The Forgotten Maxwell Equations.

[@ParthGChannel]

Hi friends, thanks for watching as always! I'd also like to thank Brilliant for sponsoring this video. To try everything Brilliant has to offer FREE for a full 30 days, visit brilliant.org/ParthG/. The first 200 of you will get 20% off Brilliant’s annual premium subscription. Also, please let me know what else to cover in future videos!

[@joshuagrumski7459]

I’m almost certain the sign convention is because of its applications to engines. The first people who really worked on thermo were working on engines and trying to make them work more efficiently, and so they cared about both how much heat you needed to put in and then how much work the gas put out, which leads to the sign convention there.

[@pyropulseIXXI]

It isn't a convention at all, and it has nothing to do with application to engines. It is purely abstract. If the system DOES WORK, then the internal energy in the system is literally leaving it. if you heat a system, then the internal energy literally increases. This has nothing to do with just assigning sign conventions, like calling electrons negative

[@misterlau5246]

@@pyropulseIXXI wasn't it that long ago they didn't know there were electrons and they used positive electric charge and then there were protons and electrons,, no neutrons yet, and the current flows to the other direction in reference of voltage? "Convention". Since it could be taking energy from a system that is built around another, you could reverse the signs there. Honestly, if everything is done correctly, the signs should not matter. I mean, which direction is + or - It's like left handed and right handed particles. 🤔 😬

[@Kob1yashi]

​@@pyropulseIXXI yes but the sign of the heat transfer is a convention

[@pyropulseIXXI]

@@Kob1yashi Energy flowing out being negative doesn't seem like a 'convention,' although it is. It is just the obvious choice

[@Kob1yashi]

@@pyropulseIXXI it is so intuitive that when I started my master in English, the sign was different than in my french bachelor 🙃

[@lesleynoblemaiden]

Those equations are the reason I decided to become a mathematician and a physicist. He's my greatest role model.

[@JackKirbyFan]

Someone in my family just got his PhD in experimental Physics so I know the work you had to do to get there. Congrats!

[@JackKirbyFan]

@@lesleynoblemaiden Thank you. I got a EE undergrad but wish I would have done Physics instead. I was fascinated by Quantum Mechanics - still am.

[@nahidhkurdi6740]

Most people do not know who Maxwell was, even in his home country. This is in spite of the fact that, whatever the importance of the work of the experimentalists was, the modern world is almost unimaginable without the fruits of Maxwell's work in Electromagnetism.

[@foxhound1008]

that was a great review! Correct me if I'm wrong, one of the interesting facts, is that for an ideal gas (no long range forces between the molecules) the enthalpy is only a function of temperature. Pressure, for an ideal gas at least, is more of an indicator of the quality of the energy. For instance, in a free expansion, no work is done, the total temperature does not change, but there is a drop in pressure, with an increase in entropy. As such. the energy content is the same, but it is now degraded do to the expansion with no work done.

[@MochiClips]

Glad youre still making these videos!! Are you still wham at badminton btw? 🤔🤔

[@lucienschmid]

Legendre transformations are hidden between the free energy, the entropy and the Gibbs free energy. And it is fascinating that all this stuff comes directly from maths! They are very useful once you got it!

[@highwaymen1237]

One of the most fascinating things I learned in chemical engineering.

[@GuyIncognitoOfficial]

Thanks for all the great videos. Can I ask what you use to make the diagrams with the semi-opaque background? I'm working on a video on a different topic and would like to be able to hand draw some diagrams and overlay them like this.

[@awebbarouni3002]

Great video ! (The last equation lacks epsilon 0 in 10:31)

[@GeoffryGifari]

hmmm i don't really know, but the minus sign convention dU = dQ - dW kind of makes sense if we look at how the system/working fluid (most of the time ideal gas in thermo courses) is placed among other mechanical parts in a heat engine. The energy source supplies heat *into* our gas system, which *outputs* work to the gears/shafts/whatever ..... so the convention says that heat in = work out if there is no change in internal energy, very straightforward for people working with engines

[@ewfewff]

Tak!

[@ParthGChannel]

Thank you very much!

[@Yashhh02]

Damn parth, Every nice explanation skills you've got love the video

[@tomoki-v6o]

maxwell contributed also to elasticity theory and strength of materials

[@spinnymathingy3149]

Also invented the possibility of colour photography

[@jonatankelu]

There’s also the Maxwellian velocity distribution.

[@tuanhungang5621]

thank you so much parth g, your videos are so so good !

[@jensphiliphohmann1876]

01:43 _...and is basically the energy of all these little atoms combined._ Minus the rest energy of each atom, of course.

[@msdmathssousdopamine8630]

07:50 Shouldn't it be partial^2 U/(partial V partial S) ?

[@whonyx6680]

Wouldn't say they are "forgotten", I still learned them in thermodynamics, but yeah, they do get much less attention than his equations for EM (which makes sense since those equations are much more important in general).

[@ib9rt]

I think if you study chemical engineering, the Maxwell relations get much more attention than the EM equations (which are not needed, unless you get into magnetohydrodynamics).

[@misterlau5246]

The other day a chemical engineer told me something about using Maxwell wibbly wobbly stuff there, because of thermodynamics. What a coincidence to see it here in your video

[@lizardwithahat4862]

Not completly sure but isn't there an epsilon_0 missing in 0:45 in the fourth equation? I don't want to sound picky or something. Just thought I'd point it out.

[@ParthGChannel]

Great spot, thank you for mentioning it! You're absolutely right - there should be an epsilon_0 before the dE/dt term in the fourth equation!

[@robertbrown5319]

I watched your series on Maxwell's equations but did not see the video exclusively devoted to the fourth Maxwell equation aka Ampere's Law. Is that a future video?

[@ParthGChannel]

Hi friends, big thanks to you for watching as always, and I'd like to thank Brilliant for sponsoring this video. To try everything Brilliant has to offer FREE for a full 30 days, visit brilliant.org/ParthG/. The first 200 of you will get 20% off Brilliant’s annual premium subscription. Also, please do let me know what other topics to cover in future videos!

[@sphakamisozondi]

What's crazy about Oliver Heaviside is that, he was a self-taught mathematician and developed vector calculus, which helped condense Maxwell's 9+ equations. Also, the entropy equation {S = kln(N)} was discovered by Planck, but gave it to Boltsmann anyway.

[@markgoretsky766]

Hello Parth, I think you're talking here about Euler-Lagrange equation, right?

[@ashishbiswas4098]

Hey there. I want to know that if there any connection btw Poisson equation and continuity equation related to semiconductor. Help me out Plz

[@jjreddick377]

This video is awesome! Thank you for explaining when and how to use calculus with these thermo problems. That always confused me 🙏🙏

[@misterlau5246]

With those partial derivatives these Mathz are pretty straightforward

[@Skellborn]

Hey Path, im currently taking a electrodynamics class. I'm confused with the phase of the E and B-field of an EM wave. Could you give any intuition on why the b E field are in phase, rather than shifted by 90°? Where does the energy of the E and B field go, when both fields hit 0 at the same time? Where is it coming back from, when they both hit their peak at the same time? How come an EM-creating dipole has phase shifted EM-waves in close proximity but not when its far away? I would love to get an answer to these questions 🙂Thanks so much

[@leonhardtkristensen4093]

I am an electronic engineer and I have the same problem as you. My explanation is that they are 90 degrees shifted but for some reason physicians like to turn the plane 90 degrees instead. Magnetic field is created by current - not voltage. It is an example where physicians have all exepted something that is wrong. In my oppinion the energy in an EM wave is constant but fluctuating between Electric and Magnetic energy. It is and occilation. It is just like a pendulum having a combination of kinetic or potential energy. Some times it is purely kinetic and some times it is purely potential. You are by the way wrong saying that it changes by distance. The EM next to a dipole and far away is the same exept for intensity. They create an occillating signal in a receiving dipole where the current is also 90 degrees out of phace with the voltage.

[@scollyer.tuition]

When the E/B fields go to 0 at a point, the values of (partial) dE/dt and dB/dt at that point will be a maximum - but from Maxwell's equations, that implies that the local fields of curl E and curl B will be at a maximum (in some sense) at that instant - so as E/B approach 0 at some point, locally (i.e. in some infinitesimal neighbourhood of that point), we see that new E/B fields develop but with increasing curl (visualisation of this is somewhat tricky, of course). So although the energy at the point of interest (proportional to |E|^2 and |B|^2) is 0, it has "leaked away" to generate new, local E/B fields with lots of local curl. And the local E/B fields with lots of curl then (again locally) regenerate the E/B fields that created them, but an infinitesimal displacement further on. As for intuition as the E/B being in phase, I don't know. But this comes from the solutions to Maxwell's equations. Maybe you can take the POV that the E/B fields behave similarly, and that propagation of an EM wave occurs because for each of them, there is some kind of local connection between the time rate-of-change of the other field at a point and the spatial rate-of-change i.e. that big dE/dt => big curl B and big dB/dt => big curl E. The point here is that the energy is not being periodically transferred from the E field to the B field and back again (one does not die away while creating the other), but is being transferred forward in space from old, local E/B fields which are changing in time to new, local E/B fields that are changing in space.

[@leonhardtkristensen4093]

@@scollyer.tuition I admit that I am not that good at the mathematics but I believe that a dipole antenna works just like an L C circuit. If you check on the internet for occilations in an L C circuit You wil find that it is just like a pendulum that the two factors (Potential and Kinetic energy, electric potential and current) are 90 degrees out of phase. I can not see that it shouldn't be the same for an EMR.

[@scollyer.tuition]

@@leonhardtkristensen4093 Well, we have to be somewhat careful: near an antenna (in the so-called "near field") the E and B fields have components which are not in phase, as you suggest. However, the strength of these field components dies off pretty quickly, and when we are far from an antenna (in the "far field"), the only significant components that remain are indeed in phase (you would have to look up one of the standard derivations for the field of a dipole antenna or whatever to get the details). So all the talk about the E and B fields being in phase only applies to the EM field a long way from an antenna. As for your comparison with an LC circuit: I'm afraid that an EM field is a different physical system, and there's no reason to assume that it behaves similarly to an LC circuit, and a mathematical analysis shows that it doesn't.

[@Skellborn]

@@scollyer.tuition Hey, thanks alot! I'm still confused, but it's starting to make a little sense now.

[@turnerburger]

I was wondering why we have subscripts on the partial derivatives to indicate which variables are being held constant. Do the partial derivatives themselves not already accomplish this?

[@trueriver1950]

Good question & good insight: Only if you have just two variables. Any more than two it becomes ambiguous, so the subscripts are there to make sure some clown doesn't invent another variable to confuse things...

[@JohnVKaravitis]

4:05 I would guess Rudolf Clausius.

[@misterlau5246]

Doctor Parth, everyone forgot HEAVISIDE. Those are the 4 EM vectorial or otherwise equations+ Lorentz force

[@DuckStorms]

Are the subscripts after the partial derivatives really necessary? They seem redundant.

[@zeynaviegas]

yeah. these two make it easy but in thermodynamics we might encounter multiple relations, and it is important to know which of them are constant as we take their derivatives

[@whonyx6680]

Unfortunately, they are necessary. You can take the same quantity as a function of different quantities (temperature as a function of volume and entropy or as a function of pressure and entropy) and the partial derivatives will be different ((dT/dS)V ≠ (dT/dS)P). It's one of the most annoying things in thermodynamics.

[@mohamednejighnimi4860]

0:45 there is an epsilon0 missing

[@misterlau5246]

Why did they use that convention? Dunno, but just looking at the dU which second term has - pressure., and the part about correlation with gradients I'd use cause Nabla is cool, you already said pressure vs what expansion does the gas performs as a derivative, a gradient. Since energy conservation works here of course, there's anyway the definition of temperature = avg kinetic inside the system. .. Then it's just a question of how do we used the systems like motors enginezz What is positive and what frame of reference. And Lagrangian please Heaviside used the 20 original equations, not the works of Maxwell. Yeah, vectorial form is excellent

[@sjswitzer1]

The work could have been defined as energy put into the system or energy taken out of the system but since the practical application at the time was steam engines the choice was obvious. You can make a similar argument about the heat.

[@KB08.a]

The minus sign because W=-PdV. If work is done on the gas the volume decreases so the minus sign with the volume term remains. Multiplying it with the outer minus sign of dW, the entire term becomes positive for the total internal energy of the gas to increase: -dW will become -P(-dV) = +PdV.

[@KB08.a]

When work is done on the gas it's volume decreases and internal energy increases. Vice versa for when the work is done by the gas on its surroundings.

[@KaliFissure]

All about those steam engines and gas expansion. This is why neutron decay Cosmology works. All matter via gravity is compressed to maximal density. Photons can be seen as atoms burping up space, so that they can get more dense. Because everything heads to maximal density. So now we have neutronium, all neutrons since the electrons got packed back up with the positron to create a second mass photon. At event horizon spacetime becomes unitary, "distance" irrelevant. Neutrons quantum tunnel or cross ER bridge, take your pick, and re-emerge from lowest energy density points of space. Where there is no resistance. In fact since you left universe over there the universe was missing that Hamiltonian for a Planck second. The neutrons having room to breathe decompose and spread their charge wings. Becoming first amorphous monatomic hydrogen, WIMPS, dark matter. And then stabilizing into very cold monatomic hydrogen. Why so cold? Because the phase change, change of state, from neutron to one cubic meter of hydrogen is a volume increase of 10⁴⁵. Dark energy. The decay expansion of neutrons. Then usual evolution, outward from voids, which are like heat cells since expansive, and condensing (cooling in a classical liquid) in the interstitial zones of the filaments. And in the more central parts of filaments more dense galaxies and stuff. Neutron decay cosmology. Path of least action. Topologically complete Physical process solution to universal process. Inevitable

[@comrade_marshal]

*during viva *Thermodynamics prof: Tell me Maxwell's 4 equations *Student who prepared for electrodynamics last night: Sure, the equations are... Student:

[@HadiLq]

The sign is not a convention! P is a positive quantity, and dV is only positive if volume increases, so the sign behind PdV is there no matter what the convention is.

[@ChaineYTXF]

I've always used dU = δQ + δW and I'm fine with that

[@mariommamtaj3624]

Thank you for the insight:)

[@elgefe5442]

I agree that @joshuagrumski7459 provided a large part of the answer about the sign convention being related to engines. However, the pressure simply being positive is probably why subsequent generations never tried to change it: dU = -P dV is simply what gasses do if you leave the alone and let them expand.

[@felixscott2002]

Pedantic, but the second order partial derivatives are only equal if they are continuous functions

[@DrDeuteron]

My _guess_ is when you heat a gas at constant pressure, it expands and does work on its container Fdx --> (PA)d(V^(1/3)) = PA/V^(2/3) dV = PA/([A^(3/2)]^(2/3) dV = PdV, maybe

[@david_porthouse]

In a nutshell, there is no vorticity in thermodynamics. Compare Maxwell’s relations to the complex stream function of two-dimensional fluid dynamics.

[@lijieallegn3186]

4:09 " It's because they wanted to mess with physicists of the future generations" lol fr we are really messed up now, they won 😂

[@sambhavgiri4007]

3:32 I know it's the same equation but it always looks scary when written that way to me. dQ = dU + dW ftw always

[@Pavan_Gaonkar]

Wow colourfull

[@evandrofilipe1526]

geometric algebra: You mean maxwell's equation right?

[@kaamesh7973]

Could you do a video on perturbation theory

[@darkkyne6261]

You made a mistake on max forrth equation (curl of B) you forgot to multiply the change of the electric field over time by epsilon 0 .

[@sonarbangla8711]

PARTH, if energy is conserved, isn't it an assumption. Moreover if true then doesn't it implies steady state theory is right?

[@spinnymathingy3149]

Einstein had a poster of Maxwell on his wall

[@swagatochatterjee7104]

Wait a sec, 0:45 the 4th equation is wrong!!

[@cadence_wav2423]

isn't the work negated because, the molecules are losing energy by working against the system ?

[@HyperFocusMarshmallow]

0:28 I don’t get the sarcasm. 🤔

[@vineethvenugopal8613]

He said " four very SIMPLE equations".in fact, Maxwell's equations are very tough . So he was just sarcastically saying .

[@HyperFocusMarshmallow]

@@vineethvenugopal8613 What's tough or not isn't an objective fact. It depends on what you compare too and what your background is. For someone who is unfamiliar with partial differential equations they might seem really difficult. And depending on the problem and boundary conditions it might get a bit complicated compared to some other problems. But as far as equations go they are quite simple in many respects as well. It's not hard to come up with useful equations that are a lot "tougher". If someone says they are four simple equations, I'd just mostly agree. No sarcasm... Though they can be bundled up into one simple equation.

[@ColeCoug]

Is it called work cause it was used to describe steam engines which were used to do work? They probably cared about how much work they could extract from a gas and try to understand how to maximize efficiency but thats just my guess

[@trueriver1950]

Pretty close. Actually they wanted to figure out how much energy they could extract from a given amount of coal, and the thermodynamics gave them the intuition that burning it hotter and superheating the steam might help. More recently, the idea of afterburners on a jet was conceived in the same way: not by an analysis of gas flow, but simply by saying that if we make it hotter then thermodynamics allows us more wiggle room to improve efficiency. That seemed like black magic to me when I learnt it as a teenager, well back in the day. But it worked, and that was good enough for the engineers... Only later on did physicists figure out the gas dynamics that actually make it work. A classic book of the external combustion era was "The thermodynamics of steam engines" by W. Inchley. Lots of thermodynamics, all the examples are steam related, bit nothing else about gases at all. Make it run hotter and it gets more efficient by magic.

[@sMeLLwAtER]

Was it to check if machine power was cost effective ...and aided in kicking off the industrial revolution?

[@raj4777]

my name is paarth g as well!

[@jamesraymond1158]

Maxwell's middle name is pronounced Clark, not Clurk. s

[@FlaminTubbyToast]

Parth, would you like to know something a physicist can’t teach you?

[@ultrametric9317]

This is dumb. It's like saying E = h nu is "the forgotton Einstein equation". And nobody "forgot" it. You could do something interesting like, say, talk about the thermodyanmic cubeoctohedron, a sort of 3D slide rule for encapsulating the Maxwell relations, but no, you opted for a clickbait title.

[@userc4187]

Communism

[@edal7066]

forgotten!? equally 'forgotten' as Navier-Stokes or Schrödinger equations ...forgotten only to ignorant people

[@gyawalisaurav000]

first

[@kevinmyers3644]

You must know his name is pronounced ‘Clark’. Look up the great vowel shift in English. Are you aiming at a US audience I wonder?

[@petejandrell4512]

It's written Clerk but pronounced Clark ya plonker

[@frogandspanner]

Clerk, not Clurk.

[@dancledan]

Really more like Clark, not clerk...