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Using Stoke's theorem

  1. Dec 13, 2016 #1
    1. The problem statement, all variables and given/known data
    i cant find the normal vector here . In my book , outwards vector is . (Refer to photo 1 )
    The question is in photo 2 , i am aksed to use stoke's theorem to evalutae line integral of vector filed
    But , now the problem is i cant express z in terms of y and x . Can anyone help ?


    2. Relevant equations


    3. The attempt at a solution
    For now , i have Δx F = (-z+ 1) j only
     

    Attached Files:

  2. jcsd
  3. Dec 13, 2016 #2

    Charles Link

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    For your first case, I don't see a boundary line to the surface. For the second case, the surface is a cylinder, and I think they might be asking you to compute ## \int \vec{F} \cdot \, dS ##. If that is the case, you could also use Gauss law and compute ## \int \nabla \cdot \vec{F} \, d^3x ##, but certainly not Stokes theorem. (the Gauss's law version would also include in its result the integration over the endfaces of the cylinder). ## \\ ## Additional item: For vector curl use " \nabla \times " in Latex. To get Latex, put " ## " on both sides of your statement or expression. (The vector gradient is " \nabla" in Latex. The divergence is " \nabla \cdot ".)
     
    Last edited: Dec 13, 2016
  4. Dec 13, 2016 #3

    LCKurtz

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    What is preventing you from typing in a complete statement of the problem? There is no question in the photo telling us what line integral (if it really is a line integral) you want.
     
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