electricity and magnetism are the same thing

[@DarthErdmaennchen23]

Engineers: Luckily we don't have to calculate all that, we just have to remember the right hand rule! Phycisists: I don't have time to remember this weird rule, I just calculate it!

[@zuzusuperfly8363]

I was working a crappy job and everyone found out I studied physics. Someone hit me with the right hand rule and I was like, eh my brother.

[@Tardsmat]

​@@rdistintidid you watch the video? She's referring to a different right hand rule

[@MarianneExJohnson]

Linear algebra FTW

[@PedroTricking]

How are you supposed to remember the orientation of the cross product then? Geometrically, your right hand points it out for you instantly.*

[@viliml2763]

@@PedroTricking Find a paper that defines the conventional orientation and cite it every time.

[@kylehill]

This is like sitting with a really good tutor.

[@denim_ak]

Crossover episode 🎉🎉🎉

[@azzydraws3107]

oh hey kyle

[@naidanac1]

Yes!@@denim_ak

[@ethanwagner]

This is the Spider-Man meme of science communication

[@aldokurti3272]

Grear teacher meets another.

[@chrisl6546]

Maxwell is totally underrated in popular culture for being a brilliant physicist. Arguably, all the discoveries of the early 20th century were only possible because E&M was so well defined that you could both look for deviations from it and reliably build experiments using electricity. And ultimately, we make almost all measurements by turning them into a voltage some way or another and measuring the voltage.

[@liquidsonly]

Certainly not underrated though if you delve into any physics realm. I studied environmental science and many equations concerning distribution of pollutants were derived for maxwell's.

[@Celia_Dawn]

@@liquidsonly Pop culture, though. Maxwell sadly doesn't quite have the same "Household name" status as someone like Einstein or Newton, or even Marie Curie.

[@thermodynamics458]

I agree. As enormous as his reputation is, he's still underrated in the light (no pun intended) of his achievements. And it wasn't just EM, and the unification of electricty+magnetism+optics. He also made significant contributions to thermodynamics and even planetary science (he correctly determined the character of Saturn's rings). Giant.

[@zuzusuperfly8363]

Here's the thing. I'm not so sure. What is popular culture right now? And after people appreciate Maxwell on an individual basis... there's not a whole lot else to talk about because people who know about Maxwell are moving onto other things. When these kinds of people meet and chat, they're probably not going to talk specifically about Maxwell. It's a hard thing to judge, but I feel like Maxwell gets enough credit. He's just not cool. And that's okay. Andrew Wiles proved Fermat's Last Theorem and nobody gives a single damn about him. I forgot his name for a second when I wrote this. Local culture and education is always going to be more valuable than whatever the hell the media decides to promote.

[@chrisl6546]

@@zuzusuperfly8363 Just looking at the various physicists well known to people outside physics - Newton, Einstein, Feynman, Oppenheimer, Hawking, Teller, and probably more. Maxwell's contributions were enormous - he built in special relativity before it was even a thing!

[@KR21925]

Ten years ago, I got 2 points off on an exam for writing 'electromagnetism' instead of 'electric force' and 'magnetic force' when asked to name all of the forces. They refused to give me a re-grade, and to this day I hold a hold a grudge for that decision.

[@fudgenuggets405]

You should use this as a response to their alumni donation drive requests.

[@erinhaury5773]

I once was disqualified from a geography bee over a similar thing. They asked where in the world Lake Baikal is located and I said Siberia. They said 'Wrong, in Russia'. Like, I'm sorry, you didn't ask which country, you just asked for a general location. Sometimes the people running these things are blockheads. 😂

[@Religion-Is-Fiction]

Just do your work, stick with science, be ethical, moral, and honest, gather your accolades, teach what you're good at. Forget your exams, that's just college stuff. It's just training to work white collar, hopefully to be paid better. It doesn't always work out. We're all the same ape with a large brain. If you can teach other people to teach, you did your job well, and you'll be respected for it. You'll get a nice eulogy 😂

[@afelias]

Should have written Electromagnetic Force and Ele __c ort m agn __e cit F o rce

[@asganaway]

That's the question I got my own -2 points, please answer: You have a clock, is the measurement you are reading quantaized?

[@sowercookie]

My absolute favourite thing is that dr Angela insists on doing the math! I think people get this skewed idea of physics, that's it's just a bunch of quirky factoids, because no one shows the math involved (and then some of them start thinking they're smarter than the physicists and start coming up with nonsense...) So thank you dr Angela!

[@АндрейДенькевич]

I hate it, but indeed ellectricity, magnetism, mass, gravity are exact same FORCE, only with different quality(dimension). Electric monopole (charge) - 0D Magnetic dipol - 1D Mass 3-pole - 2D Gravitational 4-pole - 3D This assumption explains why only charge density can fluctuate, because second pole of it connected to 4D. And increasing of charge density, i hate it, means that more candidates from 4D are pretend on 1 position in ,don't know, 3D or 2D or 1D.

[@janusprime5693]

@@АндрейДенькевич love the incoherent rambling, keep it coming!

[@Dext3rM0rg4n]

​@@АндрейДенькевичHE HATE IT

[@Musabre]

@@janusprime5693 😆🤦‍♂

[@orterves]

And such relatively simple mathematics too - deep insight into the real world all fit into a handful of elegant equations.

[@kashphlinktu]

Omg I did the same thing in a physics exam, luckily my professor was merciful and wrote “used left hand rule. Error carries “. And only deducted a few points

[@apteropith]

yeah, if you use the left hand rule everywhere, you'll get the same resulting forces (at least for EM), because you always have to use the rule twice - once for the vector field, once for the force, and the false chiralities cancel out it's just that intermediate vector-field representation that gets flipped, because the hand is arbitrary and the vectors are fake (pseudovectors)

[@physicsnerd02]

Tangent topic, but my favorite exam in grad school E&M was to derive Maxwell's equations, only assuming the existence of magnetic monopoles. We then proceeded to use those equations to solve a few other problems, and the results were somewhat spectacular in a way I didn't expect.

[@cynicviper]

Assuming the existence or non-existence? I'm confused, but don't mind me if it's a dumb question.

[@chrisglosser7318]

Yes - it is a total shame that magnetic monopoles don’t exist because they would explain so many things

[@physicsnerd02]

@@cynicviper Existence. There has never been an observation of a magnetic monopole, there is always a north and a south. Maxwell's equations are a model for electromagnetism. If you re-do them under the assumption that magnetic monopoles do exist, strange things happen.

[@cynicviper]

@physicsnerd02 Oh, that's fascinating, I was confused precisely because, to my knowledge, magnetic monopoles haven't been observed, and their non-existence is kind of taken for granted (even by one of Maxwell's laws itself if I'm not mistaken). I thought you were deriving the rest of the laws from that one law, but I realize now that would not be possible. Thank you for your reply!

[@chrisglosser7318]

Adding magnetic source terms to maxwells eqns has profound implications for quantum mechanics. For instance, you find that charge quantization is a natural result of angular momentum quantization. This happens if there is a magnetic monopole literally anywhere in the universe

[@thylacoleonkennedy7]

26:19 I actually feel sort of the same about Darwin. He had no idea about how heredity worked or how variation actually came to exist in populations but the level of understanding we've developed of evolution since the discovery of genetics and DNA, how massive the field of evolutionary biology has become and how completely it's vindicated Darwin's ideas is really mindblowing. On the other hand he died way before we discovered the kinds of concepts that would do that, but it's still realy interesting to think about.

[@azzydraws3107]

BABE WAKE UP A NEW DR. COLLIER VID DROPPED

[@kika-ge5qr]

How old is Earth?

[@personzorz]

But it's 8:00 a.m. on a Saturday

[@Uzotrups]

Yaaay

[@edwinrollins142]

Woohoo!

[@kaemonbonet4931]

Youre a new video

[@RichardKCollins]

When an electron goes for a walk, the magnetic field she produces is going down into the ground on her right. The positive charge walking beside her, his magnetic field is going down into the ground on his left.

[@wtfpwnz0red]

Watched the guys on safety third talking about radio wave emission recently, and i wish they could get someone like this to come explain it to them

[@ChaosPootato]

They need to invite her as a followup to correct all the bullshit and confusing nonsense they've said in that episode :D

[@wtfpwnz0red]

@@ChaosPootato i think after a while they were just running with it and saying more nonsense to make viewers like me crazy

[@TheShizzlemop]

honestly, lol.@@wtfpwnz0red

[@candyh4284]

@@wtfpwnz0red Why bother knowing what you're talking about if you can't say that redwoods are brassica olearica??

[@Jablicek]

Strange how much crossover there is with audiences.

[@capitano3483]

The charge is nonzero in the frame where the electrons are at rest due to length contraction, not because “we prevent the electrons from moving”. We didnt prevent them from moving, we just went to a different frame. If in the previous frame the electrons were moving to neutralize the charge, in the new frame the protons would be doing the exact opposite motion. The reason is that in a moving frame lengths contract so the densities of positive and negative charge no longer match. Alternatively, charge is the time component of the electric 4-current so it transforms under boosts. But preventing the electrons from moving doesn’t make sense. I don’t mean to be overly critical, I love these videos! But i wanted to comment on this. I’m sure Angela knows what I just said and was trying to simplify, but it felt like an oversimplification that misses the (in my opinion) coolest part of the demonstration!

[@draco7039]

Thank you, I was really confused why electrons and protons had different "behavior". I know she mentioned the length contraction but I think it deserved a little more explanation... Thanks for the addition!

[@mercad0g]

Hi, you helped clear up the confusion for me because I also realized that. I've seen this example many times and never understood why length contraction isn't involved in the first frame too. Wouldn't the electrons still have relative motion? It just seems a bit weird to only consider the length contraction in one frame. I know it might be a bit difficult to explain that, but if you could I'd appreciate it. If it helps, to know my knowledge, I've learned lower division e&m and special relativity in university.

[@capitano3483]

@@mercad0g Sure! I'll try. You start with an infinitely long wire with protons standing still and electrons flowing in some direction. And you start with the density of protons and electrons matching. This is the initial frame you consider, where you are at rest looking at the wire, which is also at rest. We consider the length of the wire (the lattice of protons) so there is no length contraction, you measure the rest length or proper length of the wire. You could also think of measuring the length of the string of electrons, as if they formed some material length of stuff. In that case, you would indeed measure a contracted length of electrons, respect to what the electrons would think their length is. But notice that we are starting the problem by saying, you have a wire, and you measure no charge, so what you are saying is that the proper length of the protons matches the contracted length of the electrons. You can also move to the frame of the electrons. You can think of that as running in the direction the electrons are flowing until you see them at rest. But then the wire is moving in the opposite direction! Then you see the contracted length of the wire, because you are measuring the length of an object that is moving relative to you. You would also see the electron column longer, since now you are at rest respect to them. But notice that by moving to the electron frame you made the proton column shorter and the electron one longer, so they don't cancel out, if anything it makes things worse! Respect to the previous frame of reference, the protons got compressed (so more positive charge density) and the electrons stretched (so less negative charge density), that means double the net increase of positive charge, which is the responsible for the force in this frame. I guess the important thing is which frame of reference is doing the experiment to measure which object's length. The frame of reference where the object is at rest always measures the biggest length, which is the proper or rest frame, any other observer moving relative to the object will see the object moving and measure a smaller, contracted length. Maybe the confusion comes from an apparent symmetry in the problem, something like: If the length the electrons see is contracted respect to the one the protons see, wouldn't the length the protons see be contracted relative to the electrons? But that's not how it works, since you are talking about two different lengths. Whoever sees an object at rest is in a privileged frame and measures proper length, the biggest length possible. There are two different objects moving with different speeds: One is the lattice of protons and the other one is the flow of electrons. Hope maybe that helps!

[@mercad0g]

@@capitano3483 Thank you! This cleared up the confusion for me, especially relating the initial condition of no charge measured in the rest frame of the wire, to the rest of the explanation. Thanks again

[@saarl99]

The question is, what is it about our reference frame (the one in which the protons are at rest) that makes so that, in this frame only, the electrons are spread out so that the total charge is zero? Why doesn't the same thing happen in other reference frames? I get that this can only ever happen in one frame because of length contraction, but the question is, what makes our frame special? I think Angela's explanation of “we're not allowing the electrons to move” is meant as a way to justify why the charge can be nonzero in the frame in which the electrons are at rest, but I don't know if I get it. The obvious answer to my question is that our frame is special because the protons are at rest there. But I don't know how to complete the explanation.

[@johnpassaniti4417]

I love your channel. Not only do you explain things far better than I was taught, you do it with humor and snark.

[@Pscribbled]

The nice thing about the right hand rule is that it makes electromagnetism immediately teachable in highschool without the need to have like half a year of learning and understanding linear algebra. I actually like the handed rules. I’d have my left hand rules for electrons and right hand rules for current. There’s not too much to memorize if you do it that.

[@apteropith]

i've hated the right hand rule since high school, because it's always been obvious to me that it's introducing arbitrary false chirality into every problem we apply it to like, i didn't know the word "chirality" (or "arbitrary") when i was 16, but the problem was still painfully visible

[@hugofontes5708]

It's even easy to memorize which hand you use for electrons, your eleft hand, and for current, your curight hand. Or you just multiply the force by the signal of the charge everytime and don't mind it

[@Graham_Wideman]

@@apteropith I would challenge your thought about "false chirality". If you are dealing with three dimensions, there are two possible ways to orient the 3rd axis. (And in fields that use 3D geometry, these are indicated as right-hand or left hand). In order to make any progress describing 3D phenomena, you have to pick one axis convention and go with it. That's OK, as it's just a matter of a negative sign here and there, and so long as the same scheme is used consistently, all is described consistently. Now when describing phenomena _using a particular axis convention_, you encounter vector formulae in which need to describe the direction of the result relative to the constituent vector variables (often involving cross-product). This may involve right-hand or left hand rule. But is not imposing an arbitrary chirality on the phenomenon, it simply reflects the original choice of third axis direction.

[@sillyking1991]

@@apteropith i wouldn't say its false chirality. current has a direction. and that direction matters, particularly when designing, building, and understanding electrical circuits. But even for theoretical calculations the concepts that lead to the RHR's are building a frame of reference, which is important for physics calculation. you *are* correct that its arbitrary, but conventions are useful for many reasons. consistency being the most prominent.

[@apteropith]

@@sillyking1991 it is, though take a nice circular current loop, or any other flat shape: if you mirror the electric current, or the electric fields driving it, or the electric potential from which that field is derived, you can always rotate these back into the original position - the structure isn't chiral if you try this with the magnetic field, derived with the right hand rule, you _cannot_ rotate it back to how it was, because you now have the left-hand-rule version of the field - the magnetic field is chiral when the electric system is not this might not seem so bad, except that the _effects_ of this chiral field on moving charges are _also not chiral,_ and this is borne out by how magnetic field vectors are considered "pseudo-vectors", which should not be reflected in the same way as "true" vectors, lest we break the mathematical relations that define them - indeed, if you physically reflect that current loop (rotating it back into position as necessary), the magnetic field it produces doesn't change at all the chirality of the magnetic field is confined to the formalism of the magnetic field, and estranged from either its originating structure _or_ its physical effects that makes it a rather suboptimal formalism, especially when better ones exist

[@naikrovek]

13:26 - "I don't think you should have to memorize things" this spoke to me on some fundamental level, and I was not prepared for it. I've been trying to communicate this to my software development colleagues, who like to just memorize things instead of finding ways to make them easy to figure out by others later.

[@fluffy_tail4365]

Maxwell is so underrated in popular science. Classical electromagnetism is already such a pretty theory by itself and the guy worked on so many other things.

[@seanys]

We still have magicians called electricians. They appear at your home and all the money in your wallet disappears.

[@eclipse369.]

nah i charge reasonable rate and you pay for your own ignorance lol you could go to that very spooky box in the house, cut off the main breaker, buy a $20 multimeter, learn how to ohm things out, learn how to check voltage......and fix most of your electrical problems easy peasy now if you want me to fix your refrigerator or oven then the rate will go up for sure

[@bryandraughn9830]

Hey! We have bosses. They're called "master" electricians. Yes, you need master certification to run an electrical contractor business. It's really weird, because they are taught all kinds of "business stuff" and it makes them forget what every journeyman knows.😅

[@candyh4284]

@@bryandraughn9830 Funny how that happens. Almost every field has some example of it. Department chairs becoming "money-smart" and losing their "book-smart."

[@workshopninjathe1st]

But you don’t kill yourself, or burn your house down…

[@ChocolatexCherries3]

yes. that's how hiring someone to do a job works? are you... advocating for people to work for free for you?

[@hipser]

you are my new #1 science communicator. It's my dream to do stuff like you

[@NateEngle]

There are several I like, but Angela brings the math.

[@djee_peetch]

3:07 This is the umpteenth time I hear on KZbin how an electrical circuit is supposed to be working, physically speaking, and every time the explanation is different. Veritasium, Electroboom, The Science Asylum all provided theirs. I would appreciate your extended take on it!

[@TheMarcQ]

When you push a stick the other end of a stick moves almost instantly independent of a speed you move the stick at. When you flick a switch the information moves almost at a speed of light and all the electrons start flowing.

[@TheMarcQ]

Every explanation mentioned above has one thing in common - speed of a single electron has nothing to do with a time needed for a light to turn on after the switch has been flipped, or time an end of a stick starts moving after you push the other one has nothing to do with a speed of a stick.

[@scottishrob13]

Thinking of current as the flow of little electron particles through a wire is a simplification. It's a useful mental model that won't lead you to any major pitfalls in realistic scenarios, but it's not the full picture. Those slow-flowing electrons aren't really bumping into each other and propagating down the wire to create a flow of elelectricity, though they do slowly drift. The stick example is another tough one, because we think of pushing an end of a stick as immediately resulting in the opposite end moving. In fact, that interaction ripples through the stick as particles bump into each other at the speed of sound in the medium of whatever the stick is made of. If this was actually how electrical current worked, then wired telecommunications infrastructure around the world would be slow indeed. The second Veritasium video explains this much better than I can here (there were some really good summaries of real experiments in it), and the follow up interview with ElectroBOOM was quite illuminating with regard to a potential mechanism for how the electron drift that still happens, though more as a byproduct of the field interactions.

[@aidenstoat5745]

the other end of the stick will begin moving after a time equal to the speed of sound in the stick travels the length of the stick.

[@orterves]

​@@aidenstoat5745which, presumably, is a whole lot faster than your hand is pushing.

[@Mag_ladroth]

Noooooooooooooo! Why isn't the video 3 hours long. Seriously I love your longer videos.

[@TheOneWhoKnocks969]

Lol

[@just_some_commenter]

The video is 3 hours long in an appropriately chosen reference frame

[@heatherofmorans]

Angela, I wish you had a PhD in every field so I could listen to you talk about every topic ever, from history to microbiology 😭 women in STEM are amazing

[@flipshod]

She doesn't need the degree to talk about anything that interests her. I love the asides as much as the physics.

[@heatherofmorans]

@@flipshod yeah you're right! i thought about it after making my comment and that maybe it came off as a little rude but i didn't mean it like that 😩

[@flipshod]

@heatherofmorans I didn't take your comment as rude. I was just joining in your call for Dr. Collier (Angela) to talk about a wider range of topics. She's a charming and brilliant teacher/explainer, and I could listen to her talk endlessly (I just discovered the channel a few days ago.)

[@cablecablecable]

@@flipshodthe background helps

[@jokubaskristapavicius4586]

I studied physics at King's College London. Had to drop out as I couldn't handle the stress of working to afford living in London and studying. I felt into deep depression during studying as I was either studying or working in hospitality every day of the week. I couldn't look at physics, I burnt out. Yet watchin your videos, learning these things again reminded me of that spark I had for this science and distate for these silly right hand rules. I miss physics, I am never coming back again as I really feel repulsed by the idea of university at this point, howeve, I'm glad to have found a channel that let's me relive the best part of it. Thank you.

[@HexanaMusic]

Adding to what others have already said, I was taught the right hand rule for the field around the wire, and the left hand rule for the force.

[@fernandososterbortolotto7315]

being a lefty I had some troubles with the right hand rule. I consistently applied it to the wrong hand side and unadvertedly kept thinking that such topics were product of baseless reasoning and lack of questioning.

[@aldokurti3272]

I can't wait for this explanation. You explain things perfectly and I've been wanting to learn more about the nature of electromagnetism.

[@JCUDOS]

13:25 "I don't think you should have to memorize things. Like we should just understand why it works" There's why I hated school ever since they tried teaching us negative numbers didn't exist in the very first year of primary. XD Love the way your mind works! Great upload!

[@PhilipRhodes-u9c]

I just thought you would like to know that the “Clerk” in “James Clerk Maxwell” is pronounced in British English “Clark” (and he was British). There are number of “er” words (mostly names of people and places (e.g. “Derby” pronounced “Darby”) that are pronounced “ar” in British English. There are historical reasons for this, think of how you pronounce the word “sergeant”. Thank you for your very enjoyable videos.

[@chrisglosser7318]

To be more specific, he was Scottish. If you try to say Clerk with a Scottish accent what comes out is Clark

[@mrmadmaxalot]

Never knew this, thanks! I'm one of those people that mispronounces all sorts of words and names because I first encountered them in print and English orthography is nonsense.

[@rakino4418]

Is this related to why Americans insist on pronouncing "Craig" as "Cregg" (rhymes with Greg)?

[@gcewing]

It's not just Scottish, "clerk" is pronounced "clark" in other British accents too. (Although "clerical" is not pronounced "clarical", because it wouldn't be English if it were consistent, would it?)

[@rakino4418]

@@cmmartti the rest of the world pronounce it Crayg (doesn't rhyme with much - the first part of pagan? Or the bayg in bagel)

[@bradwilliams7198]

The E & M textbook I used as an undergraduate actually started the discussion of magnetism from the Lorentz transformation. After covering electrostatics, it applied Lorentz transformations to static charges and showed that there had to be this "thing" (let's call it a magnetic field!) that appeared in a reference frame in which the charges were in motion.

[@dsvilko]

Was it Purcell's Electricity and Magnetism? That's a wonderful textbook. Few things in physics blew my mind like Lorentz force derivation from Coulomb law and axioms of special relativity!

[@bradwilliams7198]

@@dsvilko Actually, it wasn't Purcell, although when I was in grad school I TA''d an undergraduate E&M class that used Purcell. And yes, I agree that is a good textbook! The undergraduate textbook I used was by Schwartz (he's best known for demonstrating that muon neutrinos and electron neutrinos are distinct entities--well kind of, as we now know!). A very obscure book which was out of print, so the department actually copied and bound the book and gave it to those of us in the class. I suspect the choice of book had to do with Schwartz being a former faculty member in the department!

[@LogansBench]

I'm an electrical engineering student and I'm taking e-mag and transmission lines next semester. I kind of struggled in the E&M part of my physics courses but this made a ton of sense. In all my courses so far electrical and magnetic forces were always discussed as separate parts of a problem, but seeing that they're the same thing in different frames of reference is so fuckin cool. Thank you so much Dr. Collier!!

[@caidenkesler3945]

I'm taking emag this semester, and most of it has been E&M repeated back to me. There's some extra stuff here and there like transmission lines, but overall it's phys 2 the sequel. Have fun ig

[@punditgi]

This channel is a gold mine of information. Love the presenter as well. 😊

[@haenmaen]

to the Patreon with the name "Riemann Zeta-Jones": i had a good chuckle, thanks

[@therealcrunchyb]

I too did this math in college :D If it looks hard to someone, it's because you haven't done it ~500 times before. It gets easier every time, not everybody learns at the same pace, but you'll get there eventually.

[@MetzanV]

When I was taght the cross product first, the professor used the right-hand rule to explain it, so for most people "use the right hand rule" and "use cross product" would be the same. And if we need to actually calculate cross products "rigorously", we would need to start calculating determinants of matrices, etc. Yes, it is worth understanding where all that jazz is coming from, but the right hand rule is a very nice shorthand once you know what is going on. Now, there are two caveats - one, it might be that cross product of vectors can be explained without the determinant of {{i j k} {v1 v2 v3} {u1 u2 u3}} - I would be very happy to understand if there is one! Two, I was taught another right hand rule - it's the same, but requires much less hand gymnastics :P . Velocity of current = outstreched thumb; magnetic field = outstreched fingers; resulting force = imaginary arrow pointing away from the palm.

[@carl13579]

You don't need the determinant. You can just write each vector as a sum of elemental terms and expand the cross product of sums.

[@Tumbolisu]

I was taught the cross product without anything about matrices or determinants. The calculation just happens in a visual way, using 3 crosses and a good bit of memorization. (At least you don't need to wave your hands around.) Here comes the insane explanation of the calculation: Given the vectors (a, b, c) and (x, y, z), the cross product of these two is (bz-cy, cx-az, ay-bx). If you draw the input vectors column-wise next to each other, you can draw 3 crosses between the components. (For example, one line connecting a and y and another line connecting b and x.) Each line represents a product, and the two lines of a cross represent a difference. This result (such as ay-bx) is then written in the one component of the output vector which is on a different line than the input components. (So first and second input components make up the third output component, first and third make up the second, and second and third make up the first.) The only thing left to remember is that the middle output component needs to be negated. [I like to instead copy the first line below the calculation, since this allows the cross between the first and third components to not jump over other lines and is therefore no longer "malformed". This cross needs no negation.] When you have this whole thing memorized, the execution just becomes "make first cross, write down stuff, make second cross, write down stuff, make third cross, write down stuff, done"

[@MetzanV]

@Tumbolisu the sum you wrote is calculating the determinant of the matrix I wrote in my original comment - but without calling it so. This was done to me and from my point of view it's really anti-intuitive. Sure, writing the two vectors above each other and writing out the crosses (put a pin on that!) made it easier for me to memorise, but it did little to cobvince me there is any method behind the madness and here we come back to the crux of Angella's problem - we have to memorise stuff. Sure, it's much better to learn the rigour rather than memorise arcane spells like the right hand rule, but if you need to teach laws of magnetism to high schoolers, you cannot do much in that regard. And in my opinion, memorising the right hand rule is easier and provides better intuition than memorising the opaque formulas - which are exactly the determinants of the 2x2 sub-matrices multiplied by the directional vectors I,j,k - which in turn is how you define the determinant of a 3x3 matrix. So you were taught to calculate the cross product the rigorous way, but you were given the answer without the solution, which is what I believe what Angela is after.

[@AJcheste]

Okay haven't watched yet but I was just thinking about how cool an Acollierastro vid on electricity and magnetism would be and here it is! I think it's wild how Maxwell basically looked at symmetries in the equations for electric and magnetic forces and hypothesized their unification and then proves it right. I'm excited to watch this vid.

[@gbail9566]

Thanks!

[@mxandrew]

i loved the right hand rule completely unironically. i also liked my electrical engineering courses better than all the generalist ones (i was an ee major too) so that might just be me 😅 this video makes me want to study again 🥺

[@PedroTricking]

The right hand rule is amazing. I have decided to believe she's just trolling us because there's no way that anyone as smart as her would desecrate something as great as the right hand rule. She says that we should ignore the right hand rule and just think of the cross product, but how do you quickly tell where the cross product points? You use the right hand rule.

[@TwitchRR]

The version of the right-hand rule I learned for the magnetic force is that you orient your thumb in the direction the (positive) charge is moving, your other fingers point in the direction of the magnetic field, and then the direction your palm is facing is the direction of the force. The way I remember it is that your fingers represent the magnetic field lines, and pushing forwards with your hand represents the force. It's a bit silly but it's more intuitive to me.

[@willschannel_]

can't wait for this, im in physics 3 and our entire class has basically been about maxwell's equations all semester

[@cubandarknez]

for the simplified explanation around 3:50, of the 'filled pipe' analogy such that a small group velocity 'pushes' the group members that were 'near' the end of the pipe. Considering veritasiums and company's discussion of the whole lightbulb on c*1s wire, and I think understanding that the fields are the true mechanism that allow for the near instant turn on of the light bulb, I now feel like the simplified 'filled pipe' analogy that I feel most people grow up with actually hinders the understanding of the fields as the true mechanism. Wonder if there is a better simplified explanation that can replace the pipe one for intro physics books.

[@Graham_Wideman]

OK, but if we take a literal pipe filled with marbles, what does it mean in this supposedly mechanical analogy for the marbles to push on each other? It means that the electric fields of the electrons of the atoms on the outer surface of adjacent marbles are repelling each other. So actually the analogy has more in common with the case of a wire than at first meets the eye!

[@SmokeyLaBear]

If you've ever wondered what it's like to study engineering at a university, it's mostly classroom lectures like this.

[@adamleonardo7303]

I could listen to you teach physics all day long. Not in any kind of weird way, you just have an energy and excitement about what you're doing I rarely see in people teaching math-related fields. It's evident you love what you're doing.

[@JorenVaes]

A cool way to see the electrical and magnetic duality is that there are antenna structures of which the negative exist - ie, you have a pattern in a conductor that acts as an antenna, and in some cases you can take all the parts that are conductor and make them non-conductor and vice versa, and you will maintain a working antenna.

[@bjornfeuerbacher5514]

Sounds interesting - but what exactly does that have to do with the electrical-magnetic duality?

[@JorenVaes]

@@bjornfeuerbacher5514 It follows mathematically from the duality - the fact that you can replace all the electric currents with 'magnetic currents' and vice versa (so, change all the conductors with non conductors and vice versa) - one would for example be a magnetic dipole, the other an electric dipole.

[@bjornfeuerbacher5514]

@@JorenVaes So electric non conductors automatically are magnetic conductors, and vice versa, or what is this supposed to say?!

[@simonlinser8286]

This has to do with the fact that dielectric still have electronic properties that don't relate to conduction as much as magnetism

[@simonlinser8286]

​@@bjornfeuerbacher5514yes actually it is because it depends on the filling of the valence shells and means if they have a magnetic lobe. Dielectrics exhibit many novel effects in relation to the EM spectrum and i personally believe we will see a new wave of materials breakthrough when humans start combining together materials into highly structured or otherwise engineered materials that might combine dielectrics with conductors or in layers or any other thing you can think of. It will just be a way to have more control over the properties so as to pattern or harness the flow of energy or to tune a system to increase efficiency. Usually a dielectric is just an insulator and we think it does nothing but there's other things that are going on we don't use yet.

[@deyesed]

In my materials engineering undergrad, it was explained to me as electron drift = marbles moving, electric current = Newton's cradle. Extending the physical analogy, voltage is how hard the swing is, current is how many cradles are going, resistance/impedance is inelasticity.

[@mankdeems251]

Maxwell is underrepresented because he's Scottish. In the UK Scotophobia is a real problem. If someone is Irish, Welsh, or Scottish, hence not English, they are simply ignored by the Anglocentric historians. It's a real shame and very much a current issue. That's where the stereotype of Scottish people claiming they invented everything comes from - it's actually a reaction to achievements being wilfully ignored by Anglocentric narratives.

[@Graham_Wideman]

"If it's nawt Scottish, it's crap!"

[@mankdeems251]

@@Graham_Wideman very much not what I'm saying. I'm saying achievement should not be devalued because it is not English, in both a UK context and in the English speaking world. Feel free to extend this appropriately to other Anglophonic national contexts.

[@Graham_Wideman]

@@mankdeems251 No contradiction intended! I'm not sure if you caught that I was referencing Mike Myer's cranky Scotsman character on SNL? I made the comment first because your comment brought back some funny memories, and second because it resonates with your point about the stereotype. I was born in Scotland, and I'm not crap, so it must be true!

[@johannribert8192]

I don't think the cross product is more intuitive than the right-hand-rule. F = qE+q(v x B) is as deliberate as assigning your fingers to the direction of B and v. The equation also is just a record of experimental findings and in the end you will have to memorize it or look it up in the formulary ... unless you demonstrate how you always derive this equation from first principles in an easy way. Moreover the equation doesn't solve the problem with the direction of the magnetic field and the direction the charge is travelling. You still have to think about it and remember the right signs if you want to calculate the direction of F. So, I'm disagreeing. It's not so much a matter of what is more practical in an objectiv sense rather than a question of personal preferences.

[@matteodelgallo1983]

I have studied Relativistic EM, it would be interesting to show the maths derivation and practicalities of the electromagnetic field tensor, and how it's naturally variant in relativity, and how that just kinda pops out of a very simple construction, cos it really drives home that relativity was fundamentally baked into EM, despite EM coming first

[@raffaeledivora9517]

This always amazed me from the first time I saw it when studying relativity. It's so awesome, how perfectly and neatly it all works out. Which then makes the concept of spin even more puzzling: what is it? Why is it so completely, conceptually different, yet so unexplicably tied in with electromagnetism?

[@xponen]

is "spin" to be read as a literal spin, or is it just a name to be read only in a specific context?

[@edwardharvey7687]

The right hand rule comes in handy in quickly determining the direction of movement and force in threaded objects. Interesting that the behavior of threaded objects can be explained in a manner similar to electron flow.

[@veldin25]

I don't think there's some deep connection here, particularly given the existence of left handed threads. Certainly is convenient that it's a multi-use memory tool though

[@duckwhistle]

@@veldin25 The connection is a linguistic/conceptual one and it was worked in the other direction. They use the term handedness in physics Because of the existing convention for human mechanics of using threaded objects.

[@Heldermaior]

"Lighning an electric thing has caused a magnetism" is the most adorkable way of putting it. :)

[@JonDoe0212]

Hi Dr. Collier! Thanks for making such great videos! I took some intro to physics classes during my biology undergrad and I never understood the righthand rule, turns out I had been pointing my thumb in the direction the electrons are moving instead of the direction of the current! Damn you Ben Franklin! In case you're ever in need of video ideas, I'd love to see a video on black holes, the event horizon, hawking radiation etc. I remember finding them fascinating back in high school when I thought I wanted to be an astrophysicist!

[@channeldoesnotexist]

You do point in the direction the electrons are moving, but you reverse direction in the end due to the negative charge...

[@johannesschutz780]

I read somewhere ages ago that Einstein in one paper demonstrated that electricity and magnetism are related to each other and thereby proved relativity theory and I've never been able to find an explanation for that. You've finally given me what I've been longing for all these years, thank you.

[@candyh4284]

We took, in my high school, our finals in combined sections sorted by name and grade. So the proctors weren't necessarily able to help any given student with their test, because you'd have an english teacher proctoring physics, geometry, and history exams. This didn't really obstruct you too much, generally, because the proctor could send for a teacher who knew what they were talking about or the specific teacher who wrote the exam if it's a context question. One time, though, I was taking my electronics and robotics final, trying to remember what the fuck the right hand rule was even about, or meant, or how to read it. And the proctor came over and got in my face thinking I was cheating because I was staring at my hand, as if trying to read some writing on it with all the answers. Pretty funny stuff, in retrospect, but I did fully cry, and that wasn't suuuuuper helpful to my finals mindset.

[@8ohmrecords]

you are my favorite science communicator, in a large part because of your sincerity. keep up the good work! :)

[@aurimatic]

Luckily the right hand rule has always been super intuitive to me. It is the cross product for a right handed system, essentially, and I learned both of them together. It also does the whole cyclical index business! Maybe it’s just because I am a mechanical engineer and we used it constantly when doing free body diagrams in structural analysis in all my mechanics and dynamics classes. You had to use the right hand rule if you had to analyze a complex 3D structure and wanted to turn in the test on time.

[@mryellow6918]

My brain melts when ever I have to mess with circuits because we do it backwards and I have to constantly tell myself that.

[@Skank_and_Gutterboy]

As a mech. engr. I used right hand rule all the time. Motors also use a left-hand rule. So if electricity and magnetism are the same, why do some of these electro-magnetic things use a right-hand rule and some a left-hand rule?

[@mryellow6918]

@@Skank_and_Gutterboydoesnt a motor go the opposite direction tho? its been a while since iv done electronics and a generator the opposite?

[@Skank_and_Gutterboy]

@@mryellow6918 Me too. I'm a mechanical and it's been a LONG time since I've done anything with this. I thought that there were differences between an electrical field and magnetic field, too, but I better defer to the experts on that.

[@mryellow6918]

@@Skank_and_Gutterboy yeah i think it due to the fact that our electronic laws are backward but the magnetic ones arn't

[@rarebeeph1783]

8:46 You say "instead of letting you do the cross product, they force you to memorize the right hand rule". But the cross product being right handed as such in the first place is just as arbitrary. I've been seeing videos about geometric algebra lately, and the objects it deals with seem really nice for things like torque and magnetism; instead of representing those with a magnitude around an axis, you represent them with a magnitude in a plane. In 3d, the two notions only differ by a choice of basis--the calculations of either are almost identical--but notably, the latter doesn't come attached to a handedness convention, and both its geometric and algebraic properties naturally explain why it doesn't act like a normal vector under reflections, etc. But it also naturally generalizes to 2d problems so that you can discuss torque and magnetism without introducing a 3rd dimension, as well as to 4d space or indeed 3+1 space-time in which it becomes very natural to think of the electric and magnetic fields as being, in fact, one single bivector field, with the electric field being the component which is partially timelike.

[@Jason-gq8fo]

Thank you 🙏 I’ve needed a better explanation of this for ages

[@TalysAlankil]

your rant about the right hand rule is SUCH a mood jsdklfsjkfs especially because since it's an extremely 2D problem the cross product is super easy to do so we should just do it.

[@LordAJ12345]

16:17 Angela keeps being right about everything

[@alinoer.6569]

#liveablecities

[@yngvehafting6828]

By accepting length contraction, the magnetic force is the electric force. If you then postulate electromagnetic flux is carried by the speed of light in the observers frame, you have no need for Maxwell any more. For teaching understanding, this can be shown without the use of equations: a lenght of a wire containing more charge of one type than another will push or pull charges, and we can deduct the right hand rule. Getting a good description of all induction cases, such as why an induced coil current goes against the direction of the current causing the induced current is harder to explain. My take (w/o doing calculus) is that the brownian motion (velocities due to temperature) is what normally causes this (ie the cause of lenz law). - If you somehow could accelerate a current fast enough, that would not allow charges going the opposite direction in the secondary coil (but rather tear coil and all apart/ explode). I hope one day i will se someone elaborate on this (my challenge to you, if you did not already do this). Thank you for contributing to better understanding of physics.

[@TheJunmengo]

I Just realized that Dr. Collier loves to teach But since academy is effed up she bolted from there but still want to get her teaching on So she uses us as her little class Joke is one her because I'm not smart enough to pass in her class but she also can't fail me trough the internet

[@YayComity]

Bingo. She chose freedom over structure and so did we. It doesn't matter much if the result wasn't ideal - it was something.

[@Deesdessessesder]

I was only recently taught through the PBS Space Time and Fermilab channels of this truth and I am surprised that in my undergrad physics (And calculus-involved high school AP physics) this was never mentioned even in passing, and in my time exploring physics since (graduated undergrad 5 years ago) I haven't stumbled across it until now. I would have been thrilled back then to learn that this is the reason that the field is deemed electro-magnetic as opposed to two separate fields / origins of force. I would have struggled in high school with the involvement of relativity, but now it sounds intuitive with the addition of length contraction, and the math shows the same result in either way of framing the problem, electrically or magnetically, (except, as you pointed out, the case of moving positive charge through wire and stationary point electric charge that I think would have stumped my AP physics teacher - which either requires re-framing things back to the first scenario by making the flowing protons stationary and acting as though the electrons and external point charge are moving, which unfortunately just skips the fact that the math needs to work in all reference frames and bounces back to the frame where it does work, or the elegant relativity solution that you have presented which would work in all reference frames.) I appreciate now having a much more robust tool for describing the forced imparted by moving charges. Yours is the first video I've seen providing an example and I think it was very well-made. Thanks!

[@filipeeeeeeeee5615]

Right in time to motivate me to study for my physics II finals (I think in some universities it’s III but in mine electromagnetism is II)

[@Sam_on_YouTube]

When I studied this 20 years ago, I made sure I knew it by teaching it to a friend of mine who hadn't taken any physics. Relativity was by FAR my favorite part of both mechanics and E&M. I loved learning the way Einstein actually figured it out... even though it is MUCH easier to learn through mechanics as it is usually taught today.

[@perfidy1103]

"They force you to learn these right-hand rules, which are the worst!" I can't agree with this more. In the UK I learnt this stuff at the end of High School (age 16-18) and we learnt the right-hand rule. I was also doing a course called Further Maths, in which we did (amongst other things) vector and scaler products of vectors. After clearing it with my teacher, I simply used the vector product and never had to learn the right-hand rule

[@whiteravenstudio1]

Hey Dr. Angela, I have a question about the thought experiment in this video. I was hoping you could answer, because I'm very curious about it. If the wire is infinitely-long, then how could any current be flowing through it? If it's assumed that we're talking about DC current through a simple, infinitely-long piece of copper wire, then wouldn't Ohm's Law apply and the wire would have an infinitely high resistance? The resistance of any conductive wire is proportional to the length and the surface area of the cross-section. If that's given, wouldn't the current in the wire be 0 at all times? If the thought experiment produces a paradox, isn't that because it's a nonsensical premise? I recently saw your video on the space elevators! This thought experiment reminded me of that video, of scientists saying "sure, it maths!" but engineers saying "it doesn't engineer though." I found that very funny, and I wondered if this couldn't be something similar. Thank you!

[@LibertyMonk]

I have to say "ok, they're gone" is such a fun thing to hear.

[@marko1395]

Haha I laughed out loud when she said that.

[@tadgmaniandevil]

I recently chose to prove this example for an E&M project. It was so cool to realize how electricity and magnetism are connected through special relativity.

[@eldenfindley186]

If you’re so smart: why do I have an ELECTRIC toothbrush and not a MAGNETIC toothbrush? Checkmate Maxwellians!

[@marmoth9786]

it's been a few years since i studied physics, probably equivalent to high school level, and i very nearly failed the course, haha. i don't understand much but for some reason you talk so engagingly (?) that it feels like i do!

[@joshuahebert7972]

Science does a science and wow. Its pretty neat~!

[@TheLeobc]

Totally off-topic: THAT ENTERPRISE MODEL ON YOUR SHELF SO GORGEOUS OMG

[@pairot01]

Interesting, I was told a left hand rule. Thumb (pointing upwards) is F, index finger (pointing forwards) is B, and middle finger (pointing right) is I. And it was fun because you could make a sort of finger gun and "FBI, hands up" Edit: we used our left hand rule always, no matter the charge of the particle, because the current I already takes it into account.

[@mryellow6918]

My entire exam room looked like the naruto chunin exams.

[@oschonrock]

Yes exactly 🤩 That right hand rule way (and you have to switch it around for -ve charges)... seems quite messed up!

[@cat_jones_0076]

A great video to your knowledge without skipping the rigorous mathematics. However, there is one inconsistency in my understanding. Why is it not the case that we length-contract the separation between the moving charges in the reference frame stationary to the wire (1st case)? In the 2nd case, the protons got closer to each other under coordinate transformation, hence the non-zero charge density so, conversely, the electrons should receive the same treatement in the 1st one. How can I decide when to apply length contraction and when not to?

[@channeldoesnotexist]

Objects in motion experience length contraction by the lorentz factor - only objects in motion relative to an inertial frame of reference. The contraction is only along the direction of motion, not in any other direction. Read any textbook on relativity and this is what it will tell you.

[@KMO325]

We must’ve been on very good behavior to get another Dr. Collier video so soon! Also: [insert Insane Clown Posse joke here]

[@alfredsingh7920]

You are an excellent science communicator , that's why in my first comment I mentioned that " you are wonderfully great " . I am basically a mechanical engineer and hence can understand what ever you say , but the beauty is that you break down say complex matters into simple understandable things that even a lay person can understand . Great Angela , keep up the good work . I am your fan .

[@seijirou302]

That whole "just memorize it" bit is why I quit school. First ran into it with Trig and the opposite adjacent crap or whatever it is. It's so arbitrary it sticks to the brain like hot butter on Teflon. Failed that a few times, and every teacher refused to teach it. "You just have to memorize it" they'd say. No, I don't. It wasn't first learned by magical memorization, it was discovered through understanding. Teach _that_. To which I would get a sour look and a turned back and a repeated command to memorize. No, I'm not bitter, lol.

[@deyesed]

That's unfortunate. The unit circle presents a much more intuitive picture of trig functions. There's animations and stuff too

[@Tumbolisu]

Here in Germany, they just give you a little book with all trig identities here, and you can use it on all exams. Either way, my favorite identity was "a/sin(α) = b/sin(β) = c/sin(γ)" because it's easy to remember, works on all triangle shapes (not just the ones with a 90° corner) and single-handedly solves 80% of problems. Add the fact that all angles inside a triangle add up to 180°, and now there is only one single problem that can't be solved. This is way more than enough to get a passing grade. Although, I have heard that the US education system requires you to solve problems in the exact way the teacher wants you to, no matter how stupid it is. (The unsolvable problem mention before being that you know 2 side lengths and the angle in between these sides, but nothing else.)

[@mxpants4884]

The right hand rule is really great for one thing (and I use it on a daily basis): which way do I turn the screw/bolt/nut/threaded part (curled fingers) if I want the part to move (where the thumb points).

[@saturdaysequalsyouth]

Physicists crack me up... "Imagine an infinitely long wire..." "Imagine an infinitesimally small point..." "Imagine a plane of infinite extent..." "Imagine a machine of infinite computational power..." 🤣🤣

[@vanders626]

Yeah, wires are orders of magnitude bigger than electrical particles and it's for a situation in which the wires are much longer than the distance to the particle. In different situations, the boundaries are different.

[@joed180]

Imagine a wire so longass that we don’t give a shit right now but let’s not lie to you and say it wouldn’t actually matter

[@alonskii]

@acollierastro I was going to write a comment about why is the video is so short, but then I realised it wasn't. I guess time flies when you're having fun. Keep up the good work!

[@zviyeri9117]

the fucking content warning in the thumbnail 😭

[@PopeGoliath]

If the individual velocity of an electron is high, but the group velocity is low, does that mean there's a lot of jumbling around in random directions, with only a very small overall net motion in the group? If so, what would happen if you were able to make a coherent flow of electrons? One where all the velocities are aligned and the group speed is on the same order as the individual speed?

[@TypoKnig]

You’ve got it! Electrons move fast, but quickly bump into stuff in the wire and bounce, or stop, or rattle around a while before moving again. Like you’ve got Usain Bolt in a really crowded hallway. I think your unconstrained electrons would be a particle beam, which ought not produce radiation until it’s accelerated. I’m getting out of my former experience, which was a long time ago. All of what I said is from old memories, so corrections are welcome!

[@Graham_Wideman]

"what would happen if you were able to make a coherent flow of electrons' You just described a Cathode Ray Tube, which every household used to own, in the 60's through the early 2000's!

[@TypoKnig]

@@Graham_Wideman Thank you for posting a much more reasonable example!

[@Graham_Wideman]

​@@TypoKnig An interesting note: As commented in this video, electron group velocity is very slow, yet "electronic" systems communicate signals rapidly from one part of a circuit to another, because the useful information ("signal") is carried by voltage (electron "pressure") and voltage changes propagate very fast in wires (large fraction of c), as suggested by the marbles-in-pipe analogy. But consider a CRT -- here electrons are launched from the rear of the neck of the tube, a few millimeters later their quantity is modulated electrically by a grid, then they propel towards the screen (attracted to a high positive voltage on the screen front interior). As you probably know, along the way the beam is deflected by magnetic coils so that the beam paints out a series of lines ("raster") to cover the screen. The modulation of the beam intensity corresponds to brightness at each location that the beam paints across, resulting in an image. So the modulation of brightness near the beginning of the electron beam journey has to be coordinated with location where the beam will later land. Unlike in the situation in wires, the "signal" at any time point is carried by specific electrons traveling from the beginning of the beam to the location where they land on the screen. As it happens, in this environment (vacuum, geometry, level of high voltage), the electron beam apparently reaches a velocity around 0.1c, or 30 000 000 m/s. If a CRT is say 0.5m in depth, the travel time would be about 16 nanoseconds. For reference, in North America the NTSC standard used 15750 scan lines per second, or about 64 microsec per line. So the 16 ns travel delay corresponds to 1/4000 of the screen width, or 0.125mm on a screen say 500mm wide. That 1/4000 is far below the nominal 640x480 resolution of "high quality" video of the time, so unnoticeable. At least as important, no special delay needed to be implemented in those TV sets in order to modulate the beam "ahead of" the state of the deflection apparatus in order to have the beam fluctuations arrive at just the right locations on the screen. In those TVs, both the electron beam modulation and the deflection circuits are slaved directly to the TV signal transmitted from the TV station in real time -- there's no smarts in the TV capable of storing any length of image signal, not even one dot's worth. (Monochrome TVs didn't actually display in dots per se -- the phosphor is just a continuous coating, but we can think of a "dot" as the minimum identifiable feature size.) Imagine how awkward this system would be if the electrons in a CRT beam traveled at only a few mm/sec... and that delay would be different for different sized TV tubes!

[@DavidLindes]

re 6:00 - I'm just curious: Not using tau because... (a) you haven't heard of it (until now); (b) you've heard of it, and thought "that's stupid" (though if so, I refer you to 9:26/9:36/9:53 -- except in this case, we have an escape valve, because we're just adding a constant, not changing one); (c) heard of it, but "meh" (ok, fair enough - we can agree to disagree there, because at that point it's essentially aesthetics); (d) heard of it and even like the idea of it, and yet decided to use what more people know, so as to not confuse things; (or (e), other)? Just curious! Would love to hear your take on it. [And for anyone, not necessarily you, who's wondering what I'm talking about, look up "tau manifesto" to learn more.] P.S. Ouch, re 9:05. I hope you were able to laugh it off... though obviously you remember it still, so there's that. Anyway, easy mistake to make, IMHO.

[@joelklein3501]

Hey Angella! I am a 4th year undergraduate student of Math and Physics. I always find it a shame that we bith subjects are being taught so seperately, at least ij my country. Just as the right hand rules vs cross product you mentioned, I think there is a merit in covering those subjects together. You also gives a vibe that you have a very intuitive understanding of these math concepts, and I would love to see a video from you covering this type of topics. Only if you want of couse. Great video, keep it up😁

[@StampeSkovgaard]

I'm amazed at how fast you are able to make videos that are this interesting.

[@brianl7321]

Just came hwre from your video about string theory lying for 30+ years. Youre great at explaining this stuff! Thanks for the video!

[@gbormann71]

The cross-product is from vector-algebra. The calculus is in the divs, the rots and the grads...and in the Gauss and Green integral theorems.

[@alpacagurl92]

Interesting that most people do your version of the right hand rule. I've always found it easier to do the finger curl version, where in VxB=F you point your fingers in the direction of the first part of the cross, V, then curl them towards the second part of the cross, B. Your thumb will be pointing to the product F. You don't have to memorize which finger is which, just go in order start with the first vector and curl towards the second. This also works better for when the vectors V and B aren't perpendicular, your curling fingers still define a plane with your thumb normal to it.

[@ivano8]

I think this might be my favourite physics video I've seen on YT.

[@RockyTremblay]

Clear, concise and moving. Thanks again Angela.

[@jagthebeetle]

Regarding the paradox at 17:00, how do we know (asking this Socratically, since I assume physicists have figured this stuff out) that the magnetic field is not "positioned" relative to the protons? In other words, in the particle's frame of reference, the field is "moving" relative to the particle, just as in the wire's frame, the particle is moving relative to the field?

[@turun_ambartanen]

The right hand rule is fine, you just learned a convoluted way of doing it. mg field around a wire: thumb points in direction of movement of positive charges, finger wrap around the wire in the same direction as the field Force on a particle moving in a mag field: thumb points in the direction of movement of positive charges (look, it's same!), index finger points in direction of magnetic field, middle finger points in direction of force. If you look at an election you can just use the left hand, or make the thumb point the other way. Just like you do for the "mag field around a wire" mnemonic.

[@edwardmacnab354]

are you talking about AC or DC ? because electrons in constant velocity do nothing , they must be accelerating ! I find it odd that nobody has tried to experimentally demonstrate this . Also , it is the electrons interaction with the wire that causes these effects , not just any old bunch of electrons moving in a straight line in a vacuum. In a vacuum , if you accelerate one electron so that it bumps into the next one in front , you will not get an electric current , and in fact the reaction probably won't make it to the 3rd electron at all .

[@MrSummitville]

Actually, a steady DC flow of electrons ( not accelerating ) will make a magnetic field. We call them electromagnets

[@ericchavez5517]

Hi Angela, really liked the video. One question I have centers around the Taylor approximation you use to calculate the proton and electron charge densities in the new reference frame at around 19:30. How do all the higher order terms end up cancelling out when you subtract the two densities? If they don't then the final force calculation will be slightly different than the one from the lab frame, which would ruin everything.

[@qwadratix]

Maxwell made a start, but he was purely a mathematician, not a physicist. It wasn't until Einstein exposed the real nature of Maxwell's mathematics that we really understood the electromagnetic connection. The difference is made clear if you dig out the original papers that Maxwell published on vector fields (entirely abstract mathematics) and compare Einstein's paper (On the Electrodynamics of moving bodies), which is unquestionably physics and talks almost exclusively about concrete, real things moving.

[@eternaldoorman5228]

Thank you Angela! Happy holidays!

[@rsm3t]

It becomes even more clear why they are the same force if you take the EM field tensor and apply the Lorentz transformation. B and E components get moved around, and in some frame, it's all B, and in another frame, it's all E. I wish it had been taught that way in my EM course, which I took as an EE undergrad. But we were never taught tensors in undergrad EE; I learned it much later by reading Sean Carroll's GR textbook on my own .

[@Graham_Wideman]

"in some frame, it's all B, and in another frame, it's all E." Isn't that the same exercise shown in this video?

[@rsm3t]

@@Graham_Wideman Yes, but it directly follows from transforming the EM tensor. No need to calculate the effect of length contraction on charge density.

[@Graham_Wideman]

@@rsm3t Ah, I see what you mean.

[@jdsahr]

This was a pleasant nostalgic treatment: when I was an undergrad (dinosaurs still walked the earth), we learned about magnetism as a conjunction of electrostatics and special relativity, rather than a whole 'nother field. I still use this reasoning figure out if wires with current attract or repel. It *is* true that Maxwell's Equations forced the development of Special Relativity. Once you ask the question, "huh; I wonder what happens if you're moving at some speed compared to the apparatus?" then Maxwell's Equations start jumping up and down, shouting "Develop Special Relativity, you dingbats!" Special Relativity, by 1905, was guaranteed to be developed by *somebody*. General Relativity, however ... that's pretty amazing, and a truly major extension of Special Relativity.

[@Chris.4345]

lol I like how the justification for the right hand rule being the way it is at 9:50 boils down to “suck it up we ain’t changin’ it”

[@MihaiNicaMath]

I loved this new format! Great work!!!!!!

[@Naedlus]

I've had to help a few people who used the "hose as an analogy" trope in the past. The fact that you need to explain the hose is pre-filled with a substance that won't drain out on release seems to be mandatory. I like jam as the substance.

[@Guishan_Lingyou]

I am electrician, but I have taken some physics classes, which makes it a little hard for me to remember when to use right hand rules and left hand rules (electricians use electron flow for the direction of current). I find it counter-intuitive that electricians use electron flow current direction and physicists use conventional current flow. If I didn't know, and had to guess, I would think the physicists who know what electrons are, and not the electricians who couldn't care less about electrons, would use electron flow for current.

[@Tumbolisu]

I guess the physicist don't want to switch to the proper electron flow because it would require them to write new books, and prevents them from citing/quoting old stuff. It's also not too uncommon for laws to get into the way of change.