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)
Is there two possible ways of going about this:
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:
Parameterize S using spherical polar coordinates
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:
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!