1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    rock.freak667

    User Avatar
    Homework Helper

    Try parameterizing the surface in polar coordinates and then use

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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
    -sqrt(7)≤x≤sqrt≤(7)?

    Thanks everyone for posting
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Flux through a surface Question Help Please
  1. Flux through a surface (Replies: 1)

  2. Flux through surface (Replies: 2)

Loading...