Curl Test

  • #1
trying to remember rules for curl test applicability.

is it just simple closed curve?

is F=-ysin(x)i+cos(x)j able to use the curl test?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
956
It would help if you would cite the "curl test" you are talking about. I think you are referring to the fact that a two variable differential, f(x,y)dx+ g(x,y)dy, is an "exact differential", that is, that there exist F(x,y) such that dF= f(x,y)dx+ g(x,y)dy, if and only if
[tex]\frac{\partial f}{\partial y}= \frac{\partial g}{\partial x}[/tex]
which the same as saying
[tex]curl \vec{f}= \nabla\times\vec{f}= \vec{0}[/tex] where
[tex]\vec{f}= f(x,y)\vec{i}+ g(x,y)\vec{j}[/tex].
It follows from that that the integral of f(x,y)dx+ g(x,y)dy around any closed path is 0 and that the integral from one point to another in the xy-plane is independent of the path. Which of those are you referring to?
 
  • #3
i was referring to the df/dy-dg/dx.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
956
Actually, that doesn't answer my question- were you refering to the fact that if df/dy- dg/dx= 0 implies that the integral around a closed path is 0 or to the fact that it implies the integral, from one point to another, is independent of the path.

The first obviously requires a closed path- it says so! The second does not.
 

Related Threads on Curl Test

Replies
6
Views
876
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
5
Views
6K
Replies
6
Views
14K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
8
Views
12K
  • Last Post
Replies
6
Views
3K
Top