต.ค. 2023
- Let's intuitively learn two Maxwell's equations - Gauss's Law - intuitively. And solve in minutes, what Newton couldn't in years.
The first two Maxwell equations - The Gauss law - comes directly from Coulomb's law. That's right, by rearranging terms and doing some clever arguments, we can logically show that the flux through a closed surface must indeed equal the total charge enclosed by the surface. And in doing so, we will uncover why we define electric flux as the dot product of electric field and the area in the first place.
Then, we apply this to find the electric field due to a sphere of charge, outside it. Newton did a similar calculation - finding the gravitational field due to sphere of mass - using integrals. You can find the proof of that online Search for Shell theorem.
But, using Gauss's law, we can find the answer much quicker.
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43 years ago I struggled with Gauss' Theorem and have stayed trapped in it.. I feel somewhat liberated now, thank you Mahesh.
Such a wholesome comment, Rajan. Thank you!
You don't even have a clue what is the fundamental theorem of calculus, never mind Gauss' Theorem.
@@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..
@@Mahesh_Shenoy HSAs theewuuupà
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
That’s very encouraging! Thanks :)
@@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 TH-cam explaining it well enough.
@@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.
@@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.
Mahesh, I am so glad you have Feynman's daemon on your shoulder, along with Maxwell's. Oh, the conversations you must have!
haha :D
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
Wow, that’s encouraging! Thanks
@ffggddss it's been so long since I saw you in the comment section
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 ) !
SIMPLY Brilliant Brother!!!
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.
Why are you so good at explaining?!?!? You make me feel like im good at physics😭😭
You might be giving the best explanations that exist on TH-cam. I think even Richard Feynman would be impressed
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.
True!
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
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!
Very interesting. I need to look it up!
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.
@@douginorlando6260That’s a lot to unpack 😅
Added it to my list though
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
This was pure genius! I’m a physics teacher, and I found your video to be amazing, the idea of the water was incredible.
The entire video is excellent but the final five minutes is a tour de force!
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
Oh I loved that. The clearest explanation ever. Thank you so much for posting. What a teacher you are.
Your enthusiasm and passion made this not only amazingly informative (and I really mean that) but a pure joy to watch. Wonderful, thank you.
Beautifully described. After a lifetime I now understand Gauss' Law
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.
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👍
I love your sense of amazement. That's what drives the best physicists.
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.
Well, he more or less reports what R. Feynman wrote: if anything, Feynman was (is) a talented man.
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.
The discussion also motivates why we define Electric flux the way it is! Amazing Sir.
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!
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!!!!
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.
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
Thanks, buddy :)
This channel is going to blow with such quality videos
Mind blown. You are really good at this! Wish I had your vids back in university
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!
Every video from this channel is a treasure. Incredible explanations and enthusiasm. Keep it up man
Best 20 minutes I've spent this month!
Great video!
Dude thanks for becoming a content creator. You are helping so many of us understand the most fascinating things!
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)
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.
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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.
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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.
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! ;)
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
An elegant and simple explanation. Remarkably clear.
What an incredible job explaining this concept. Thanks so much Mahesh!
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 :)
You are doing a really good job with these explanations. First rate.
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.
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.
This is fantastic! I never understood this concept well but you did it! Thank you!
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.
The way you lay out your explanations is very clear.
Thanks :)
Your story telling is just on next level!
Great explanation! Also your enthusiasm is contagious.
This channel is truly underrated.
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.
Finally I truely felt the physics of this law, Sir thank you so much I am so greatful I found this video❤❤ It was the first video I saw in your channel and I subscribed, please keep up this work
I love the way of teaching and your energy ❤❤
You're really good at this! I will share this with all my friends. Real modern preaching.
I think Mahesh sir is one of the most underrated physics teachers in today’s era. Respect and ❤ from🇧🇩..
Awwww…. 🥺
It is so much easy when the teacher understands what he is explainig. Excelente job brother.
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!
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.
Just wow! Brilliantly explained sir!
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.
Gauss was a genius of his time
Truly
He contributed a lot to even mathematics!
Sir do you refer to any other resources other than Feynman sir's lectures ????? BTW love you so much , the way you explain the topics with such clarity that it seems that if we had sat with that particular thought in our mind and would had argued with prefect logic we could have discovered those theories by our selves.
Beautifully done. Looking forward to the rest
Gonna watch this after chem exam tmrw.
Can already tell its another banger.
All the best :)
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.
I absolutely love your presentations.
Now i can feel physics with my heart,
Thank you sir
Mahesh the more fundamental question here is why is Coulombs law the way it is? The process you outlined (and Feynman had been my personal hero since my childhood) is essentially mathematical jugglery - not something which reveals more than what Coulomb's law states. Why does Coulombs law resemble the law of gravitation so closely (the inverse square dependence and also the multiplication of charges or masses in the numerator)? What if there was a more obvious way of looking at Nature - that these laws would have just popped out from 'common-sense' logic? I have been exploring this field for the past 4 decades, and have some interesting and surprising results (yet to publish these as a book, have only given seminars at prominent universities around the globe).
One could go even more basic. For example do you have a fundamental notion of what is "mass" or "momentum" or "energy", etc? Sure our school and university textbooks teach us some vague notions, but that is about it - vague notions. For example, ask anyone what is kinetic energy, and they are likely to chirp out "half m v square". But do you really have a feel when you write KE = 0.5*m*v^2, that it represents something called "energy"? Probably not ... for most (if not all) of us it is just a definition we mugged up in childhood and did not bother to question it again.
Liked your presentation though. I did watch the whole video. Keep up the good work !
the durag just earned you a sub, good sir 🙏
Thank you for explaining Maxwell's law. Suddenly become easy. Love your enthusiasm! It is a beautiful equation!!!
Thank you for the video. Subscribed.
You are a really really great at explaining physics.
Thanks for your great work.
Keep up, and I'll be there watching ;)
This is genuinely the first time I understand wtf those Maxwell equations are about
Thank you for this glimpse of hope
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)
Kudos! Best explanation ever.
Beautiful, easy explanation Sir❤
Very elegantly explained. Thanks Mahesh
As always. Loving your vids!!!❤❤
Well explained Mahesh. You nailed it !
Ten minutes of standing ovation for triste vídeo! Congrats!
Thank you for this wonderful explanation Mahesh !
I have a question
what If there are 2 point charges in the gaussian sphere one is R/2 to the up and R/2 the the down
is then the electric flux is same every point ?
Or this only holds when the point charges inside are equidistant from each other ?
Thank you in advance
So happy just to listen to this.
It is so easy with you. Thanks
Was anyone else 'screaming' the whole time, the area and E are dotted! :D You are great Mahesh, love the way you teach!
man this guy is such a good teacher
Fantastic explanation.
You do it great, thanks.
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.
Brilliant explanation!
Absolutely brilliant. Thanks a ton.
I loved your explanation, still watching but this is very edutaining!
Glad to hear that :) :)
Wonderful stuff! Thanks for making that video. It was very well explained.
Beautiful !
great video. thanks for sharing.
Thank you Mahesh!
You are great sir I always get to know something new from the topic I already know about, after watching your video 😅❤❤❤
very good explanation.
Very good explanation 👍🏻
Wow, blow my mind, You are amazing, keep it up.
Richard Feynman,. No ordinary genius!
A very good video . Thank you
Very well explained