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 $0 \leq r<1,0<\theta<2\pi$.

Stokes' Theorem Multivariable Calculus
Rafalpha Rafalpha
39
Report
  • Daniel90 Daniel90
    +2

    Low bounty!

  • Mathe Mathe
    +2

    Bounty seems too low.

  • Mathe Mathe
    0

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

  • M F H M F H
    +1

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

  • Erdos Erdos
    0

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

    • Rafalpha Rafalpha
      0

      Ok, I changed it.

    • Mathe Mathe
      0

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

Answer

Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer

1 Attachment

Mathe Mathe
3.6K
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.