- #1
bowlbase
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Homework Statement
Flux:
a. Calculate the flux of the vector v1 = (1, 3 5) through a 2×2 square in the x-z plane (i.e., y = 0).
b. Calculate the flux of the vector v2=(z, y, -x) through this rectangle:0≤ x ≤3, 0≤ y ≤ 2, z = 0..
The Attempt at a Solution
I guess flux is suppose to be some kind of surface integral though I don't recall doing these in calculus before. That's not to say I didn't.. but I simply don't remember them. I've looked up the integral methods and this is what I got:
A. [itex]\int \vec{v_1}da[/itex]
z=0, da=dxdy[itex]\hat{z}[/itex]
[itex]\int^2_0 5 dxdy[/itex] = 5(2)(2)=20
B. [itex]\int \vec{v_3}da[/itex]
again z=0, da=dxdy[itex]\hat{z}[/itex]
[itex]\int -x dxdy[/itex]
[itex]\int^3_0 -x dx[/itex]= -9/2
[itex]\int^2_0 dy[/itex]=2
=-5/2
First thing that strikes me is the negative in B. I don't think that I should have a negative flux if I'm understanding this right. Can anyone help me understand this?