I never understood why a moving charge produces a magnetic field... until now!

Does it, really? Let's explore what Einstein has to say about this question
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[@douglasstrother6584]

It's pretty wild that the generation of magnetic fields by currents is an everyday relativistic phenomena, and ferromagnetism is an everyday quantum phenomenon.

[@douglasstrother6584]

@@fdsphone6854 Yes, but the point is that electromagnets and permanment magnets are everyday objects but have relativistic and quanutm mechanical foundations.

[@honumoorea873]

I can't see why it's wild.... nature is full of rules we barely scratch the surface, and even in this smallest atom there are already an insane number of those rules.

[@maha-madpedo-gayphukumber1533]

​@@douglasstrother6584the question is how to unify both phenomenon.😂😂😂😂

[@tinkeringtim7999]

​@honumoorea873 but we're not. Quantum rules are linear. They are mathematically incapable, even in principle, of modelling a human (or even anything whose effects cross wide ranging areas of influence - e.g. membranes & potentials around complex structures like veins). That's like one of the central open problems with the whole quantum doctrine and the question about how the classical/quantum crossover could be defined.

[@zabity]

plot twist: it's magic

[@Feynman_Fries]

Hi Mahesh, I don't know much about you but your passion for physics seeps through and resonates with me. I quit my high profile MNC job for my sheer passion for physics and turned to school teaching. During one of my brainstorming sessions while preparing for a lesson I stumbled upon a video from khan academy. Now I generally do not appreciate the way physics is treated by Indians or Indian teaching fraternity, reducing it a rote body of formulas and derivations (one of the reasons that drove me to be a teacher), and so I only really head to Feynman's lectures, Resnick Halliday or lectures by Walter Lewin, but jeez I was shocked and intrigued by the passion that your voice had, and the way you explained it (I think it was Maxwell's correction of ampere's law). Since then I've regularly followed you, and your work and admire the what you're doing. India needs good physics teachers, that know that physics is not a subject or a tool to crack petty exams like JEE or PMT, but an attempt to understand the laws that govern the universe with the most critical assessment of evidence. Kudos to you! Keep up.

[@Mahesh_Shenoy]

WOw, thank you. Means a lot coming from another educator!

[@williamlavallee8916]

I hope you didn't teach this to your students. It's not even wrong.

[@paxshild4924]

​@@Mahesh_Shenoy The explanation was neat, but I have two major questions on this explanation. One, why don't we see the same length contraction effect when the electron is stationary outside? So, the current inside the wire, which is the result of the electrons inside moving in one direction, must be length contracted relative to the electron that is stationary outside with respect to the protons. Hence, inducing a negative charge, creating a repulsive force, why doesn't it happen?

[@paxshild4924]

​@@Mahesh_Shenoy and my second question is that that when a charge in a similar setup is made to move perpendicular to the direction of current it experiences a horizontal magnetic force how does relativity explains this?

[@markbrownfield1174]

I suggest you take the laws with a grain of rice. This was all made up by individuals and may mathematically line up and sound good, but I have been looking with more of an open mind with this in mind and drawn on my theories and hypothesis. I have some atomic models that work way better than our current models. Don't takes it the wrong way, just saying, an open mind can open technologies. "I could be wrong, I usually I'm." MadMarkTech

[@davidofearth]

I remember first deriving in grad school the force between two current carrying wires with only coulomb attraction and Lorentz , and getting the same answer as the standard formula that uses magnetic fields. This absolutely blew me just like it did the OP. Awesome to see another person having the same experience.

[@DrDeuteron]

dF = J in different inertial frames is mind blowing

[@1dgram]

same, as a high school junior

[@varunh6342]

@@1dgram Wait how did you do it? the charges would be zero as mentioned in the video right?

[@1dgram]

@@varunh6342 Maybe I'd need to watch the whole video to fully understand your question, but there's an apparent length contraction in the parallel wire in the direction of motion along the first wire due to relativity. When you do the math for the electric force (coulomb attraction only) in that situation, taking into account the Loretz factor, you discover the magnetic force. It turns out that the electric and magnetic fields are different facets of the same electromagnetic field! It's an amazing feeling to have a hunch like that and see it work out perfectly in the math... I was wondering at the time whether it was only part of the story. It was also great going from having a confusion about the nature of magnetism (while trying to get an intuitive grasp of it in my Physics AP class) to it actually making sense to me.

[@jssamp4442]

I think everyone has a similar experience. Those who didn't get that feeling, still don't understand it.

[@Mahesh_Shenoy]

What’s the next topic you want the video on? (I prefer specific deep nuanced questions of high school science topics)

[@kusy]

Why Snell's law and "phase velocities" in a dispersive prism when light speed is a constant and cannot be slowed.

[@theastuteangler]

Fluid dynamics and specifically pressure loss and flow rate reduction through a system of ductwork due to friction, turbulence, and leakage. Change in flow rate of open registers when other registers close. Does Bernoulli hold up or does the HVAC fan become a compressor that cannot overcome the resistance from the remaining open duct registers.

[@ranasuryaghosh2545]

In high schools we are taught how to calculate the angular speed, time period of of revolution, orbital radius etc of an Electron considering it as a "particle" (Bohr's postulates), and also we can calculate the magnetic moment of the atom due to the moving electrons. But we also know that electrons does not exist in orbits, but rather something called Orbitals in the form of "elctron clouds" which describes the probability of finding an electron in it. Moreover, De broglie hypothesis states that orbiting electrons is associated with a stationary matter wave. So my question is that how all these things are related? Which one is true in practical life? Exactly in what form electrons exists in a stable atom?

[@kuldeepbhalodiya2559]

How can we conclude that speed of electron in conductor is same as the speed of electron. Speed of current is nearly equal to light ( since it's a wave that travels) while speed of electron is nearly 1 cm/s , which is very less to compare for length contraction and theory of relativity should not play a role here. Could you elaborate it further.

[@ranasuryaghosh2545]

@@kuldeepbhalodiya2559 You should study about drift velocity. Speed of dc current in a conductor is measurable and much much slower than the speed of light (even in superconductors). For example, the speed of an electron in room temperature, in a 12 gauge copper wire carring a current of 10A will approximately be 0.0508 cm/s.

[@civildiscourse2000]

Your enthusiasm is a pleasure to share. Sometimes I teach basic electrical theory to beginner electricians. We don't need to delve into the physics to this degree, but I always make it crystal clear that we are using simplified models and that the underlying mechanisms are much more nuanced, magical and utterly fascinating. I like to feature examples like this occasionally in case there is a future engineering student in my class who just doesn't know it yet.

[@tmst2199]

I recently studied electricity in junior college and it quickly became apparent to me that if anyone really understands how it works then they're not teaching tech students.

[@aluink]

I love how you talk about Einstein like you're talking to him in real time. You're bringing him to life and I love it.

[@michael-j-harrison]

Magnetics expert here. I have spent over 45 years designing transformers. I have a great intuitive insight into their design, have used FEA design tools, and even created new magnetics FEA design engines. Taking a classical view of magnetics theory is certainly valid and will give very good design results, however this relativistic view point does end up with some design nuances that will result in better design solutions.

[@copernicofelinis]

Can you make an example?

[@michael-j-harrison]

@@copernicofelinis A classical viewpoint of magnetics works well with most 'typical' transformer designs, however when designing transformers that have extreme characteristics then this classical viewpoint has limitations. Two extreme design cases that come to mind here are transformers designed with extremely low and extremely high leakage inductance. In the extremely low leakage inductance design case - what you typically care about is the mutual winding leakage inductance rather than the leakage between any one winding and the core. It turns out that it is actually possible to end up with a design that results in lower mutual winding leakage inductance than the leakage between the windings to the core - classical magnetics theory does not allow for this possibility as it predicts that the mutual winding leakage inductance must be higher than the leakage between any single winding and the core. In the extremely high leakage inductance design case it is possible to design integrated magnetics structures (including a transformer and inductors) with extremely high mutual winding leakage inductance that exhibit a greater winding coupling factor than what classical magnetics predicts based on the winding leakage inductance.

[@devarmont87]

Magnetics expert? Okay then 😅

[@AB-wf8ek]

​@devarmont87 If the guy has been designing industrial electrical components for longer than most people have been alive, why wouldn't he be qualified to have an opinion about the relevance between different frameworks of understanding electrical magnetic fields?

[@markmcgoveran6811]

@@michael-j-harrison I studied a lot of things about magnetics and at the point I ran out of money to buy books the books were old. They said they actually built prototypes after they made a prediction and took gueses to get a little better performance in the twenties and thirties

[@maxv.d.9391]

For the question at the end: if we were to look at a complete eletric circut, there would also be a part of the wire where the current would move in the opposite direction. At this part the laws of length contraction would still aply, and the protons would move away from each other and the electrons would move closer to each other. So there wouldnt be a lack of protons at the end because the Charge of the whole wire would add up to Zero.

[@johnwythe1409]

I don't get that the opposite is true in the other part of the circuit, sure the current is in the opposite direction, but length contraction as far as I know is only dependent on movement, not the direction of movement.

[@christofferberg3840]

@@johnwythe1409 The positive charges in the opposite part of the wire will be length contracted the same amount as in the part we’ve been looking at, so nothing strange there. The same number of positive charges in both parts of the wire, just closer together. But the electrons in the opposite part of the wire will be moving upwards at twice the speed (in the RF of the single electron) and therefore their length contraction will be greater than that of the positive charges and so there will be more electrons in the opposite part of the wire. With that said, the electrons don’t magically jump to the other part of the wire just because we change reference frame. I’m guessing relativity of simultaneity comes into play here.

[@srinivastatachar4951]

@@johnwythe1409 From the external electron's POV. Draw the diagram, you'll see what maxv.d.9391 is saying. ==========================================================================================================

[@jgri1324]

@@christofferberg3840 I think you're fundamentally in the right, but I think in can be explained exclusively with relativity and its consequential length contraction. Basically, the moving electron perceives a modified charge density distribution (not homogeneous throughout the circuit, but polar, which doesn't mean the net charge is different from zero, just unevenly distributed) where the piece of wire closest to it in every moment of its movement is positive (what the video explains), whereas the opposite piece of the wire is negative (what you explain in the third sentence of your comment). I must say, the nature of magnetic fields escapes what I recall from my physics lectures and I should really recheck the theory of electromagnetism.

[@kaushikchopra21]

I also arised same question bro

[@jayall00]

As soon as I ditched the idea of particles and started to think of electricity in terms of waves and relativity, everything started to make more sense, including electromagnetism. I still don't know why I'm just learning about this now, 100 years after Einstein conceptualized it.

[@PenguinSharkHybrid]

I came here to watch some fun thought experiment before going to sleep. Didn't expect to have my whole mind catapulted to the ends of space and turned upside down... Absolutely amazing. I never really understood the "right hand rule" of magnetic fields and their forces. This explains it so much better!

[@BigJ_FPV]

Your videos answer the questions I tried to ask my science teacher, and got the “because they do” response. We are tought that these rules are just facts, and that there’s no real answer to them, other than that’s just how the univers works. Until seeing your videos, I have just learned to not question it, because I know that no one will ever give e a real response. Its so satisfying to watch your videos and Finally answer the questions I have wondered my entire life. Thank you!

[@Krokodil986]

Sadly I know exactly what you mean

[@WonderRave]

But don't get too hyped and start questioning deeper and deeper, you will go insane, because questions will never end. Remember to be practical and a little ignorant to keep living sanely.

[@Spectacurl]

Very good video. I have a degree in physics but sadly I had to move to Data Science and this is helpful to remember this concepts

[@sambulls]

I hope you get back into physics, I was in aerospace engineering and moved back to physics by emailing a professor now im starting a graduate degree.

[@cheeseinmypocketsvelveeta2195]

I'm sorry about that :( . I hope you find joy in it and whatever must swing your way to get back in to physics does.

[@dodokgp]

This explanation is quite widespread, but should be taken with a extreme caution. It only validates special relativity by showing that it is consistent with the "magnetic" forces that we observe in everyday life for moving charges, like in a current carrying conductor. However, many people wrongly consider this explanation as the cause of magnetism. It is not. On the atomic and particle level, magnetism originates due to magnetic moments and spins of fermions, which are fundamental properties that we know to exists in matter. Of course, this explanation does help in understanding how special relativity and its consequence is consistent with the observations of forces in moving charges.

[@Songfugel]

I'm guessing you didn't watch the video to then end?

[@sophiophile]

​@@SongfugelIt's a point that is worth belabouring IMO, especially when most viewing a video like this haven't had a super rigorous introduction to the topic.

[@WalterSamuels]

This does not invalidate the claim of there being only a singular field (i.e. the electric field and the magnetic field are one and the same, and not opposites or orthogonal to each-other).

[@louisrobitaille5810]

For all we know, this might be the reason behind the magnetic forces/fields and the length contraction could be caused by the fermions' spins? Is this a rational hypothesis or complete nonsense? I have basically no knowledge when it comes to fields and particle spin but I know about general relativity and I'm very interested in anything QM/QFT/GR related.

[@nonchalant-turtle]

​​@@WalterSamuelsThe EM field has 4 degrees of freedom. Without that context it is inaccurate to say there is only one field, because there is no single 3-vector field that can represent every possible EM configuration. This is related to the fact that, while you can Lorentz boost to eliminate the magnetic component at any single point, there are many fields (like a lone electrons EM field) that will always have both electric and magnetic components when you look at any region of space.

[@MuhammadJasoor]

You know what , Einstein's explanation to the above questions reminds me of my school days when I used to blabber some random excuses to my teacher to justify why i didn't complete my homework 😂... except in Einstein's case he was not lying and had mathematical proofs

[@douglasstrother6584]

In Ch. 6 of "Electromagnetic Fields and Waves" (2nd ed.) by Lorrain & Corson, they derive the Lorentz force from the Lorentz transformation of Coulomb's Law. They also do a similar derivation of the magnetic field near a straight wire carrying a steady current. Ch. 12 of "Classical Electrodynamics" (2nd ed.) by Jackson contains further discussion and analysis.

[@arctic_haze]

Also Chapter 6 of Purcell's 'Electricity and Magnetism,, the 2nd book in the Berkeley Course. By the way, I was pretty sure I have figured out myself that magnetic field is a relativistic correction to the Coulomb law until I remembered there was a chapter on that in the very handbook I used as a student. I don't think we discuses this issue in class but I might have seen it browsing the book.

[@douglasstrother6584]

@@arctic_haze Cool! Good to know.

[@spinhalflight8153]

Thanks @douglasstrother6584 -- I was thinking the same thing. Jackson writes in caution of Lorrain & Corson's derivation, saying in part (p. 578, sec. 12.2) "At present it is popular ... to attempt to derive magnetic fields and even the Maxwell equations from Coulomb's law of electrostatics and the kinematics of special relativity. It should be immediately apparent that without additional assumptions this is impossible... The confusion arises chiefly because the Lorentz transformation properties of force are such that a *magnetic-like force term* appears when the force in one inertial frame is expressed in terms of the force in another frame. It is tempting to give this extra force term an independent existence and so identify the magnetic field as a separate entity. But such a step is unwarranted without additional assumptions." He explains these and then refers the reader to Frisch and Wilets, Am. J. Phys. v. 24, p. 574 (1956) for an accurate derivation of Maxwell's equations using special relativity. Nevertheless, the fact that the Lorentz force law on a single charge can be derived from Coulomb's law and the Lorentz transformations shows how intimately connected Maxwell's equations are with special relativity. Remarkable.

[@arctic_haze]

@@spinhalflight8153 Maxwell's equations do not transfer between frames of reference without relativity and this was one of the reasons they were not that popular at first as we now believe. Lorenz knew how to fix this but did not believe himself in the physical reality of the transformation he derived which still has his name. We needed Einstein for that.

[@geometerfpv2804]

​@@spinhalflight8153It's extremely well-known how the two things are related. In graduate physics, you stop thinking of the electric and magnetic field separately, and learn the Faraday Tensor and 4-potential instead. The E and B fields all out as special cases in certain coordinate systems. This stuff is ancient classical work at this point, there is really no contention. Your author must be nit-picking some minor point about postulates, which is sort of silly in physics...I am a professional mathematician, and from a true logical point of view, nothing in physics is correctly derived from axioms...so why fight about the extent to which it is "incorrectly" done? Physics employs intuition more than pure logic, and that's OK, it would be incredibly slow to do it axiomatically.

[@rajeevsharma6108]

DAMN!!!! you are person behind the voice who teaches physics in Khan Academy!!!! THANKYOU SOOO MUCH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! You have no idea how much you have helped me not just for studying for exams but for in keeping my interest and love for physics alive since years!!! so grateful for discovering this channel, it has all what I want to live!!! I was interested in this higher level physics since 7th grade, and in 8th (lockdown) I started watching khan academy lectures of 9th and 10th as well. Now my 12th is about to end and I am regaining my curiosity in physics for its own sake (lost it due to rigid systems of competition, exams and marks as well as distractions). And this channel is helping me Your explanation, enthusiasm, clarity, knowledge and love for teaching is just✨✨✨

[@Mahesh_Shenoy]

@@rajeevsharma6108 Hey, I am glad to hear that :) All the best :)

[@kishoreprabakar]

You didn't stop from just making videos on Khan academy (Ch:4 Moving Charges & Magnetism), but you also made this video. This is the sort of education everyone wants, this is the sort feeling one should get after learning. Thanks for inspiring me to educate myself! (PS: I have boards coming up in 3 weeks, can't help myself from looking at your content for Physics. >.

[@Mahesh_Shenoy]

Wow, that’s very powerful Kishore!

[@kazukawasaki97]

​@@Mahesh_Shenoythe last question,how about the charge was not created, the net charge remained algebraicly the same,but due to contraction of space,more charge was experienced by the single electron

[@PAWAN.]

​@@kazukawasaki97I am also imagining that and watching comment if other think so too😂

[@TheLoadedLongboard]

My answer to your final question, which was "what about conservation of charge?" The wire's charge is conserved, it's spatial dimensions are not. The wire changes size because the particles change in size. The change in size creates a dipole that is oriented non-normal to the length of the wire. The negative charge of the wire exists, but it is the orientation of the dipole within the wire that creates the net positive force. Great video, love your enthusiasm.

[@VinyJones2]

Yes, it a circuit so others parts of the circuit will balance the charge as the circuit and the electron move in others direction

[@SkaggsFamily]

...and in a rare demonstration of time contraction, a 17 minute video was just summarized in 17 seconds. 🏁

[@TreXsJournal-Coming-Soon]

​@@SkaggsFamily that wasn't even the point of the video. What are you talking about?

[@SkaggsFamily]

@@TreXsJournal-Coming-Soon Ummm, humor? Here you go... The video was 17 minutes long, and summarized in 17 seconds. Bonus! A demonstration of time contraction in addition to the subject! (That's all. And now I've lost time explaining it. Humor fail!)

[@Rocksidion]

​@@SkaggsFamily Point of reference really matters!

[@reinerwilhelms-tricarico344]

I was taught this as a physics student about 50 years ago. I didn't believe it, and seriously thought the prof was trying to troll us. Then we did the math; it made sense, but I still didn't believe it. Eventually, when I got deeper in the math I believed it because I could do the math myself. I admit, it felt like it took a certain amount of brainwashing before you begin to not just trust your common sense. In that respect you made an important argument that made a difference, namely the intuition about the effect reaching macroscopic relevance because of the enormous number of particles in the wire. On the other hand, the story with time dilatation explaining the reduction of the Coulomb force, that still feels as weird as before. To this day, at 70 years old now, I quite frankly find most of these results still a bit weird just like the first time in the 2nd or 3rd semester of undergrad physics.

[@louisrobitaille5810]

Like Richard Feynmann famously said: "If you think you understand quantum mechanics, then you don't understand quantum mechanics." Science is the best tool we have at our disposal to understand reality as it is, even if it's contradictory to what our senses tell us. Our senses are flawed, that's why we build instruments and machines to "see" the world for us.

[@carmelowanthony7946]

Exactly and also this fact along with other parts of science that are so unintuitive for me totally eliminates any possibility of God demons or anything spiritual cuz modern science is like 500 years old and that’s how long we’ve been able to mesure reality in ways isolated from ourselves and your intuition and we’ve discovered that none of this shit makes sense so the idea that the ultimate answer the key to reality is a God and theres a forever good place and a forever bad place and like that stuff at this point is terribly ridiculous to believe at this point but it makes so much sense to us that people continue to believe

[@FreakGUY-007]

​@@louisrobitaille5810 well it's a debate that the laws that we know shows reality as it is. In other words are we sure we learning about the laws as it is?

[@bigbang259]

but if it were true, it would be the same with permanent magnets. Can it explain permanent magnets?

[@Tawbah0101]

​@@carmelowanthony7946if you love science and nature soo much and have seen the beauty of physics and maths and the insane patterns there is ,how can you not believe in the existence of God ?

[@Familyproud-e9h]

Very well explained. What's so interesting is that even when we don't know the exact mechanism of a particular phenomenon, we can still use the laws and equations with reasonable accuracy for a lot of everyday applications.

[@sqlexp]

How does he explain if the electrons in the wire move at 1.5 times the speed of the external electron and the wire moves at 0.5 time of the speed of the electron in the same direction? Then in the reference frame of the external electron, the electrons in the wire and the wire move at the same speed in opposite directions.

[@jotabe777]

I´m a high school Physics teacher. This is like watching adult content to me, lol!! It reminded me of my Modern Physics classes, which I loved. Awesome video, subscribed!!

[@atfti]

Interesting. I didn't think people literally get off to physics, but whatever floats your boat lmao

[@evildaddysteve]

Very well explained. My physics textbook agrees with you. I have gotten pushback when I tried to explain this concept. Thank You, and keep up the good work!

[@User00571]

So what is answer? Why they produce magnetic field?

[@Songfugel]

Ok, not only did explain relativity in electro-magnetism, but also time-dilation better than anything I have come across so far! Oh boy, if only I had seen this sort of video (well, YT didn't exist yet) in University when first studying these topics

[@louisrobitaille5810]

Time dilation is expertly explained (vulgarisation) on Science Clic (English) in his General Relativity playlist. You should definitely check it out 👀.

[@varshard0]

Can you be a teacher in every subject 😂? Your contagious enthusiastic and ability to explain in such a simple manner is phenomenal.

[@finnvankoutrik7131]

quik question, from the electrons reference frame the protons are moving so they get closer to each other, yet from the protons reference frame the electrons are moving and they should get closer to each other. This doesn't happen, why?? why doesn't the wire become negatively charged and repulse the electron on the outside?

[@louisrobitaille5810]

From the electrons' Frame Of Reference (FOR), the protons are moving but they're not getting closer to each other. They're all moving at a constant rate so they stay at the same distance from each other. Same thing for the electrons from the protons' FOR. This changes ever so slightly for the electron outside the wire though. Just enough for it to feel an attraction towards the wire.

[@ashercorbett8089]

This dude is literally talking to a dead dude like he’s his best friend

[@michaelkovalenko1429]

This is great. I've graduated with MS in Physics, In college, I was curious why the Lorentz formulas were similar to the special relativity ones. Now I know: it is the same! The magnetic force is a pseudo-force!

[@zabity]

pseudo-force or pseudo-explanation?

[@sleepinbed]

but, the magnetic force is not a pesudo-force... the magnetic field is pseudo vector though! this question has been asked (and answered!) a relatively long time ago, the EM field definitely does exist, and if we try to assume either the magnetic or electric field to be fundamental, an illusion caused by relativistic phenomena, we can craft a theory, but we will not get it to be Lorentz convariant. there is also an I think simpler explanation as to why this does not work: our assumption is that, due to relativistic phenomena, there is a difference in charge density which causes an electromagnetic force. so let's see what we can derive from this: the force on a particle ought to be higher in a boosted reference frame, but we cannot say this because special relativity automatically assumes that the force on an object doesn't depend on the speed of the reference frame. so we cannot say that this is all one force, we see there is a new force. we can say that this force is the magnetic force. the electric and magnetic fields are both components of the electromagnetic field, they are different, have different properties, and most importantly: all of them do exist and are not illusions of relativism :)

[@jaydenwilson9522]

Electricity is one force that splits into 2.

[@mehuldangar6660]

You are wrong magnetic force is not pseudo force it had energy so it must be real pseudo force are just introductie for relativistic transformation

[@jaydenwilson9522]

true dat... relativity abstracted reality and our classical equations @@mehuldangar6660

[@diyvideojunk2066]

Next time I look at an electric motor I will now have to think about length contraction of the charges within the coil ! Thanks for this intriguing video

[@jssamp4442]

About 7:15 you should have stopped after the length contraction of the protons. Remember, you said the electron was moving the same speed as the electrons in the wire. So they would still be at the proper length as they have no relative motion from the electron's frame.

[@deinauge7894]

no. the electrons are moving in the wire-frame. But not moving in the electron-frame, and therefore their distance is bigger from the electron's perspective

[@jssamp4442]

@@deinauge7894 One of the conditions specified when the hypothetical was introduced was that the electrons outside the wire were moving the same speed as the electrons in the wire.

[@deinauge7894]

@@jssamp4442 i know. that means, they are moving in the lab frame, and not moving in the electron frame.... as i wrote

[@jssamp4442]

@deinauge7894 I think I see the disconnect. You said the electrons are not moving in the electrons frame, and therefore THEIR distance is bigger from the electrons view. It's the object of the pronoun "their", if by their you meant the electrons distance, that is incorrect. If you meant the protons distance, that is correct, because in the frame in which electrons are still, the protons of the wire are moving and therefore length contracted.

[@deinauge7894]

@jssamp4442 you don't understand... the distance betweenthe ELECTRONS is smaller in the lab frame because they are moving. and therefore it's bigger, compared to the lab frame, in the electron's perspective.

[@Familyproud-e9h]

I came back to this video so many times as I still had confusion in my mind. It's all clear now meaning that I can explain this phenomenon to someone else. Thanks again 👍🏻

[@danieleciavatta7522]

Why length contraction applies to protons (positive charges), in the moving charge frame of reference (6:58) and not to moving electrons, in viewer frame of reference (2:29)?

[@geeb009]

Because electrons in the wire and the electron outside are moving at the same speed.

[@coniccinoc]

I do not know of a better instructor. Top shelf excellence.

[@MrCuriousYogi]

Really mindboggling explanation. Hat's off Sir.

[@Mahesh_Shenoy]

Thanks, Yogesh!

[@Jam-c2g]

I rarely comment on videos, but your enthusiasm is absolutely contagious. Keep up the good work!

[@hardpanchal2821]

I Have No Words...The Way You Explained...I was in another world...Too good, TYSM for this

[@Mahesh_Shenoy]

I am glad you loved it 😊

[@nikthefix8918]

A very important and interesting topic - not only as it demonstrates the explanatory power of SR in the most unexpected of nooks and crannies but also that it shows that SR is largely compatible with Coulomb. Indeed, a magnetic field can be seen as an electric field and vice versa depending on your frame of reference. I think you described the situation admirably and made it easier for us to see just how and why the magnetic and electric forces were ultimately unified. I'd love to see an equally well explained follow up video on how accelerated frames give rise (from the observer POV) to radiated EM energy. Your very own 'explanatory power' and passion have given rise to a wonderful YT channel IMHO.

[@EMAngel2718]

One hangup I have with this explanation is the fact that it implies that an electron that's stationary relative to the wire should be repelled since the electrons would be closer together, but everything I've seen says that stationary charges are unaffected by magnetic fields

[@johndoggett808]

I also wonder how radio waves (Electro Magnetic radiation) can propigate through a vacume, if there is no M field.

[@rickroller1566]

Why would the electrons be closer together?

[@WonderUniverse_]

Hi, no it is not! From the point of view of a stationary electron, the length contraction applies only to the single moving electrons that are into the wires (because they are moving) and so they appears to be squeezed, not to the wire and neither to the distance between the electrons that are flowing, since the conductor is at rest also in the reference frame of the stationary electron! Only when we are into the reference frame of a single moving electron outside the wire we will see the wire (and thus the distance between protons) to be contracted because from our perspective the whole conductor is moving with respect to us (and thus it appears contracted)!

[@BenjaminK2]

@@rickroller1566Because they would be moving relative to the single stationary electron outside the wire. Thus length contracted. Thus closer together.

[@BenjaminK2]

⁠​⁠@@WonderUniverse_ I’m not sure I follow. “The length contraction only applies to the single moving electrons in the wires”. Not sure what you mean by “single moving” here, aren’t they all moving together? “They appear to be squeezed…”. Yes I agree, just another way of saying contracted. “… not to wires…” do you mean the stationary wire (ie positive ions) are not contracted, as yes I agree. “… and neither to the electrons that are flowing”. Lost me here, are you saying the flowing electrons haven’t contracted? I guess you don’t mean this as I thought you established above “the single moving electrons, which are in the wire, are contracted”. And just to make sure we are on same page, by “the conductor” do you mean the stationary wire / ions?

[@Super_Beast124]

I love that we have full conversations and lessons with long dead key figures from history, a very fun approach

[@JuanPAMaldonado1]

small correction. the electrons don't go farther away from each other. On the electron frame of reference, the other electrons have *always* been at rest. With only the protons being closer to each other you can explain the phenomenon

[@alspezial2747]

Thought so too. What also bothers me is that the attracting force would be dependent on the direction the single electron was moving to. So considering a random average, it should be "stationary" in a macroscopic sense.

[@mullergyula4174]

Love how you smile during presenting. Keep it up.

[@entropy576]

I am soo glad that I found your channel sir I rly had this question haunting me from a very long time I have asked my teachers and many other people but none of them came up with an convincing answer and also often I keep getting such very niche doubts while I am studying physics and science in general but often I do not get convincing answers or I just get to hear "how does it matter" and I also have my friends telling me not to waste too much time on such things as no questions would be asked (as I am preparing for jee) but I just can't leave those questions like that because they just keep haunting me But yea thanks a lot sir Also I have many such questions I hope you can answer then

[@amandeepsaha]

Beginning of the video my reaction - " what the heck" End of the video - "okay! u convinced me"

[@siddharthannandhakumar6187]

When we assume a complete circuit around the electron, the state of charges on the other side of the electron relative to the electron would appear to be opposite (like electrons are closer and protons are farther), conserving the total number of charges

[@oojikarasuma1]

Thanks for explaining

[@Krokodil986]

What about if the circuit is broken at the opposite side? Then it would take a split second for the information of the breaking to travel and "inform" the electrons on our side. During this split second the electrons on the opposite side would have stopped however the electrons on our side will be still in motion. During this split second I almost want to say charge isn't conserved? It changes hence net change in charge ≠ 0, for a very short amount of time

[@jonschreiners5006]

⁠​⁠@@Krokodil986I’m sure this problem is likely solved by relativity of simultaneity. I don’t have the brainpower to work it out, but this is likely similar to the train going through a tunnel “paradox”.

[@Krokodil986]

@@jonschreiners5006 maybe it goes like this - Either way (whether the circuit is broken or complete) the total number of charges N doesn't change. It's like an elastic band being stretched at one side but compressed at the other. This "wave of compression" travels at the speed of light (along with the disturbance of the field, or perhaps marginally slower since electrons have mass and take time to accelerate) but N is still constant. Alternatively, taking into account relativity of simultaneity - Relativity is local and doesn't work on environments where the measurement takes less time than light would take to cross this environment. So we should count N not instantly but at the speed of light, as the "measurement/information" makes its way along the wire. This means it will travel along with the "compression wave" which informs the electrons of the sudden break in the circuit. So the density of charges inside each local section of the wire will be constant for the time it takes for the measurement to pass thru the wire, so net charge remains constant, as this "wave" (or whatever you wish to call it) affects electrons and protons at the same time. But this does mean that although observers will agree on total charge, they won't agree on specific numbers of electrons e and protons p, but only on the ratio e:p?

[@aguven]

Paradox of Changing Charge: The apparent change in charge density of the wire as observed from different frames of reference is not a true change in charge. It's a consequence of how different observers perceive lengths and distances due to relativistic effects. Electromagnetic interactions, including the attraction between the electron and the wire, are invariant under Lorentz transformations, meaning they are consistent across different frames of reference.

[@johnbennett1465]

Interesting explanation. So how does apply to magnetic field lines? The standard experiment with a magnet, a piece of paper and iron fillings clearly show them. What does Einstein have to say about this?

[@KlaasVictor]

This is a question I could not figure out for 30 years. Seriously. Thank you!!!

[@UDHAV79]

Amazing Video! This is going in my physics playlist

[@Mahesh_Shenoy]

Glad to hear that! :)

[@kentkagle3850]

Great well paced ...like to see you do a never ending series..

[@cmilkau]

15:50 yes indeed, in special relativity, electric and magnetic fields combine to a single field, and the electric and magnetic amplitudes depend on the reference frame, with the Lorentz transformation defining the relationship. A similar thing happens with energy and momentum.

[@maeton-gaming]

The dielectric field IS magnetism, when the dielectric field experiences loss of energy it manifests as magnetic effects :)

[@mathfobia]

Superb explanation. ❤ for u.

[@mariosmusik4898]

7:40 From the perspective of the Lab frame: wouldn't the electrons come closer together. So the picture Lab frame would be the opposite of the Electrons R.F and the electron should be repeld from the wire? What am I missing?

[@mariosmusik4898]

ok, watched another video if a got it right the length contraction also just happens for the moving part from the perspective of the observer. Still got other questions: From lab frame would the electron get smaller or does length contraction mean elektrons, neutrons and positrons getting closer together so it doesn't apply to a single electron?(guess the answer is not relevant for the context of magnetic fields) Is there an equal force pushing the wire to the left to the force repelling the electron? If yes, why can't the force be explained with coloumbs law from the lab frame? (wire is macroscopic neutral there) Why couldn't it be the opposite, that the wire is neutral from the electrons perspective and chardged in the labs view? (Maybe a silly question but I have no really physics background besides school physics). Wanted to understand electric motors better, but Lorentz force alwasy was so unintuitive for me (wtf is the force orthogonal to v and the magnetic field, feels weird). Do I maybe have to study physics and relativity theory to feel better🥲? Btw has anybody a recommendation for a video about ferromagnetism, also fells still weird to me? Or maybe a good book that dives deeper into electromagnetism than books you would read in electrical engineering but too deep.

[@jurgenjurgens9680]

Many thanks for your high quality videos. What I do not really understand is the following: The electrons inside the wire move with protons in the same direction. So they should also move closer together, seen from outside the wire. Can you give me another hint? Thank you so much and greetings from Germany

[@tuxat_]

your videos are so good I have to force myself to stop binging them and finish my homework

[@abstractvolume9160]

Energy is still conserved as the charges are distributed that is making one side electrically positive and another side negative and so hence the net charge in the closed system is conserved

[@Mahesh_Shenoy]

Nice!

[@karanasstelios6141]

Can you explain it to me?

[@sylverfyre]

@@karanasstelios6141 A complete circuit must be some kind of loop. That means, if you're looking at Mahesh's diagram, somewhere off screen, you have the "return wire" where current is flowing in the opposite direction, thus the electrons on that side (which are moving in the opposite direction in the lab's reference frame or "up" in our electron's ref frame) are appearing even closer together than the protons on that side of the wire. I haven't done the math, but I assume that adding up length contraction in various directions around the entire closed loop of the circuit, it works out that we end up with total charge being 0 within the wire.

[@PaulThronson]

This is the best if not an excellent video explaining how electromagnetism is the same force, and how It proves that space and time are the same dimension.

[@roccodimonda4298]

The electrons in the wire would not move further away from each other as you said in the video at around 7:30, they are at the same velocity so would experience no length conteaction relative to the external electron, or am I mistaken? Or was it just done to help visually?

[@sealofapoorval7437]

So because from the moving electron's perspective all the other electrons in the wire are standing still. Because they are all moving in the same direction at the same speed. So now we have a bunch of electrons in the wire that are standing still next to each other (from the moving electron's perspective). And what happens to a bunch of electrons close together just standing there with no external force? They repel each other. That's why its not length contraction but a regular law of like charges repel that makes the electrons move further apart. Hope this helps.

[@ffcreations5192]

This video is awasome ❤ & very helpful for me 😊

[@JPGonzalez2011]

This is amazing. Your level of knowledge and ability to use it to convey these ideas is truly special. So happy that I have found your channel. Also, so much respect for being able to say that you were approaching the edge of your knowledge towards the end. Such humility is rare in a person with so much knowledge and ability. Thank you, Mahesh!

[@remsupport8984]

Great job explaining something complicated in a way that everyone can understand! I learned something (:

[@vwcanter]

I was just about to pose the question about a point charges, and then you answered it. Thanks, that's the part that is never mentioned in other lectures.

[@straightdrive6192]

you my friend, are just too good, keep it up.

[@michelegambirasio5445]

The point for the electrons that feel the "magnetic force" Is not how many protons are in the wire, but how many protons their point of view brings close to them. Thats means that a single Proton seems ti be in different location for different electrons

[@gualbertovega3218]

My dear super explainer, please enunciate All sentences all the way to the end, I am having trouble understanding the end of the sentences. I write this because you are very good, and want to continue learning from your videos. Thanks

[@shreyashbhanderi3720]

ok but lets say there was a stationary negative charge near a wire with current passing in it. from the stationarz negative charge's perspective the electrons in the wire would be moving and the protons would be stationary. so the electrons would contract, creating a percived negative charge. meaning the stationary negative charge would be repelled. so the forces would change depending on the speed of the charged particle and when the speed is 0 it would be repelled?!? this doesnt make any sense am i doing something wrong? or does the magnetic field switches directions?

[@Mahesh_Shenoy]

You know what? That’s the exact question I don’t have an answer too. I searched a lot, but just couldn’t find an answer for it. So kudos! Let me know if you find something!

[@carlosvazquez4401]

That is the point: The electrons moving inside the wire make the distance between them shorter (Lorentz contraction) than that of the nuclei. Then the linear density of electrons would be higher than that of the nuclei, producing an effective electric field that the charge outside the wire would feel, no matter if it is moving or not. In synthesis, your explanation is not convincent.

[@Mahesh_Shenoy]

@@carlosvazquez4401 Agreed. But, if you ignore that, for a while, and assume that the wire with running current has the same electron and positive charge density, then the math works out. You can derive the expression for the magnetic field using relativity and perfectly matches with the Bio-Savart and Lorentz force. But, why isn't there an electric field in the stationary reference frame is something beyond me. If I had to guess, then it could have something to do with the fact that electrons aren't moving in a straight line. There random motion maybe counteracting the whole contraction. But, when the charge starts moving and we jump into it's reference frame, the wire and the electrons inside ARE moving in a straight line. But, again, this sounds very shaky to me.

[@hosh1313]

You are 100% correct!

[@GalilErme]

​@Ali S. If I understood that correctly, when the electron outside the wire is stationary relative to the protons, it is stationary relative to the laboratory frame; only the electrons inside the wire are moving, so only they contract. When the electron outside the wire is moving relative to the protons, it is actually moving relative to the whole laboratory and the whole wire, so both the protons and the space between the protons contract. This means that the charge density changes in the (outside) electron's frame only when it is moving. This really sounds as a good explanation to solve that doubt, but I have a couple of questions. First of all: where did you get this explanation? Is it from a book or some other source I can find online? Second question: the electrons are considered to be pointlike particles, dimensionless, so does this mean that electrons cannot actually be length contracted?

[@John-pp2jr]

❤❤wonderful explanation, the best I have ever seen.❤❤ WOW.

[@justgivemethetruth]

That's interesting, but it seems more difficult to look at things this way. Also ... how does that explain electromagnetic wages where the E and the B fields are our of phase? When would looking at things or modeling then this way be helpful?

[@neiloppa2620]

I wondered about this off and on for a long time. Thank you for the answer ❤

[@jamesmorrison7989]

This was the best electromagnetism video I’ve seen in awhile. Reminded me of my college days - I studied physics. Thank you (:

[@Tyuiiiizxvb]

An Indian called "James Morrison"..ha ha ha ha 😂😂😂😂😂😂😂😂😂😂😂😂

[@jamesmorrison7989]

@ I’m not Indian.

[@ajaybhardwaj2547]

It feels really good that someone has come outta the well and has started teaching for knowledge distribution. Well, i have a question which always ticks my mind whenever i study this relation between charges and relativity. I hope it may reach you. In our first example, we made the electron run at a velocity equal to that of other electrons (ofc assuming that velocity of all the electrons is the same). Let's, just for the sake of this question, assume that our electron which is out of the wire is at rest. When looked at the electrons in the wire from its perspective, we will find that they are in relative motion with this electron. So, the length between electrons must shrink down and they must come closer. Ions on the other hand must go apart. this must make the wire negatively charged and get the electron repelled. If you say that the coulomb's law is the reason behind magnetism of current carrying conductors, then how can one counter this problem. This seems to affirm magnetism as a property of charges at rest.

[@Crimsonraziel]

For the question at the end: It's not about where the charge comes from, because it didn't change at all. The length contraction spreads the same charge over less space. The charge density changes and that's what matters.

[@AccelYT]

So, with the circular wire what would happen? The radius of wire would decrease? (specifically the radius of wire сrystal structure, and the radius of space that holds electrons would stay the same, so these two spaces wouldn't coincide anymore). I'm afraid, as in all cases where Einstein is involved, there would be no clear and intuitive explanation for that.

[@louisrobitaille5810]

@@AccelYT As Richard Feynmann famously said: "If you think you understand quantum mechanics, then you don't understand quantum mechanics." In other words, if something relating to quantum mechanics feels intuitive or seems to make sense, you're probably missing something important. In this case, it's special relativity applies at the quantum scale and particles.

[@Crimsonraziel]

@@AccelYTFirst of all, basically nothing is intuitive when it comes to SRT/GRT. Second, from the electrons perspective the entire structure containing the protons is moving and therefore appears to be clinched in the direction it is moving. If it looks like perfect cubes from the proton perspective, it's just a rectangular prism from the electron's view (squished in direction of movement). But you can't make an entire circuit in a straight line and with the curve there comes change in direction of the moving particles, which means acceleration, which in turn leaves the realm of SRT and requires GRT. And here I'm not confident to be able to explain this in the comment section. I could try with paper, crayons and cookie, but probably still fail. :3 What might help: look for relativity and why simultaneity ist not conserved when changing the reference frame.

[@Erbureth]

@@AccelYTWire forms a closed loop, so from the reference frame of a moving particle, for each part of the wire that appears positively charged there would be another part of the wire that would appear to be charged negatively.

[@GrahamRounce]

Yes, but if we put a grounded aluminium sheet between the electron and the wire, it would block the electric attraction, but magnetism isn't blocked like that. So how does that work?

[@Nobody_114]

@7:05 Actually, the electrons do not move further away from each other because you are discussing this part from the electron's reference frame, showing the electrons are basically stationary to each other assuming the electron mobility is the same for both conductors. Also, you talk nothing about the electrons spin, and how its alignment works in an electric field while the electron is moving. Isn't there a contribution to the magnetic field there?

[@ShivamVerma-hg2iv]

Ya true, electrons don't move with respect to electrons reference frame. But with proton refrence frame when proton is moving these proton see the electrons move away.

[@quantisedspace7047]

​@@ShivamVerma-hg2ivI am still confused. This idea of particles moving closer together suggests that they ate simply under some sort of compression force: they aren't; they are only 'closer together' because EVERYTHING is closer together in that reference frame, because the concept of length is different. What appears to be being said here is 'there are 100 protons on this side but, due to length contraction, there are 110 electrons on the other side', implying that the protons are now interacting with a larger number of electrons on 'the other' side ? Why would the ly interact like this, surely the various forces and fields between the two sites would 'fan out', leaving the original 1:1 correspondence.

[@Sharu-rh2rz]

@@quantisedspace7047 No it only means that before, when we are not considering relativity and we take a section of the wire , the amount of protons and electrons cancel each other out. But after looking from the electrons point of view, length contraction is taking place for the protons so the amount of them don't change, only how much we can find them in the same section of the wire will change, so now there will be more protons than electrons in that section, but not overall.

[@welldonehuang9133]

This is a great topic! I always struggled with understanding why a moving charge produces a magnetic field. Thanks for sharing this insight. 😊 Looking forward to more such educational content. 🎓

[@matthewlind3102]

this is awesome, thanks man. Great explanation. I was thinking about solid state magnets. Maybe you could use this framework to explain attraction if you consider electron orbits?

[@Ihopeitsnottoobig]

Thank you for sharing this was insightful. Its interesting how people can come together to form the same conclusions from different perspectives.

[@waynerawlings8599]

Thanks for that. I’ve always been a bit confused about the magnetic field. I had an image in my mind of the electric field being distorted somehow when the charge is moving, it’s lagging, making it look like a “magnetic field” but when you introduce length contraction and time dilation, that makes it clearer

[@מעייןאריאלי]

same ! i honestly still feel like magnetism isnt actually a thing, and its just electric forces being distorted due to movement or quantum spin

[@levshyrokov6464]

​@@מעייןאריאלי oh yeah, I just started to think this way for about few months. It makes sense, since there's no "magnetic charges". And there's no need for magnetic fields even with electromagnetic waves, since they can be explained as a distortion of an electric field of charge, produced by its motion.

[@chad872]

I love your excitement in your presentations…

[@adritajindal9261]

hello sir.. thankyou so much for this video.. I am from class 10th and interested in physics. actually I was searching for this answer since a very long time.. but everybody was ignoring my this question. you really explained it very well. thankyou so much.

[@Mahesh_Shenoy]

I am glad you enjoyed it, Adrita :)

[@atafali6337]

it blew away my mind Thanks from the bottom of my mind!!

[@jensphiliphohmann1876]

Though I first learned about Relativity from my grandfather even before I did in school, I kind of feel that I really understood it relatively recently, and it were Relativity deniers of all people who helped me quite a lot in leaving some misconceptions I used to fall for.

[@MrBrunoMi]

mind-blowing! Thanks!

[@MuhammadFareedRaza]

But the columbs law is valid only in case of stationary charges.

[@ashwin372]

listen again

[@egotist-ical]

All the power of Indian YT tutorials encompassed in one man... He's too powerful!

[@TAR68311]

I think I found an explanation for the two comoving electrons: When the two electrons move with respect to an observer at rest with respect to them then they are basically at rest with respect to each other. So, the only force they experience - from their perspective - is the repulsive electrostatic force. In the same way they do, when they are at rest with respect to the observer (or comoving). Now, what does the observer see when the electrons are moving with respect to him or her? Because of Lorentz contraction the observer sees a higher charge density. As a consequence, the electrons must repel with a larger force than before. Since they obviously don’t - the physics must be the same - there must be a counteracting force making the net force as large as if the electrons and the observer were comoving. This counteracting force is the magnetic force due to the relative motion. And like the electron moving in the same direction as the electrons in the wire this force is attractive just balancing the additional repulsive electrostatic force.

[@realdomdom]

1 minute in and I already know where this is going. Very clever of you to explain the definition of a magnetic field. That was sarcasm.

[@Tenraiden]

All this thinking is literally making bro's hair fall out 🥲

[@wallahhabibiiii]

small price to pay in order to understand reality

[@hemank7186]

Great , Brilliant way of explanation

[@aryanbasu8686]

Q1: In the length contraction model, the charge will be deflected towards the wire. But in tbe magnetic field model, the charge was supposed to deflect towards the wire then move in a circular path (not perfectly circular since the magnetic field will vary with distance from the wire) F=q(v x B). How do we explain that circular patch with length contraction? Q2: When two equal like charges are moving parallely, can there be a velocity for which the force of repulsion and attraction become balanced, and this velocity will be a function of the separation between the charges ig?

[@parthibanspace]

Great explanation about interaction between moving charges through coulomb's law. I'd love to hear an explanation about how a magnet gets affected in the presence of moving charge.

[@flamencoprof]

2:36 Yes, the wire as a whole is neutral, but when a current is flowing the free electrons repel each other and thus all flow at the surface. Thus an approaching electron "sees" only the surface electrons, and should be repelled!

[@BinkyTheToaster]

it makes sense as well given that electromagnetic forces are one of the strongest in the universe, second only to the strong force, and then only when the radius between the charges is big enough. So that we can see macro effects with so small a relativistic effect shouldn't come as much of a surprise. Heck, it even overwhelms the strong force in the nucleus because the distance is so small; it's why you can't have a Helium-2 atom with only the two protons. Their charges repel so hard the strong force can't keep a grip on the two particles.

[@Govstuff137]

Well you are welcome! In a Feynman kind of approach by making these podcasts you are now able to see things better in your mind as you explain them too others. As Richard Feynman said if you can't explain a thing in simple language then you don't really understand a thing. I paraphrase. I hope we have helped you as much as you have helped us. I like your explanation. I can see how it applies to videos of how a current appears to move through a wire. And until something else comes along to replace it. I like your explanation it makes very good sense. I hope we can help you understand lots more things in the future. I look forward for more explanations so we can help make you a better scientist. Your welcome! 😊

[@SultanInStem-t3i]

honestly one of the best physics channels

[@v1298]

This video really was mind blowing. You're great at explaining these things, too.

[@wilsongomes3360]

Nice explanation.Clear and concise

[@VallabhStudies]

everytime i watch yr videos it blows my mind

[@kinslayer202]

This is such a great explanation! I never considered the effect that length contraction would have on electromagnetic interactions but this year made it make so much intuitive sense

[@jonathanbyers791]

Glad I found your channel, I particularly like your video on spin.. Def the best explanation to date. This video is also great except using the word 'Proton' instead of Nuclei is very confusing, and describing atoms being closer together on Lorentz contracted conductor is also confusing.. you could have said something like.. as measured from the Electron (rest) frame the Nuclei are closer together.

[@jeremielhomme8572]

Always clear and interesting!

[@avoiceinsupportoftruth5]

Thank you for taking the time to explain these things!

[@sinsitis]

Great video, thank you !