Converting Maxwells Equations from Differential to Integral Form
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- Опубликовано: 24 июл 2024
- In this video I show how to make use of Stokes and Divergence Theorem in order to convert between Differential and Integral form of Maxwell's equations. I also try to explain their connection to fluid dynamics, as well as motivation for each form.
Dude I love this. Maxwell's equations are so cool. My professor showed us how to get the wave equation from Maxwell's equations and I nearly passed out from excitement 😂😂😂😂
As a freshman starting my physics degree, I really appreciate your videos. Keep it up plzz
jroxygen00 good luck and thank you!
Hey so i finished highschool this summer and i start my undergrad in Physics in Jan 2020, i have a few questions which i would really appreciate answers to if you could spare some time from your schedule please🙏🙏..any tips to use these remaining 2 months wisely so I am prepared for what's coming? Also, how did you find the transition from highschool to undergrad? Were you a straight A student in highschool? If so, how did it reflect on your progress later on? Also, what made you chose physics? Will you be aiming for a researcher position later on?
Thanks in advance
@@AndrewDotsonvideos can you also help me with the above questions please?
@@farhannoor3935I know no one answered your questions, but I'm basically in the same spot as you were four years ago. Now that you (probably) have experience, can you answer those questions you asked four years ago because they'd help me out a lot. Thank you.
Someone get my camera an adderall, it needs some help focusing...
Andrew Dotson yeah dude but good video tho keep up the good work Andrew.
ruclips.net/video/R_1znDPww3E/видео.html
Gold :D
Au*
Andrew, I took modern physics at NMSU and you were our TA around the time you made this. I knew I recognized your voice but was thrilled to have realized it was you and that you were in fact from my alma mater!! I’m so happy to have found your channel. E&M was a class I worked my way around but grad school has made it an absolute necessity. I appreciate your videos and love the way you lecture- thank you for continuing to teach me things even years later and congrats on your candidacy!! I hope to follow suit here soon enough ^^
Small world! Are you in grad school for physics now?
@@AndrewDotsonvideos Adjacent to it, going for physical chemistry at Berkeley!
The best explanation ever thanks bro
I might just watch this video every month just so when the EMF exam comes I'll be ready... and stoked.
Sorry, I'll be leaving.
*door closes*
The no monopole law is the easiest in a couple of ways. The differential form says "in a tiny region, there are as many incoming field lines as outgoing", which pretty obviously extends to "in any region, there are as many field lines coming in as there are going out."
I'd just like to point out that Maxwell didn't actually use the vector notation when he devised his equations and it took Oliver Heaviside to do so some time later. So there was no Curl or Divergence in Maxwell's original (20) equations.
Sources?
Maxwell used Quaternions
@@bonbonpony Wikipedia
@@pranjaltiwari1663 Is Wikipedia more accurate on that than Maxwell's original works, smart ass? :q
@@bonbonpony No, you can check Maxwell's original works, Heavyside developed the equations we used today. He reduced Maxwell's orginal about 20 equations to the 4 equations we know today using the Vector Calculus he discovered independently.
I'm also a physicist whos done a masters, but I decided to take a break from physics. I may do a PhD in the future, but til then i doin easy stuff for a bit xD. Still its nice seeing good sir Andrew Dotson helping people in reviewing the good old stuff, back when the math was still fully rigorous and I was not confused by the funkiness of renormalization in QFT xD
i found you bc of your meme videos but this is the first time i come here to learn, and i even didnt realized it was you until i paused and read the account name haha. Great vid ofc!
Excellent Mr. Dotson.
So for anyone looking for a nice and easy proof for Stokes Theorem and the Divergence Theorem, look no further than the generalized stokes theorem, which states that the integral over a k+1 dimensional manifold of the exterior derivative of a k form is equal to the integral over the boundary of the manifold of that k form. I know it sounds weird because of weird vocabulary, but a quick look at an intro to differentiak forms will clear this up, and the theorem itself can be easily shown by converting the integral over the whole manifold into the integral over its boundary of the integral of the differentiated k form. Nicely enough, this yields a bunch of neat theorems super easily in a way that almost seems trivial.
amazing teaching style
Getting anxiety from watching this and I took this class over a year ago haha. I know this is nowhere near the hardest class a physics major takes but it was pretty intense for an EE :P
Loved it Andrew.
@ 2:14 , why is only the bottom right infinitesimal, (da), a vector when the other dl, da & d3V are not?
Thank you so much!! This has been so helpful!!
Beckie Lait glad you thought so!
Really helpful! Thanks Andrew :)
Magic at 9:43 !! :P ..Very helpful video !
Simple and nice presentation. Wow!! DrRahul Rohtak Haryana India
Awesome mate nice explanation
Thank you for using SI units. When I was first taking E&M, we used a text by Purcell, which used cgs. I hated it with a passion.
@Canol Onar This was 35 years ago, so quite possibly a different Purcell. At one point, while describing how E and B transform under a Lorentz transformation, he wrote the cgs version using 'beta'. To demonstrate the 'inferiority' of SI, he wrote the same equations using 'beta/sqrt(mu_0 eps_0)' to make them appear needlessly complicated, rather than simply using 'v'. I found this to be duplicitous.
Came for the memes, stayed for the learning. First time I used one of your videos to study, thank you!
Wonderful. Thank you.
So helpful☺️👍
is the da & dl in stokes theorem & d3r in divergence theorem a vector or scalar?
I miss you "helo smart people"....do no omit this part...besides....this is your more thougfull video,...2 chops up andrew !!!!!
What is the mathematical justification for converting the partial derivative into the total? Also you can factor it out of the integral because since its a surface, its continuous?
I know this is an old comment, but I think we are under the assumption that our boundary conditions are not functions of time. This is part of Leibniz Special Case for taking derivatives of integrals just in the reverse direction. You can justify this exchange of limits UNDER THE ASSUMPTION your boundary conditions are under no influence of time
@@cartermikovich1369 , is this the same logic for proving that the shroginer equation's psi remains normalized with time, if it is initially normalized?
Well explained. Thanks. But I think for divergence of B = 0 is (no magnetic monopol)
Can you convert from integral form to differential form now? Please!
its almost the same , but you have to know the definition of divergence and rotation
The integral form is concerned with the flux, which concerns itself with the total amount (a scalar quantity) of a vector field coming out of a surface area. The differential form on the other hand concerns itself with one point in the vector field only. So there is no field flux, but rather a single point relation to another variable. Notice that when the curl is involved, you must dot it against a surface infinitesimal area; otherwise your quantity would be a resulting vector as in the Stokes Theorem. This usually happen when there is a relationship between two variables like magnetic filed and electric field which are perpendicular to each other (Faraday Law). Just remember that integral form is concerned with the sum of many parts; while the differential form is concerned with one point in the distribution.
Can you convert them to simple quadratic equations?
I'm finally able to understand this hell yeah
How about the Generalized Stokes Theorem, = ?
I love how I watching videos like this before and after taking the classes that teach the maths. It’s just so orgasmic!!! Watched this while I was in highschool, the math made no sense at all, I could kind of get some ideas from my IB physics HL class. And comparing it to now, after taking calc 3 and diff eq last semester...... orgasmic. When he mentions stokes and divergence theorem!!!!!!!!
Maybe it’ll be even nicer after PDE’s cause gradient
Amé este video!
This may need further evaluation but conceptually it is for geometric construction for object at high speed to survive heat and frictional drag force in Space
What is the difference of the double integral and the one integral with a circle on it, i ask about the notation of gauss law , min 4:15
Sir plz make video on ,how to get the differential form of maxwell equation ...??
If you mean going from integral to differential form, then you just do the whole process in reverse: convert LHS line integrals into surface integrals of the curl, write the RHS as a surface integral, then you equate the terms under the integrals.
If you mean deriving them from scratch, I'm afraid that that might be impossible. Maxwell's equations are an agglomeration of postulates resulting from empirical findings. You could derive the first and third ones from the Coulomb and Biot-Savart laws, but I would contend that the Maxwell equations are more fundamental and that accepting them as postulates makes more sense.
very good
how is he convertig the partial dervatives wrt time to total derivatives
Think about it, if I'm taking the time derivative inside the integral, then at this point there is still x dependence. So the field still depends on x and t, making d/dt a partial derivative. If I pull the derivative outside of the integral, then I'm taking the time derivative of something that has had all of it's x dependence summed over. So there will be nothing else to take the derivative with respect to, making it a total derivative.
@@AndrewDotsonvideos is that the famous feynman technique for integration?
@@abdullahalmasri612 if I'm not mistaken, isn't called the Leibniz Integral rule right? The more general original formulation
What is a close line integral?
a line that s closed e.g. a circle in 2d - the shape is given by the other side of the equation
and the line is the edge of that area
11:13 Just a small correction there, Divergence is actually a glorified way of saying that we're taking a DOT (not CROSS) product of a differential operator and a vector field.
Yeah, and I think he meant to say CURL instead of DIVERGENCE at that specific time spot.
do a video deriving maxwells equations
That marker is so fucking smooth
Wow. You're the first person I've seen who writes his a
Hi Andrew.
Im having a stroke trying to get an understanding..these equations are hard work
For Gauss' Law, why is it not a closed surface integral of E? The symbol you have just shows a regular double integral? I'm trying to relearn those calc 3 theorems again that I didn't quite master.
Alex Strasser yes it should be. His notation isn’t the best. The dL and da should also be vectors but he didn’t write that
4:10
It Should be closed surface integral
You forgot to mention what they mean I think.
what does the line integral of B means?
i know the surface integral means the line field flux, and I think the line integral of E is the voltage, but for B???
and in this case the continuity equation stands for the charge conservation, in which the varying of charge density can only be produced when there is a current leaving or going inside
Hi! I would recommend that you look into a little bit of basic vector calculus for a better understanding of this. However, let me try to explain.
A line integral of a vector over a curve is when you take infinitesimal pieces of the curve you are integrating over, then taking the dot product with the vector, and then adding all that up along the curve.
Now, for the electric field, it is the electric voltage. For a magnetic field, it is the magnetic voltage drop. It becomes relevant in the study of magnetic circuits, which is used for calculating how the magnetic flux behaves in transformer cores and stuff.
I'm from India. I'm in third year BSc(physics). I need your help to find solutions in Mathematical Physics. (Power series solutions for differential equations)......
Reply positive..... waiting....
SANJAY BHOSALE I suggest Schaums outlines for differential equations. Tons of worked problems and examples
Andrew Dotson
Thanks...
Andrew Dotson ....
I would you like to friendship with you?? We can help each other to understand the beauty of ....PHYSICS.....??
What you are searching for is special functions. Which there are some tutorials here on RUclips and are mostly made by people from your country, though I must say their english is hard to understand.
Tried to understand Bessel functions and left non the wiser.
12:03 what is c here ?
Using stoke's theorem and stoke's theorem
But how to turn them into electricity?
_good explication_rotE=_dB/dt and rotH=J+dD/dt and HrotE--ErotH=div(H*E) formulla for ellectric generator_motor and difuzor_speak sound_ archaicxn lord
Thank You! AND ESQ. ME, PLEASE!
Shouldn't it be dr³ instead of d³r?
rednax No because you can think of d^3r being the same thing as d^3(x_i) with i running from 1 to 3. i = 1,2,3 corresponds to x,y,z or whatever your respective differential element for your chosen coordinate system is. So technically if you were to write d(x_i^3), that would be dxdxdxdydydydzdzdz. In the end, if you know what space you're integrating, it doesn't matter what you call it, though
In reality, call it what you want. I just didn't want to write dxdydz over and over again
Could just write dV otherwise
_beautyfull lex biot_savart and lex maxwell etc of leibniz_newton lex differntiall_integrall for... ___archaicxn lord
Who else is 14 and is dying to be a theoretical physicist
If you die at age 14, I don't think you will become one :q Better keep surviving...
CODENG HATI + MA DOKTER KECIL
Your cam had one too many bourbon, I know the feeling 😂🤣
This is not a video for year 10 students I must have skipped a few classes
GA KASIan pesimis
Idk it just seems like you memorized the sh!t out of each step you aren't really explaining the why at all between each step (except for the continuity equation you explained the steps well there). That being said I like the video a lot, still!
Me in 12th grade.....