Maxwell's Equations - Basic derivation

[@ProfessorMastermind]

One of the best teachers . I wish I had a teacher like him in college . So clear and precise .

[@gahangwasteve8789]

Now you do

[@jacobvandijk6525]

Or didn't you pay enough attention at the time? It's always the other guy, huh?

[@alwaysdisputin9930]

@@jacobvandijk6525 Yes. It usually is. For example it's not impossible to derive e = mc² quickly & mathematically in YT videos. However, 95% of teachers are not able to do it. They simply do not have the skill that DrPhysicsA has. The ones that try don't get many views because their videos are confusing & unsuccessful. Great teachers are like gems I found some other things that have gem-like properties: 1) A book: Engineering Mathematics by Stroud - very gentle & clear with many questions & problems to work through 2) Supermemo software uses flashcards to make it almost impossible to forget the stuff we learn 3) Meditation on compassion & loving-heartedness.

[@verysimplephysicsinthamil1436]

Good Expectation

[@lawliet2263]

@@alwaysdisputin9930 hey man i too love goddesses but in bed since they hav huggge bobos

[@lesking6541]

At school, we were given a copy of George Gamows Biography of Physics to read. I was bowled over by the story of James Maxwell showing mathematically that radio waves are emitted by an oscillating charge and that he had calculated the velocity of these waves and it was the same as the velocity of light. I think it was this that enthused me to do a degree in Physics, along with Special Relativity. Unfortunately, my maths wasn't up to the task, so I changed to a Mechanical Engineering degree, but I have always regarded Maxwells equations with awe. I now understand them, at seventy-seven years of age. Got there eventually.

[@DrPhysicsA]

I'm not sure either. It's not my doing. I welcome all comments, although I can't respond to them all. I would delete comments only if they were rude or abusive. And I'm pleased to say that so far, that has not been the case for any of my videos. A tribute to physics enthusiasts.

[@meroxyersox]

You have saved my degree, that's not a joke or an exaggeration, I honestly do not believe I could have passed my electromagnetism module without the help of this video. Thank you DrPhysics!

[@DrPhysicsA]

+HighFiveTRex Thanks.

[@robertoflavioarguellesarre5836]

HighFiveTRex This comment made me suscribe without even watching the video yet.

[@ssemakulapheastus2651]

HighFiveTRex thank n keep up

[@qwerty90615]

I sure wish I had this video when I was taking electromagnetics. It is the same basic materials presented by countless others, but the clarity, the delivery, and pace are excellent. The handwriting and screen movements are natural, quick and legible. I get the idea DrPhysics has been delivering such material for some time.

[@jeroenfeher8107]

Understanding how to explain a subject is an incredibly undervalued communication skill isn't it.

[@osoyconam]

I'm spanish, and I have to say this is the best video I have found about the Maxwell's Equations. GOOD JOB!

[@imagination7710]

Net flux and chill

[@imagination7710]

BLUUUEERRGGHHH

[@FingerThatO]

+Abhinav Sharma Anal much?

[@christianthaisen397]

Imagination ii

[@xx_faze_rolf_xxl4029]

Yeah enjoy your VAC ban for that

[@jibran8410]

weird flux, but ok

[@DrPhysicsA]

Classes are really important. I just cover the basics or provide revision material. Classes go deeper and allow you to do worked examples. Good luck.

[@MarcelRGuimond]

Wow ! Who needs a classroom when you have this quality of presentation and delivery?!

[@warrenchu6319]

7:54 Maxwell's 1st Equation; 17:29 Maxwell's 2nd Equation; 37:44 Maxwell's 3rd Equation; 50:40 Maxwell's 4th Equation.

[@seannyman5844]

you are freaking awesome. I've been through a few physics/engineering classes and none of them know how to "dumb" down the idea and equations as well as you have. You're a great teacher.

Ahh - to the point. No background music, animations etc. Always enjoyable to listen to a teacher that knows his stuff and sets the right level.

[@fergaltierney8672]

Brilliant. It's almost 30 years since I studied these in university but I never remember them being explained in such an intelligent way.

[@cartermonroe4377]

This is the best presentation of Maxwell's original theory that I have ever seen. You really captured the spirit in which he went about solving the problem. He was not afraid to let geometry be his guide, which of course yielded astounding results. I never pass up a chance to look at any of his original derivations, since they are so beautifully done. Thanks again.

[@bluefishactcl1464]

Excellent !!!!! Basic, complete, accessible !! Entertaining!!! Brings Maxwells equations down to its most basic truths . Thank you

[@pbraju123456]

I wish I had such a tutor in my engineering days. You have dissected down every equation to tiniest bit and explained I can really call you Master of Electromangetic Engineering. Awesome

[@brianb2627]

Simply put... This is a prime example of an excellent educational video. Thank you very much for not only sharing your knowledge, but delivering it spot on!

[@DrPhysicsA]

Thanks for drawing this to my attention. You are quite right. I had intended to say that the dot product was the product of two vectors. But as I suspect you are aware, the dot product is actually called the SCALAR product. The “vector product” can also be called the cross product. I have made a small annotation on the video to make this clear. Thanks again.

[@Christe4N]

re: magnet partly inside the sphere (18:23): Even then the equations still hold. The magnetic flux outside of the magnet goes from the north pole to the south pole. Inside the magnet the flux always goes (back) from the south pole to the north pole. If the magnet is placed such that only the north pole is inside the sphere the amount of flux exiting and entering the sphere is still equal: the same amount of flux going from the north pole, out of the sphere to the south pole is going inside the magnet from the south pole, entering the sphere to the north pole.

[@StephenRayner]

19:00 I agree with Pablo P, the magnetic field lines travel through the bar magnet. So although they don't spread out like they would at the edge of the south pole, there is just as many magnetic field lines passing through the midpoint of the magnet as there are field lines exiting the norht point. Not suggesting Dr Physics is wrong, just that there are different ways to look at this and I hope it helps others to consider this from different angles.

[@missmakeupzombie]

Stephen Rayner ldl MmEu

[@johngayton2078]

I just discovered these jewels of knowledge

[@gctl4313]

Thanks. As a retired chemist with maths anxiety, I found this very helpful. I'll need to re-watch it and make notes. 😊

[@DrPhysicsA]

Thanks. And greetings from the UK.

[@philoso377]

Of all the KZbin on this topic, this is the only one I understand completely. Thank you.

[@abrahamgetahun39]

This man is literally awesome! Thanks for the crystal clear explanations sir!

[@Overunity357]

You sir, have just created a future physicist. This is the coolest stuff i have ever seen.

[@diogomussum]

A very simple explanation , you summed up one book in little time.

[@StephenRayner]

30 minutes in, this is bloody good!

[@steveschein2619]

Wow, brought back my entire EM fields one course, okay maybe not all of it. This is one of the best derivations of Maxwell's Equations I've seen.

[@natrajsarma9938]

One of the best physics teachers . Makes even the hard topics easy and clear .

[@hugoperozo4895]

This is the BEST explanation I have seen on a complex subject. Thank you for taking the time to make these videos. All your videos explain the concept in simple terms and the math behind it with simple derivations. I know there is more to it but derivations clearly outline the concepts behind the equations. Thank you.

[@mfelix3511]

Thank you so much, I cannot even express how much better you are at teaching this than my lecturers are. You are saving my degree.

[@ParamjitSingh-gz3de]

how so?

[@cochisewolf]

Thanks. I very much appreciate the time, energy and effort put in to making these available.

[@DrPhysicsA]

Thanks. As the title explains, this is only supposed to be a very basic derivation. My approach with a number of these videos is to give enough basic information to enable the viewer to derive a broad sense of what is going on. If they want the detail and the rigour of the derivation they can then go to more advanced sources.

[@DrPhysicsA]

We integrate dA over the entire surface of a sphere. The surface area is 4 pi r squared. It means that the entire field at distance r from the source must pass through the surface of the sphere of radius r, and that is the total flux.

[@jamesmaybury7452]

Difference between a physicist and and engineer: when he said “when you see an arrow going away from you you see the tail feathers, when you see it coming towards you, you see a point” he’s a physicist. An engineer would say “when you see an arrow coming towards you, duck”

[@fuahuahuatime5196]

19:00 I think even if you could do that, there would be just as many magnetic field lines leaving the area as magnetic fields going into the area, so it would still be 0 either way.

[@clakoclakson]

It's amazing how easy you make it look. Your pace of speaking, the pronounciation (I'm not english), and the presentation is excelent. Thank you very very much!!! Greetings from Spain

[@m3g4nf0x1zH0T]

This is the perfect summary of my undergraduate physics course. Excellently explained! thank you very much for your efforts :)

[@danieldanieldadada]

As someone who saw this 2 years ago in college and needs none of it in my faculty (civil engineering) I can say this was pretty neat. I thought I'd never unverstand Maxwell's equations. At this moment I understand 100% of the 1st equation.

[@hacsince1991]

dan iel I was just thinking the same thing. I couldn't even remember more than one definition out of every two hour Chem class.. and that in the tenth grade. Hahaha i and I'm 25 and can't believe how beautiful it is now. New favorite subscription!

[@shield543]

Great stuff, but at roughly 3.00, I believe a dot represents a scalar product, where as a cross represents a vector product

[@dae1366]

As with your lecture on the General theory of relativity. Extreme clarity achieved by explaining what all the terms mean and not assuming that we know them. Extremely useful for the none physicist.. many thanks

[@EmyllSomar]

I needed this. I spent about an hour trying to explain it to a friend a few days ago. This video would saved me that time. ;)

[@michaeljburt]

Wow this video is incredible! Just took a physics course last semester on electricity and magnetism, and this is an excellent refresher. Going in to my second year of electrical engineering in the fall and this is the perfect video to review. Your explanation of fields is very clear and simple- if anyone asks me about them I will definitely point them here. Thanks!!

[@sablezubshruz9811]

Very, very clear and clean explanation. Probably best i see so far on youtube.

[@garyraab9132]

Numerous responders found this very useful, as I did. If however you found this difficult to follow as it progressed, it’s not the physics, it’s the learning teaching style. Variables were clearly defined at the start, like r for radius, combined with a visual diagram. E for electric field, with two dimensional field lines drawn, ε0 commonly called the vacuum permittivity. The variables in the equations (r), became arrr, instead of radius. The instruction went from understanding abstract physics concept to manipulating math equations, maybe to rapidly for some learners. If you were a bit confused at the end, save this to your physics library, but also stop the video, write out the variables, with the variable names. Pause the video, and search for an animation of electric flux and magnetic flux in the 3-D animation. I love physics, but in a multi-verse learning how to learn is just as important😃

[@alibabatwist]

your method of presentation, your fantastic accent, and the clarity of your teaching made me impressed and I sincerely say : thank you very much.

[@DrPhysicsA]

+Ali Baba Thanks.

[@georgegrech5347]

18.50.I think that the second law holds because the flux going from south to north inside the bar magnet balances out the flux emerging from the N pole and then going out of the closed surface. The closed surface is just a mental construction and may be considered closed even when a bar magnet goes through it. A great teacher.

[@Silentkidgaming]

19:00 it is allowed bcz B lines travel from N to S outside and from S to N inside the magnet..... They cancel each other

[@jaideepdadi8119]

Your video saved my QA session in college. Thanks a lot

[@DrPhysicsA]

You are right. I have made that clear in other videos on electromagnetism. This was intended to be a basic derivation and I missed out the explanation that the EMF is always such as to oppose the change that causes it.

[@DrPhysicsA]

The key is that the plate has to be infinite for the situation you describe. So at any point in space the E field is the vectorial sum of the fields from all the charges on an infinite plate.

[@fcslash]

OMG I love you. If it wasn't for your wasn't for your videos I would be struggling so hard studying for my General Physics exam!!! All of this is SO well explained

[@zacht4368]

Thank you so much for these videos. I can not tell you how much they have helped me learn new material and refresh through older material in electromagnetism!

[@dudeskidaddy]

Wish I had this guy teaching my electrical engineering classes. Great jon

[@markkinnard796]

Excellent discussion. The best I have ever seen. I wish I had you as a professor when I was in college. Keep up the good work and thank you very much.

[@TheR971]

Thank you very much for this summarization! Concise and does not require too much knowledge. Very nicely done!

[@adrianboni2132]

i remember my Physics 73 instructor Mr Lozano with your lecture. Very informative. Feels like i was a in college again.

[@outrospection4all]

Excellent lecture, many thanks. One simplification, to derive the displacement current, you only need to multiply and divide by epsilon, q/epsilon is the flux... no need for the dA

[@itseasyitspractical]

One of the best physics videos I have ever watched! Congratulations! Great explanation!!!

[@Andratos95]

At 5:48, when you integrate, you didn't point out the reason why you are able to get the E out of the integral. For someone wondering, it is due to the fact that we chose a sphere, a surface of points equidistant to its center, so we can assume that E is constant on every point on the sphere. If E is constant, we can take it out of the integral and only compute the integral of dA, which is A, the surface of the sphere.

[@MCWaffles2003-1]

at 19:00 this was explained incorrectly, the sphere would not gave a hole as the sphere can be imagined to penetrate the magnet. the law is preserved as the magnetic field exists inside the magnet as well and just as much field comes in through from behind the N of the magnet as is exuded throughout the surface of the sphere

[@onemonsterceo]

+Corry Tuskey it can thought of as either way but your way of thinking gives much more insight and it was what I was thinking when I watched the video as well

[@PleochroicSpodumene]

+Corry Tuskey Thanks, it did my head in a bit when we came to looking at the parallel charge plates, where the surface cylinder passed through one plate. My brain said, 'hang on I thought we cant do that' but under your explanation everything works out.

[@aadityakiran_s]

Corry Tuskey Exactly

[@wurttmapper2200]

You are right. That's because is a dipole. The law also works if the sphere is outside the magnet or if it penetrates it.

[@SolveEtCoagula93]

I don’t agree that’s DrPhysics explanation is incorrect - it’s just a simplification. There are several ways of resolving the apparent anomaly but getting into a discussion about them would have interrupted the flow of the main aim which is to examine Maxwells equations.

[@arjunvadlamani3248]

This is what I'm doing my IB Math Internal Assessment on. Absolutely spectacular.

[@fantasticmrbond]

Fantastic video. It is exactly as you described: if you already have a grasp on these topics, than this video will help you prepare for a test as well as fill in any possible gaps in your understanding. The definition of flux at 22:22 is missing the integral symbol; or you could just suppose the flux is phi = B*A (not B*dA) and you still get the correct form of the Emf. Again, thank you so much for posting this. Your videos are fantastic.

[@yourbossforever]

My English is no that good , but I really understood this better than my teacher who is explaining in my language ! Thank you for using simple English words :)

[@rayyan21d]

I'm a high schooler and thanks for helping me 🥺

[@chriscross1152]

Thanks for this very interesting work. About the Maxwell's Third Equation it seems to me that there is some problem. You didn't take Lenz's Law in account. There is "a minus" missing ! The electromotive force is equal to minus the variation of flux over time and as consequence equal to minus the integral over the dB/dt.dA.

[@hanzishiguro8866]

We need more teachers you like you sir.

[@tanmoydutta5846]

At 20:18 it is the lenz law that explains it...if you push the N of the magnet towards the coil, then it will also produce N pole by the anticlockwise direction of current and vice-versa

[@soumya508]

The equations that made me fall in love with Electromagnetism and finally i spent 4 years of my life learning Electronics and communication engineering! Ah Good old days :)

[@ayushipandey3857]

From Electrostatics to the starting chapters of Wave optics, this video covers everything! (I even remember the equations now XD ) Thank you so much DrPhysics!

[@lawliet2263]

Hey baby, where do you live?

[@drstrangelove09]

I think it might help to point out, at 14m40s that although the charge may initially not experience a force (assuming it came into existence at the given point), it will interact and force the charges on the metal to move and so then experience a force, which will eventually lead it to move to the surface of the sphere.

[@robertsalazar2770]

Best treatment of this topic I've seen.

[@DrPhysicsA]

I am currently producing a series of videos on electromagnetic radiation. The first, “what is the light?” Is already up. I am using Maxwell's equations to derive the nature of electromagnetic radiation and the wave equation.

[@monkerud2108]

As to the example on equation 2, the flux on the sphere is 0 but there area majority of field lines in the domains inside the magnet equal to the outgoing flux.

[@xueqiang-michaelpan9606]

at 38:00 it is an integration of B on a open surface, which should not have the circle on the integral sign.

[@danieletagliaferri8496]

that's right! if it were a closed surface it couldn't possibly be equal to a closed line integral, simply because a closed surface cannot contain any closed loop (or closed curve) enclosing that surface... in fact the closed curve in the line integral (int E.dl) is supposed to be the contour of the open surface... Green's theorem? or maybe Stoke's theorem...

[@Supermario0727]

33:19.-There is a proof for electric potential energy of a test point charge relative to a source point charge that involves finding the area beneath the curve of a function representing the electrostatic force between the charges versus the distance between them for some arbitrary interval.

[@blancaroca8786]

Defining flux as the field strength times the area can seem mysterious for those not in the know. Whereas taking as primary Faradays conception of flux coming from charges then naturally leads to the idea of field strength being flux density or flux per unit perpendicular area. Starting with flux is powerful and intuitive. The only problem is how many lines should emanate from a unit charge. Of course we really need a kind of limiting infinite number but controlled. The 4 pi r squared is immediately seen as a consequence of surface area of a spherical surface in 3 d. Also stuff like the field near a charged plate or line are obvious and we don’t need to do integrals or anything and the gauss idea which held newton back is also pretty obvious.

[@enriquecruse310]

This video helped me a lot....Because I am not good in electrostatic and this helped to make my base strong for PGRE entrance.

[@jamesmaybury7452]

The comment at the end is the bit that intrigues me most, C is related to the permativity and permeability of free space. Which actually suggests it is related to the character of space and the idea of luminiferous aether. Having done the calculations it doesn’t seem to hold true for the speed of light in other substances and the permativity and permeability of those materials, am I doing the calculation wrong or is there a reason it doesn’t work for other materials?

[@Furiouslyfunnyfizzix]

Really liked this video. Very clearly and succinctly explained - well done. Thanks!

[@bolt6127]

@DrPhysicaA I have question E=mc^2 means E=Energy m=mass c=(velocity of light)^2 Eventually Energy=mass×(velocity of light)^2 But to complete formula we need to find what mass is?

[@bablobko]

Best, The Best derivation on Internet.

[@DrPhysicsA]

I agree that it is taking a liberty. But for a basic derivation it serves the purpose and is allowable.

[@eternalblue2119]

Could you make one giving examples and defining the constants please?

[@kirilavramov8061]

at 33:50 technically the potential energy in this case is not simply force*distance it's actually the integral of the force with respect to distance from infinity to a point

[@raymondblake5765]

Regarding Maxwell's first equation, What if there is no charge in the sphere, but there is a charge nearby... wouldn't the integral of the electric flux over the surface be non-zero, while the charge within the sphere is zero? How do I think about this ?

[@bennokrickl8135]

At about 19:00 I would rather say, that the same amount of magnetic field going out of the sphere will get in again inside the bar magnet, or that you could see the magnet as two magnets, one inside and one outside the sphere, and a cut magnet has a 'new' south or north pole, depending on wich side you're looking ant. Saying it doesn't apply is just closing your eyes, because it is an imaginary sphere with no holes, and therefore is would still apply, but there is more to consider (as mentioned)

[@thetimijs]

Thank You for covering this material! As You've already said, this if perfect stuff for revising the material for the upcoming exam! I am verry pleased, that I found this channel at the right time so thanks again and greetings from Latvia! :)

[@TON-vz3pe]

In Maxwell first equation, if we dumb it down a bit, it basically means that net flux is equal to Charge carried right. so flux is constant no matter what distance the charge is; as long as the Charge is of a fixed value. But how can that be. Wouldn't we see a drop in flux with distance like a million kilometres or infinity?

[@dkblack1289]

Dr Physics and Jason ( Maths and Science) are the best teachers.

[@linggarbangun4589]

13:21 I think that the electric field is zero is not because there is not charge inside, but because the electric field or flux cancel each other.

[@jimdogma1537]

For the 4th equation, around 48:55, you move the dA term in front of the time derivative. Same thing at 48:05, you move the "epsilon dA" to the right side of the time derivative to make the quotient Q/epsilon dA. I know this a math question, but can you be that liberal with just moving terms in and out of the derivative like that? I always thought that there was a "derivative of some term" which was an entity to itself, that was then multiplied by other terms in the expression. Thanks.

[@MrNathanParrott]

At 32:55 in the derivation of Maxwells third law you have that F = 0 at r = inf. However the force will actually = 0 anywhere from r > sqrt(inf). Does this have any other implications ?

[@jmiiea1810]

Very good explanatión . How change the Maxwell's laws if the electricidad charge changes with the time?

[@akarshsingh1540]

Thank u Dr. physics for providing such in depth knowledge of basics of em

[@barryhughes9764]

DrPhysicsA. Why ,at 4.40, is the flux only described in terms of cos theta in one plane and not two, since the ' window' could be skewed in two orientations? Any clarification would be gratefully appreciated.

[@sakuraudyani3576]

I'm having a great time with your videos. They are really interesting and very helpful. Thank you so much Sir

[@DrPhysicsA]

Thanks. Very kind of you to say so.

[@KlaasBaas]

at 23:10, how does the proportional sign turn into an equal sign?

[@anthonyyee7481]

by including a constant of proportionality.

[@samtux762]

@DrPhysicsA, i like your derivation of Einstein field equations. Do you derive Maxwell distribution somewhere?

[@Hythloday71]

This is great. Normally this element seems rushed in the lectures on youtube. This probably because they're aiming to bring them together to form a wave equation. Do you plan to do this? Also do you plan to derive the nabla forms ?

[@adyday1656]

Force and motion inertia and acceleration....magnetic permubility and dielectric permetivity.......you say tomatoes and I say tomatoes...a little confusion at my end....please ignore the last comment...good to see someone making a video to learn the next generation...👍