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Homework Help: Flux through a surface Question Help Please

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Let S be the part of the surface z=49-(x2+y2)2 above the xy-plane, oriented upward.

    Let vector field F= (yz) i +(xz) j + (-17+xy) k

    Compute the flux of F through S.

    2. Relevant equations
    Flux through surface equation ∫s F(x,y,f(x,y)) dot product (-fx i-fy j + k) dxdy

    3. The attempt at a solution
    I used the equation to find flux through a surface plugging in F(x,y,(49-(x2+y2)2) for the vector field, I took the dot product. I believe the limits are -sqrt(7)≤x≤sqrt(7) and -sqrt(7)≤y≤sqrt(7). The answer I integrated out was -476 which was incorrect.

    I appreciate your time and help!
  2. jcsd
  3. Dec 6, 2009 #2


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    Homework Helper

    Try parameterizing the surface in polar coordinates and then use

    ∫∫F.n ds = ∫∫F |rrxrθ| dA
  4. Dec 6, 2009 #3


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    The first of these should be a single path integral, not a double integral, shouldn't it? Also I am puzzled by your "F.n". I would have used [itex]\vec{F}\cdot d\vec{s}[/itex] where "[itex]d\vec{s}[/itex]" is the vector tangent to the curve, not normal to it, with length ds.
  5. Dec 6, 2009 #4
    So if I do use polar coordinates would the limits be 0≤r≤sqrt(7), 0≤θ≤2∏ and a normal vector of n= k?
  6. Dec 6, 2009 #5
    using polar coordinates I calculated an answer -238pi
  7. Dec 7, 2009 #6
    If I stick with cartesian coordinates would the limits be -sqrt(7)≤y≤sqrt(7) and

    Thanks everyone for posting
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