Curl & Line Integral of Vector Field: Calculations & Results

In summary, the conversation discussed calculating the curl and line integral of a given vector field F within a unit circle. The calculated curl was 0, but the line integral was found to be 2π. There was also discussion about the possibility of the field having a non-zero curl based on its rotation. The suggestion was made to show the work and carefully consider the requirements for applying Stoke's theorem.
  • #1
peterpang1994
37
0

Homework Statement


Given a vector field
F=-y/(x^2+y^2) i +x/(x^2 +y^2)
Calculate the curl of it the line integral of it in a unit circle centered at O


Homework Equations





The Attempt at a Solution


I calculated that the curl is 0 but the line integral is 2π. I don't think this field should have a zero curl as you can imagine that the field is rotating.
 
Physics news on Phys.org
  • #2
Show your work. Just telling us your incorrect answers doesn't let us see where your mistakes are (if there are indeed any).

You might want to look more carefully at the requirements for applying Stoke's theorem.
 
Last edited:

What is a Curl and Line Integral of a Vector Field?

A Curl is a mathematical operation that describes the rotation of a vector field at a particular point. It is represented by a vector quantity and is used to understand the flow of a fluid or electromagnetic field. A Line Integral is a mathematical tool used to calculate the total effect of a vector field along a specific path or curve.

How is a Curl Calculated?

A Curl can be calculated by taking the partial derivatives of a vector field with respect to each coordinate and then combining them using the cross product. This results in a vector quantity that represents the magnitude and direction of the rotation at a given point.

What is a Line Integral Used For?

A Line Integral is used to calculate the total effect of a vector field along a specific path or curve. This can be useful in understanding the flow of a fluid or the work done by a force field along a certain path.

How is a Line Integral Calculated?

A Line Integral is calculated by taking the dot product of the vector field and a small segment of the curve, then integrating over the entire length of the curve. This is often done using calculus and can be solved using various techniques such as the Fundamental Theorem of Calculus or Green's Theorem.

What Are the Results of a Curl and Line Integral?

The result of a Curl is a vector quantity that describes the rotation of a vector field at a particular point. The result of a Line Integral is a scalar quantity that represents the total effect of the vector field along a specific path or curve. These results can be used to gain insight into the behavior of the vector field and to solve various physical problems in fields such as fluid mechanics and electromagnetism.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
809
  • Calculus and Beyond Homework Help
Replies
4
Views
751
  • Calculus and Beyond Homework Help
Replies
10
Views
271
  • Calculus and Beyond Homework Help
Replies
1
Views
902
Replies
33
Views
3K
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
684
Back
Top