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Flux of a Vector Field Across a Surface // Vector Calculus
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- เผยแพร่เมื่อ 7 ธ.ค. 2020
- in his video we derive the formula for the flux of a vector field across a surface. This is very analogous to our two dimensional story about the flux across a curve. We can describe surfaces either parametrically, explicitly, or implicitly and so we come up with formula for the flux across a surface for each description.
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At 5:57 I have a typo. I forget to change back from dudv which I was using parametrically to dxdy which is used when it is implicit over the xy-plane. So everything is dxdy after this.
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I enjoy this series more and more. I suddenly notice that the major conclusions in vector calculus are as remarkable as those derived from calculus 1, 2 and 3.
isn't that so cool!
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OH MY FUCKING GOD. I UNDERSTAND!!!! I'VE BEEN STRUGLING WITH LINE INTEGRALS THIS ENTIRE SEMESTER. THANK YOU
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Thank you Professor
What software do you use for plotting functions in general? Multivariable functions, surfaces, tangent planes, vector fields, etc. Is it matlab? It would be really helpful if you made a video about that
It is! I might do so one of these days that is a good idea
@@DrTrefor omg please do it, I would love that! Thank you. Huge fan from Brazil
Thank u Dr. Trefor Bazett . Keep it up ..
Thank you, I will!
So we're essentially doing the same as earlier, finding the relationship between the unit normal and the F vector at that point, and then making it computational for both parameterized and implicit functions. Question to self: what would be the difference between the orientation of unit normal vectors being outwards vs inwards? Using right hand rule, I assume that would be the order or the cross product, meaning r_u X r_v or r_v X r_u for the parametric one. For the implicit one though, how would that be? The only variable there would be p_hat. I'm assuming that p_hat is the normal vector to the surface, so it couldn't be exactly i_hat, j_hat or k_hat, but some combination of the three? Computationally, my guess is it will look like p_hat = x*i_hat + y*j_hat + z*k_hat, where sqrt( these^2 ) = 1, but I'm not certain. We'll probably get to this in a later example.
I want to apply that on Gauss law in electrostatic and magnetostatic
There is going to be a video on just that coming up in about two weeks!
Good day. Could I ask you, what programs do you use for drawing formulas, figures and animations in your content?
At the end of the video, what does the p vector represent?
I have a question in the proof of Gauss law in all textbooks they prove it by integral of electric field of a charge on the area of spherical surface and the result will be of course, that integral [E.n.dA]=q/€ so why this result genarlized on all surface areas however they are sometimes not be spherical?
Ah yes, I'll be doing a whole video on that exact thing, but it comes a a property of the divergence theorem for fields with zero divergence that you can replace one surface with any other.
what is the p vector
I like how you explain it, thank you so much that's help me a lot ^-^
Happy to help!
Hey, great video! I have one question: when you use the vector p-hat, what is supposed to signify? Is it an arbitrary unit vector, or is it supposed to be identified as either i-hat, j-hat, or k-hat? And what's the purpose of it? Thanks a lot, your videos are a great supplement to the text I'm reading. They help a lot.
Sir you are awesome sir I am a physics undergrad student ❤❤❤
nice my undergrad was physics too!
Thank you very much
Good video :)
which textbook can I refer to for practicing problems on vector calculus?
We use multivariable calculus Stewart 7th edition. Available online
I think a charge has electric flux around it. Electric field appears only when flux of one charge interacts with flux of other charge.
What you just said makes absolutely no sense
this is so explanatory.... he even came up with this flux of a vector nonsense😂😂