Flux of a Vector Field Across a Surface // Vector Calculus

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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[@DrTrefor]

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.

[@utsavdesai3451]

Best Ever Playlists for Mathematics!!!!!

[@BoZhaoengineering]

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.

[@DrTrefor]

isn't that so cool!

[@shubhamsatyaprakash54]

You will reach 1 million soon. Thank you for your time and quality content..

[@DrTrefor]

I hope so!

[@hrkalita159]

Yaa bro

[@willm6598]

dude these videos are incredible

[@Sasuke-Uchiha]

OH MY FUCKING GOD. I UNDERSTAND!!!! I'VE BEEN STRUGLING WITH LINE INTEGRALS THIS ENTIRE SEMESTER. THANK YOU

[@hhhh-os4lz]

You helped us clear all our exams
Thank you Professor

[@canal_interpolo]

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

[@DrTrefor]

It is! I might do so one of these days that is a good idea

[@canal_interpolo]

@@DrTrefor omg please do it, I would love that! Thank you. Huge fan from Brazil

[@qamarmoavia4031]

Thank u Dr. Trefor Bazett . Keep it up ..

[@DrTrefor]

Thank you, I will!

[@j.o.5957]

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.

[@momen8839]

I want to apply that on Gauss law in electrostatic and magnetostatic

[@DrTrefor]

There is going to be a video on just that coming up in about two weeks!

[@evdmalphysics]

Good day. Could I ask you, what programs do you use for drawing formulas, figures and animations in your content?

[@user-lw9tn4pk3d]

At the end of the video, what does the p vector represent?

[@momen8839]

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?

[@DrTrefor]

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.

[@peterhindes56]

what is the p vector

[@shoshoshapan4982]

I like how you explain it, thank you so much that's help me a lot ^-^

[@DrTrefor]

Happy to help!

[@bendavis2234]

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.

[@sudiptaroyarts3861]

Sir you are awesome sir I am a physics undergrad student ❤❤❤

[@DrTrefor]

nice my undergrad was physics too!

[@sarajann5493]

Thank you very much

[@sergiolucas38]

Good video :)

[@andyralph9495]

which textbook can I refer to for practicing problems on vector calculus?

[@PiniiXever]

We use multivariable calculus Stewart 7th edition. Available online

[@zakirhussain-js9ku]

I think a charge has electric flux around it. Electric field appears only when flux of one charge interacts with flux of other charge.

[@jscruz685]

What you just said makes absolutely no sense

[@eddie-fu3zt]

this is so explanatory.... he even came up with this flux of a vector nonsense😂😂