Stoke's Theorem

In the next problem you must use and explain in detail how do you use the Stoke's Theorem to get to the answer. It should also include an analysis on the orientation of the surface and its boundary.

Find the work done by the vector field $F(x,y,z)=(-y,x,0)$  when displacing a particle on the boundary of the surface parameterized by $p(r,\theta)=(r(2+cos \theta)cos\theta, r(2+cos \theta)sin \theta, sin \theta)$  where $0 \leq r<1,0<\theta<2\pi$.

  • Low bounty!

  • Mathe Mathe

    Bounty seems too low.

  • Mathe Mathe

    The range of theta looks suspicious too, it probably goes from 0 to 2pi.

  • M F H M F H

    very suspicious. also, p(.) has only 2 components, how's that a surface in R^3?

  • Erdos Erdos

    Please double check the statement of your question. There seems to be typoes.

    • Ok, I changed it.

    • Mathe Mathe

      There is still a typo on the first component of p(r,theta)


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Mathe Mathe
The answer is accepted.
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