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 $0 \leq r<1,0<\theta<2\pi$.
Answer
Answers can be viewed only if
- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.
1 Attachment
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.
- answered
- 150 views
- $10.00
Related Questions
- Optimization Quick Problem
- Prove that $f$ is a diffeomorphism $C^∞$, that maps... (More inside)
- Surface Parameterization
- Double, Triple, and Change in Variables of Integrals Problems
- Compounding interest of principal P, where a compounding withdrawal amount W get withdrawn from P before each compounding of P.
- Convex subset
- Compute $\oint_C y^2dx+3xydy $ where where $C$ is the counter clickwise oriented boundary of upper-half unit disk
- Explain in detail how you use triple integrals to find the volume of the solid.
Low bounty!
Bounty seems too low.
The range of theta looks suspicious too, it probably goes from 0 to 2pi.
very suspicious. also, p(.) has only 2 components, how's that a surface in R^3?
Please double check the statement of your question. There seems to be typoes.
Ok, I changed it.
There is still a typo on the first component of p(r,theta)