# Flux of vector field through a surface.

• May 8th 2011, 04:03 AM
Ant
Flux of vector field through a surface.
I'm I'm calculating the flux of

v = (y, x)

upwards across the upper half of the unit sphere. (sphere such that z >= 0)

Find N = ( - (partial derivative function wrt x) , - (particial derivative wrt y, 1, )

the integrate v dot N with respect to x and y with the following limits:
$x \in [-1, 2]$
$y \in [ -\sqrt{1 - x^2}, \sqrt{1 - x^2}$

OR

Parameterize S using spherical polar coordinates $\theta , \phi$

Find N as the cross product between the partial derivative wrt theta and phi.

Then integrate v dot N with respect to theta and phi with the following limits:

$\phi \in [0, 2\pi ]$
$\theta \in [0, 2/\pi ]$

I THINK this is correct but I'm a little confused because in the first case I integral with limts corresponding to a unit circle in R2 but in the second case it seems like my limits are drawing out the actual unit sphere?

Sorry for the lack of LateX I tried but failed to make it work!!

Anyhelp really appreciated!
• May 8th 2011, 04:08 AM
topsquark
Quote:

Originally Posted by Ant
Sorry for the lack of LateX I tried but failed to make it work!!

Check out the general announcement near the top of any forum or search page. Use [tex] tags instead of [tex] for now.

-Dan