- #1
imagemania
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Homework Statement
A surface S is defined by z = 1-x^2-y^2 between 0≤ z ≤1
I need to calculate the flux of the vector field F = (y)i + (z)j through S.
Homework Equations
Cylindrical polar coordinates, Normal etc
The Attempt at a Solution
By changing the variables using cylindrical polar coordinates:
[tex]
\iint{\vec{F}.d\vec{S}}=\iint{\vec{F}.\vec{n}d{S}}
\vec{n} = \vec{N}/|{\vec{N}|}[/tex]
[tex]\vec{N} = \nabla g{(\rho,\phi,z)}[/tex]
Where \rho,\phi,z are the cyldrical coordinate symbols.
Then
[tex]ds = \frac{dA}{\vec{n}\vec{k}} = \frac{d\rho d\phi}{\vec{n}\vec{k}}[/tex]Doing the above i get to (after cancellations between the fraction and the the absolute value within unit vector)
[tex]\iint 2{\rho}^{2}sin{\phi} d\rho d\phi[/tex]
Im not 100% sure if this is correct, but it doesn't seem too complicated. Though i am not sure how to deal with the limits of integration from this points onwards.
Hope you can help me :)