# Flux through a square and rectangle

1. Aug 24, 2013

### bowlbase

1. The problem statement, all variables and given/known data
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..

3. 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 dont remember them. I've looked up the integral methods and this is what I got:
A. $\int \vec{v_1}da$
z=0, da=dxdy$\hat{z}$
$\int^2_0 5 dxdy$ = 5(2)(2)=20

B. $\int \vec{v_3}da$
again z=0, da=dxdy$\hat{z}$
$\int -x dxdy$
$\int^3_0 -x dx$= -9/2
$\int^2_0 dy$=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?

2. Aug 24, 2013

### tiny-tim

hi bowlbase!
it depends whether you regard the normal as being in the positive or negative z direction

since the question doesn't say, it doesn't matter
correct method, but
i] you've misread the question … the normal is in the y direction!
ii] please always write ∫∫ not ∫ for a double integral, and you're less likely to make mistake
no, you seem to have evaluated ∫∫ xdxdy as a sum of two integrals

you need to integrate wrt x first, then integrate that result wrt y

3. Aug 24, 2013

### bowlbase

A) its funny that I have done it correctly on paper but incorrectly here. I'm not paying enough attention I guess.

B) no idea why I added those. I'm glad that I at least had the correct idea.

thanks for the help!