Deriving the speed of light from Maxwell's Equations using A-Level mathematics!

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  • Опубликовано: 28 ноя 2024

Комментарии • 135

  • @sinny_rl8845
    @sinny_rl8845 8 месяцев назад +137

    As a Master's student in Physics, I really commend that you take the effort to make fundamental physics concepts accessible to high school students using A-level maths. It's nice to demystify seemingly complex theories and encourage a deeper engagement with the subject from an early age. It's initiatives like these that bridge the gap between high school and university-level physics to foster a deeper appreciation and understanding. I hope to be able to teach in a similar way in the future.

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +26

      Thank you. This is a regular feature of my lessons at school, but I have the good fortune of teaching in a school where the majority of students will go on to study Engineering or Physics at university (with a large minority going on to study medicine). When I teach relativity, I go a bit beyond the specification too. I have found that the specification stops just short of the topics being understandable, so going just a bit further has a huge impact on the students' conceptual understanding.

  • @lucbraeckman4654
    @lucbraeckman4654 8 месяцев назад +18

    40 years ago, on my exam for antennas and feeders I got this exact same question. Good and clear explanation. Well done

  • @peterhall6656
    @peterhall6656 9 месяцев назад +46

    Yep, all accessible to an A-level student. Maxwell's velocity distribution law from 1859 is also accessible to a good A-level student. Lord Kelvin read Fourier's treatise on heat all the way through when he was 14. Those were the days!

    • @20shourya
      @20shourya 8 месяцев назад +6

      I remember Maxwell's velocity distribution being covered in chemistry, for catalysts.

  • @Blah1119
    @Blah1119 8 месяцев назад +19

    As a pupil at that school , hearing the school bell whilst at home was a mildly terrifying experience

  • @machinephile
    @machinephile 8 месяцев назад +15

    I was excited through the whole video like a child, the derived outcome was so satisfying. Your voice combined with your explanation combined with the style of the video was therapy to me.

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      That's a very kind thing to say, thank you

  • @gvza
    @gvza 9 месяцев назад +55

    i love the video format, paper writting looks so nice

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +12

      Thank you, I'm glad you find it helpful. Sometimes low-tech has its uses 😂

  • @kr-sd3ni
    @kr-sd3ni 9 месяцев назад +23

    excellent derivation

    • @PhysicswithKeith
      @PhysicswithKeith  9 месяцев назад +3

      Thank you. I've seen the speed of light derived by taking the curl of both sides and comparing to the others wave equation before, but I don't think that's very A-Level accessible.

  • @GSMusicMusic
    @GSMusicMusic 9 месяцев назад +23

    Very clear and well explained.

  • @peterjohnston8507
    @peterjohnston8507 8 месяцев назад

    Thank you . First time I've had a chance to follow through how Maxwell's equations work.

  • @AweSean-wv3xo
    @AweSean-wv3xo 8 месяцев назад +6

    Was thinking about this around the SAME EXACT moment this landed in my recommended lol, incredible video.

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      Thank you, and what wonderful timing! 😂

  • @jendf654
    @jendf654 6 месяцев назад

    If there wasn't Your good Will and a bit of an effort, I would be condamned to search further through heavy, uncomprehensible littérature of an authors uncapables to speak to someone like me (I do apolgize for my bad english), or to bother some proffesor, discusted with my low level. So I thank You for such a clear, no cutting corners, explanation.

  • @ianboard544
    @ianboard544 8 месяцев назад +1

    I remember doing this as an undergraduate - both in a physics course and a multi-variate calculus course. I always wondered about the significance.

  • @Andromeda4482
    @Andromeda4482 8 месяцев назад +10

    Can't wait for this to be the 6 marker on AQA Physics Paper 1 for 2024, just when you thought the 2023 papers weren't hard enough!

  • @overlyfatman9722
    @overlyfatman9722 8 месяцев назад +1

    This some quality physics class. The writing and the voice kept me engaged the whole time watching. Gonna come back with a pen n paper next time

  • @PhysicsOnline
    @PhysicsOnline 8 месяцев назад +4

    Check out the views - great work Keith!

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +2

      A comment from the legend! Thanks Lewis ♥️

  • @logogistiks8857
    @logogistiks8857 9 месяцев назад +10

    Very understandably explained, the math explanations were really helpful!

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +1

      Thank you. I know the mathematics goes on a bit, but I really dislike it when videos skip too many steps

  • @AllanKobelansky
    @AllanKobelansky 8 месяцев назад

    As a former Ph.D student, I too commend your teaching style.

  • @Nezha-Ishibashi
    @Nezha-Ishibashi 8 месяцев назад

    I just learned the Maxwell equations and i was thinking about the eletromagnetic waves, because of the consequences of 3 and 4 equations. Then i have see the propagation of that wave is equal to the light speed, comparing the general linear wave formula. Now that? That derivation in so much, like better, goddam what a video. Thank u so much for that, like it's free :). Thanks a lot

  • @skebettaja
    @skebettaja 8 месяцев назад +4

    Thanks, great video! I'm just currently in my last year of the equivalent of A-levels in my country and actually did understand it in full, and especially huge thanks for explaining partial derivatives which have been mysterious to me for a long time now :) Got me interested again in studying for the standardized test in phys I'll be having in a few weeks! :D

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +1

      Best wishes for your standardized tests 🙏

  • @a.b3203
    @a.b3203 8 месяцев назад +2

    Looks like A-level students learn much more math than we do here in the Netherlands 😅. Great video!

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +1

      Well, much of this is "beyond A-Level" in the sense that it isn't on the specification, but I still teach it to A-Level students and it's definitely A-Level accessible

  • @pooroldpedro
    @pooroldpedro 8 месяцев назад +1

    In passing you explained partial derivatives in a way that makes complete sense to me, only 45 years too late :)

    • @jean-jacquescharlet5296
      @jean-jacquescharlet5296 8 месяцев назад

      Welcome to the club (I am 66 years old). I am located in the French ALPS. I love watching maths and coding on youtube. Take care

  • @danishhamid7925
    @danishhamid7925 8 месяцев назад +1

    Cd not stop watching whole video.....keep it up professor

  • @lachenmann
    @lachenmann 8 месяцев назад +1

    Maxwell-Heaviside equations. Great video.

  • @jim2376
    @jim2376 8 месяцев назад

    Maxwell calculates the speed of light using paper, a pencil, and his brain. An astonishing accomplishment. An astonishing intellect.

  • @bernard3690
    @bernard3690 8 месяцев назад

    the missing final step is to inquire are the measured permittivity and permeability of free space inertial frame dependent .

  • @eliteteamkiller319
    @eliteteamkiller319 7 месяцев назад

    I previously knew how to get a wave equation that had the speed of light from them, but I'm interested to see how this is done. EDIT: I did not do it using trig functions, just a second order partial differential equation with a speed that is the speed of light from Maxwell's equations.

  • @navneetsinghr4290
    @navneetsinghr4290 8 месяцев назад

    Loved this
    and tried to do this myself after, got stuck sometimes but finally made it.
    Thankyou

  • @KakoriGames
    @KakoriGames 8 месяцев назад

    The only thing that is really missing from the video is where the electromagnetic wave equations come from, as in the video we just assume that they work as a model for light, but I guess that's a deduction for another time. Great video.

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      Yes, I decided that I would take Maxwell's equations as a starting point. They are met very briefly by A-Level Physicists (if they are doing AQA Option D, for example), but not used at all. I think the first three are fairly easy to follow, but the fourth would need a bit more time and I knew the video would be too long as it was.
      Maybe I'll derive Maxwell's Equations another time

  • @larryevans2806
    @larryevans2806 8 месяцев назад +1

    Excellent! Very good.

  • @ths3100
    @ths3100 8 месяцев назад

    Excellent explanation! 👍

  • @midnighttutor
    @midnighttutor 6 месяцев назад

    This was a very good presentation of the calculation. Just curious: is it possible to accurately measure those two constants in the final formula for c (or I guess first n) without first knowing the speed of light, and if so how? Thank you.

  • @isaacmedina9962
    @isaacmedina9962 8 месяцев назад

    learned more from this video than my entire semester of electricity and magnetism course at a university thus far. crazy how bad my professor can be at explaining physics but you are the best i have seen.

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      That's such a kind thing to say, thank you.

  • @jpv512
    @jpv512 8 месяцев назад

    very detailed, very accessible, just are missing constants values and dimensions (dimensional équations are crucial and help showing mistakes)

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +1

      Yes, I could have finished off by substituting the constants, that's a good point. The video was already quite long, so I'm not sure if a quick dimensions check would have been a good idea, but I agree it's always worth doing when you do a derivation 👍

  • @leonardobertolani7789
    @leonardobertolani7789 8 месяцев назад

    Everything so clear! Just one question: how do we know that the electromagnetic field has that specific geometry and functions that describes it? I mean, how do Maxell knew that electric field and magnetic field are perpendicular to each other and are described by those specific cosine functions? Thank you!

    • @epicchocolate1866
      @epicchocolate1866 8 месяцев назад +1

      They don’t have any geometry. These functions describe the amplitudes of the electric and magnetic fields, they travel together as waves outwards but they don’t look like anything.the electric and magnetic fields being perpendicular is a mathematical thing, but there’s are more advanced theorems called the Divergence Theorem, Stokes and Greens theorem, that end up showing you that E and B must be perpendicular.

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      I'm modelling the E- and B-fields using cosines that are perpendicular because, for plane polarised light, that's exactly what we have. That was demonstrated experimentally by Heinrich Hertz in 1888 (I think). Each of Maxwell's equations stands alone describing these fields, and can be verified independently from each other. Maxwell's third equation, for example, can help us understand how transformers work.

    • @tobystewart4403
      @tobystewart4403 8 месяцев назад

      You are right that the model for the "electromagnetic wave" owes itself to Hetz, and the notes he made when discovering radio waves. However, this is something of a contentious issue, because light is not affected by magnetic fields, implying that it is an electrostatic wave, without a magnetic component. It is possible that Hertz was measuring the magnetic field induced within the media in which the change in electric field was present. That was copper ring, held at varying distances from the source of the electrostatic wave.
      It is a tricky issue. So many people believe in "electromagnetic" waves today, it it almost heresy to point out that magnetic fields don't influence light, or other fluctuations in electrostatic force. Nevertheless, there is a wealth of evidence to show this to be the case, and indeed Maxwell's thesis essentially demands the distinction between a current, which is moving charge, and which generates magnetic fields, on the one hand, and a fluctuation in electrostatic force, which is not a moving charge, on the other.
      It was a lovely exhibition of math, in any case.

  • @gholmes182
    @gholmes182 8 месяцев назад

    Amazing, thanks. Absolutely brilliantly clear.

  • @thomasolson7447
    @thomasolson7447 8 месяцев назад

    I'm thinking there might be a better explanation for △•F
    I suspect it has more to do with sec, tan, and the quadratic formula than it does with this.

  • @fermatica1
    @fermatica1 8 месяцев назад

    Nice to see you make little mistakes here and there, and so cross them out. Likewise when you pause for a moment to reassemble your thoughts. (Have I got it right?) Very authentic. Remember it well!

  • @zhelyo_physics
    @zhelyo_physics 8 месяцев назад

    Excellent work! : )

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +1

      Thanks a lot! See why I wanted to use this method? 😂

  • @BigOttomatic
    @BigOttomatic 8 месяцев назад

    Good derivation of dot and cross, but I hate applying vector rules to operands like del because the dot product is supposed to be commutative (a.b=b.a) and that is not true with del since del.v != v.del (cross product has the same issue since is supposed to be anti-commutative but that does not work with del due to del being an operand)

  • @richardrigling4906
    @richardrigling4906 8 месяцев назад +1

    Well done!

  • @jaanuskiipli4647
    @jaanuskiipli4647 8 месяцев назад

    The whole business relies on premise that electic field and magnetic field vectors are always perpendicular, does this premise come from measurements or where from?

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +1

      Heinrich Hertz demonstrated this was true for plane polarised waves by using a split ring to detect magnetic fields and a dipole detector for electric fields

  • @husamzaheer5415
    @husamzaheer5415 8 месяцев назад

    This was a well thought-out and clear explanation! However, this isn't using A-level maths, it may come up in further maths but definitely not A-level maths. That doesn't take away from the fact that this is explained very well :)

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      Thank you for the kind comment 🙂 you're quite right that curl and partial derivatives aren't included on A-Level mathematics syllabuses; however, differentiation is included, as is using vectors. The reason I spent so long at the start of the video deriving the expression for curl is precisely because A-Level mathematics students are unlikely to have seen it before. I do think it's A-Level accessible though, which was the point of this video. A-Level mathematics was the starting point and it doesn't really get any more advanced than that. A good A-Level mathematics student will be able to follow all of the steps and be able to do this derivation themselves, and in doing so gain some context as to why we learn what we learn in A-Level mathematics

    • @20shourya
      @20shourya 8 месяцев назад

      @@PhysicswithKeithI am surprised to hear that about partial derivatives, can't recall if we did it for C4 or FP1 though.

  • @arsenvokrug4198
    @arsenvokrug4198 8 месяцев назад

    Thank you, I loved it! (But, full disclosure, as a former engineer and physics teacher, I would, wouldn’t I?)

  • @georgesringeisen5365
    @georgesringeisen5365 8 месяцев назад

    May I suggest To do The same task with "Geometric algebra" , much simpler !

  • @robertsalazar2770
    @robertsalazar2770 5 месяцев назад

    Most excellent!

  • @Blah1119
    @Blah1119 8 месяцев назад

    Amazing video

  • @goblin003
    @goblin003 8 месяцев назад

    But WHY are e0 and u0 what they are? What do those values tell us about "empty" space?

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      They indicate the strengths of the electric and magnetic fields. The greater epsilon, for example, the weaker the electric field for a given charge at a given distance.

    • @lucasbachmann
      @lucasbachmann 8 месяцев назад

      @@PhysicswithKeith the point is the WHY of c=299,792,458 m/s is still a mystery. Or the specific values of e0 and u0 being what they are to make c what it is. Last I checked this was a mystery as one would assume a more powerful theory would make specific values an emergent property. Otherwise we have a multiverse with every possible combination.

    • @AlainPaulikevitch
      @AlainPaulikevitch 8 месяцев назад

      ​​@@lucasbachmann glad to see people who seem to share my intuitive belief on why the claim in the title is misleading. My uni days are way too far behind me to be able to follow the match however by skipping to the end i gather that this is only an indirect way to measure the speed of light by measuring electric and magnetic fields. Which seems ridiculous as the propagation equation is based on the assumption that the speed of light is a limit. The whole thing is in no way a validation of the speed of light being an immutable constant that can be derived from fundamental electromagnetism but a circonvoluted way to get back a constant which was here by definition in the first place.

    • @dieterbaecher2975
      @dieterbaecher2975 7 месяцев назад

      @@lucasbachmann best comment here!

    • @dieterbaecher2975
      @dieterbaecher2975 7 месяцев назад

      @@PhysicswithKeith But c is still fundamental. The relation between c, e0 and u0 does not change this. All three are fundamental, or at least two. Not defined which one.

  • @Ensign_Cthulhu
    @Ensign_Cthulhu 8 месяцев назад

    Looking at the things you have to explain to an A-level student at 5:16 makes me terrified for how far the final year of high school has fallen in mathematical competence since I did it.

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      My caveat is that I don't teach A-Level mathematics so it might be that unit vectors don't need the time I've given them, but sadly unit vectors aren't on the A-Level physics specification. I teach them anyway, because they make working with vectors far easier

    • @core-nix1885
      @core-nix1885 8 месяцев назад

      They use "Further Maths" A-Levels nowadays to separate the geeks from the normies.

  • @IngeKosing
    @IngeKosing 4 месяца назад

    Amazing!

  • @padraiggluck2980
    @padraiggluck2980 8 месяцев назад

    C = sqrt(1/(ε0.μ0))

  • @F.E.Terman
    @F.E.Terman 8 месяцев назад

    It took you rather longer than it took Maxwell. Then again, he didn't have to explain every step as he went along. 😊

  • @Flaystray
    @Flaystray 8 месяцев назад

    28:39 why were these equations used

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      Light was observed to diffract, so the prevailing theory at the time was wave theory, which predicted diffraction (corpuscular theory didn't). The simplest wave function is a cosine.
      It's just modelling; finding a function and trying it out. Hertz identified that radio waves had an electric field and magnetic field component and that they were orthogonal to each other, hence the E and B equations modelled as perpendicular cosine wave functions

    • @Flaystray
      @Flaystray 8 месяцев назад

      @@PhysicswithKeith So are periodic functions the only ones that can describe light?

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      Electromagnetic radiation is a particular consequence of the way electric and magnetic fields behave together. You can get effects such as what happens in transformers where energy is transferred from the primary to the secondary coil, where you wouldn't call that an electromagnetic wave, but it's essentially the same physics (and even in transformers we have periodic functions).
      Even a pulse can be described as an infinite sum of sinusoidal functions (Fourier series).
      So, I reckon the answer to your question is 'yes', unless you can think of an alternative?

  • @zachansen8293
    @zachansen8293 8 месяцев назад

    what does "a level" mean?

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +1

      It's the UK education system. A-Level is the qualification 16-18 year olds can choose to study. It's short for AGCE, which means Advanced General Certificate of Education. The most advanced A-Level stuff is broadly equivalent in difficulty to first-year undergraduate degree study.

  • @JupiterThunder
    @JupiterThunder 8 месяцев назад

    Half-way in, and it doesn't look like A-level maths to me!

  • @yoniziv
    @yoniziv 8 месяцев назад

    Loved it

  • @sohamsuke
    @sohamsuke 8 месяцев назад

    ty :)

  • @miminorka
    @miminorka 8 месяцев назад

    awesome!

  • @walkerjian
    @walkerjian 8 месяцев назад

    strikes me that it would be possible for 'High Schools' to teach and graduate students to at least bachelors level. It would save a lot of wasted time and frustration. Why not let the good ones accelerate through and do this? They will still be with their age cohort to deflect other issues ...

  • @donwald3436
    @donwald3436 8 месяцев назад

    How do you spell pointing with a y wouldn't that be yointing lol.

  • @bobbybannerjee5156
    @bobbybannerjee5156 8 месяцев назад

    I didn't know an A level student learns of divergence and curl of vector functions.

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      They don't, but they do learn differentiation and they do learn scalar and vector products, so I think it's A-Level accessible. That's why I explain div and curl in so much detail; they'll be new to A-Level students.

  • @ElCidPhysics90
    @ElCidPhysics90 8 месяцев назад

    It’s del, lol. Have always used del and partial derivative. Good lecture though

    • @ElCidPhysics90
      @ElCidPhysics90 8 месяцев назад

      Namely because it is the partial derivative.

  • @vansf3433
    @vansf3433 7 месяцев назад

    The sppedvof light or laser beams invented by some individual humans' limited knowledge?

  • @awkwardhamster8541
    @awkwardhamster8541 8 месяцев назад

    That ring is giving me pain

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад

      The school bell ringing? Yes, it is too loud.

  • @isaacpianos5208
    @isaacpianos5208 8 месяцев назад

    Knowing calculus I and II but being shamefully delayed in physics, this title sounds completely absurd lol
    Great video!!

  • @gumby2241
    @gumby2241 8 месяцев назад

    WTF is 'nabla'?

  • @Ivankaramazov-lx5mg
    @Ivankaramazov-lx5mg 8 месяцев назад +1

    An A-level student doesn't know matrices?!

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +1

      No idea, I'm not a mathematics teacher, but I was told by someone who is a mathematics teacher that matrices aren't part of A-Level mathematics 🤷

    • @AweSean-wv3xo
      @AweSean-wv3xo 8 месяцев назад

      We sure as hell didn't learn matrices or the Dot and Cross products in A level math

    • @PhysicswithKeith
      @PhysicswithKeith  8 месяцев назад +1

      Ah that's good to know, thank you. Maybe I should record a video to show how to do the same derivation using matrices so that A-Level further mathematics students have some context when they learn matrices. I'm afraid I've seen far too much mathematics teaching where the context has been stripped away to the point that the maths looks far too abstract. My own A-Levels were like that, and I performed woefully in Mathematics because of it, but as soon as I was taught mathematics by a physicist at university it all clicked into place.

    • @Ivankaramazov-lx5mg
      @Ivankaramazov-lx5mg 8 месяцев назад

      ​@@PhysicswithKeith that would be great!

  • @michael.forkert
    @michael.forkert 8 месяцев назад

    _Speed of Light doesn’t exist._

  • @BrandonBiden-m2q
    @BrandonBiden-m2q 8 месяцев назад

    Re: title. Uh, yes. That’s how Maxwell did it originally. These RUclips videos are so effing stupid. 🙄

  • @MichaelDutch-mq4ns
    @MichaelDutch-mq4ns 9 месяцев назад +2

    Paper and pen? Really? No, man, tech it up.

    • @PhysicswithKeith
      @PhysicswithKeith  9 месяцев назад +6

      I've a few derivations where I've used a bit more tech, but the advantage of pen and paper here was the ability to easily manipulate the pages so that different written parts could be shown alongside each other. I think the physics here stands up regardless of the delivery medium, and I'm hoping I was able to make it clearer using the media that students would be using in the classroom.

    • @EDITᲽ
      @EDITᲽ 9 месяцев назад +19

      @@PhysicswithKeith I love the explanations on paper idk

    • @ArdaYavuz-id2cf
      @ArdaYavuz-id2cf 9 месяцев назад +15

      @@PhysicswithKeithI would say no need to listen to him. The explanations on the paper looks amazing and i can follow it up easily with my own paper and pen.

    • @MichaelDutch-mq4ns
      @MichaelDutch-mq4ns 9 месяцев назад

      @@PhysicswithKeith The students are on RUclips watching 3Blue1Brown, Numberphile, Mathloger, among others. Then they enter the classroom and are faced with that eternal poverty of media and resources. And that's why they come to RUclips. My advice was exactly to increase your coverage, your audience, so that you can share your excellent teaching with more people.

    • @timangar9771
      @timangar9771 9 месяцев назад +1

      I personally think it's the physics that's important, not the medium. That said, the above comment does reflect the general consensus of the community, which is, if you want to reach a large audience, make it visually pleasing.

  • @mrimmpossible
    @mrimmpossible 8 месяцев назад

    Very very nice