Question

Flux integral questions:

I am given the vector field F= i-j+3k and I need to find the flux through "a disk of radius 2 in the xy-plane, oriented upward."

I have the solution to the problem, but I am not quite understanding it. I am using the formula :

Answer 1

but I am not sure how to interpret it. Is it "the inegral of the field dotted with the area of the region? or is it the integral of the dot product of those two things?

Answer 2

The book says "On the surface, dA = kdA, so only the k component of v contributes to the flux" ... Im not sure I understand that.

Answer 3

I assume the formula for the disk is x^2+y^2 = 4. Given the radius is 2, its clear that the are of the disk is pi * r^2, in this case, 4pi. So my next question is, how is the vector dA related to the area?

Answer 4

archer +1, they never show any new episodes tho

Answer 5

I haven't learned this material yet, but maybe this link will help?

http://tutorial.math.lamar.edu/Classes/CalcIII/SurfIntVectorField.aspx

Answer 6

Thanks, Ill take a look.

Answer 7

Yeah, that's where I would look for stuff like that. I was just perusing through it but it was greek as far as I was concerned :/

Answer 8

@oldrin.bataku Know anything about this stuff?

Answer 9

i'll take a peek soon

Answer 10

I am given the vector field F= i-j+3k and I need to find the flux through "a disk of radius 2 in the xy-plane, oriented upward."

@xartaan the oriented area element \(d\vec{A}\) has magnitude equivalent to the cross-product of the tangent vectors of the parameterization: