Using Stoke's theorem

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Homework Statement


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 ?


Homework Equations




The Attempt at a Solution


For now , i have Δx F = (-z+ 1) j only
 

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Answers and Replies

  • #2
Charles Link
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Homework Statement


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 ?


Homework Equations




The Attempt at a Solution


For now , i have Δx F = (-z+ 1) j only
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 ".)
 
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  • #3
LCKurtz
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Homework Statement


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 ?


Homework Equations




The Attempt at a Solution


For now , i have Δx F = (-z+ 1) j only

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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