Could anyone help me with this question? I need to compute the flux of vector field curl F through the hemisphere x=sqrt(1-y^2-z^2)

nabakhi72

nabakhi72

Open question

2022-08-16

Could anyone help me with this question?
I need to compute the flux of vector field curl F through the hemisphere
x = 1 y 2 z 2
Positively oriented, with the vector field
F ( x , y , z ) = e x y c o s z , x 2 z , x y

Answer & Explanation

Brennan Parks

Brennan Parks

Beginner2022-08-17Added 14 answers

Use Stokes Theorem:
S × F d S = S F d r
where the line integral is along the open boundary of the hemisphere - which for your geometry is just the unit circle in the yz-plane at x = 0; from here the computation should be straightforward.

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