How Do You Calculate the Flux of a Vector Field Through a Parametric Surface?

AI Thread Summary
To calculate the flux of the vector field F = [x,y,z] through the parametric surface S defined by r(u,v) = [u cos v, u sin v, u^2], one must first determine the surface area element dA using the Jacobian of the transformation. The flux can be computed using the integral of the dot product of the vector field and the surface area element, expressed as flux = ∫(F · dA). It is important to correctly set the limits for the parameters u and v, which range from 0 to 2 and 0 to 2π, respectively. The discussion also highlights the need for clarity on whether the divergence of F is relevant to the problem. Understanding these concepts will ensure the correct approach to solving the flux calculation.
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Homework Statement


1. The expression F = [x,y,z] defines a vector field. Given the parametric representation of a surface S:[u cos v, u sin v, u^2] = r (u,v), where the parameters cover the ranges 0 ≤ u ≤ 2 and 0 ≤ v ≤ 2π, calculate the flux F through the surface S.

Homework Equations


How do i start this problem?

The Attempt at a Solution


I know the transformation equations for the cylindrical coordinates, and:
flux=Int(E dot dA=Int(divergence of E d tao
Im not sure if i should find the jackobian, but if so how do i work with the parametric representation vector r??

P.S. sry about spelling
 
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Am i even in the right department with those questions?
 

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