Finding Curl from a vector field picture

In summary, the conversation is about analyzing pictures for homework and finding the curl of a vector field at a specific point. The person is unsure of how to approach this and is seeking assistance or suggestions. One approach mentioned is calculating curl and divergence mathematically, but the person is unsure of how to apply this to a picture. Another method suggested is to imagine a loop around the point in question and determine the net result of a line integral for each axis. Care must be taken with conventions.
  • #1
sjrrkb
2
0

Homework Statement


I need to analyze these pictures for my homework and find out the curl of the vector field at the point (red) on the picture.


Homework Equations



http://i1242.photobucket.com/albums/gg525/sjrrkb/ScreenShot2012-11-26at61615PM.png

The Attempt at a Solution


basically I can calculate curl and divergence and evaluate them mathematically...but when it comes to analyzing a picture and determining the curl at a given point on a vector field I am totally lost. Any assistance...in the form of answers, places I can go to get help, or just suggestions would be appreciated.
 
Physics news on Phys.org
  • #2
For the k component of curl, imagine a loop in the xy plane around the point in question, now imagine a line integral around the loop, what is the net result? Consider this for each axis and you should get close. You'll need to be careful with convention, to decide on +-.
 

1. What is the concept of curl in a vector field?

The curl of a vector field is a measure of the rotation of the vector field at a particular point. It is a vector quantity that represents the tendency of the vector field to swirl around that point.

2. How do you calculate the curl of a vector field from a picture?

To calculate the curl of a vector field from a picture, you can use the graphical method, which involves drawing small circles around the point of interest and measuring the rotation of the vectors at the circumference of the circles. Alternatively, you can use the mathematical formula for curl, which involves taking the partial derivatives of the vector field components with respect to the spatial coordinates.

3. What does a positive/negative curl indicate in a vector field picture?

A positive curl indicates counterclockwise rotation of the vector field, while a negative curl indicates clockwise rotation. A zero curl indicates no rotation, and the vector field is said to be irrotational.

4. Can a vector field have a different curl at different points?

Yes, the curl of a vector field can vary at different points. This is because the rotation of a vector field can change in magnitude and direction at different points, depending on the nature of the vector field.

5. How is the concept of curl used in real-world applications?

The concept of curl is used in various fields, such as fluid dynamics, electromagnetism, and computer graphics. It helps in understanding the flow patterns of fluids, determining the magnetic field strength and direction, and creating realistic visual effects in computer-generated imagery.

Similar threads

How to observe if a vector field has curl or not?
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
Finding Scalar Curl and Divergence from a Picture of Vector Field
    • Calculus and Beyond Homework Help
Replies
1
Views
948
How to find the curl of a vector field which points in the theta direction?
    • Calculus and Beyond Homework Help
Replies
33
Views
3K
I What's the physical meaning of Curl of Curl of a Vector Field?
    • Classical Physics
Replies
4
Views
273
MATLAB MATLAB: Fluid Flow - Curl of a Vector Field
    • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
818
Question about vector fields, div, curl grad
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Proving the Dot Product Identity for Vector Fields and Their Curl
    • Calculus and Beyond Homework Help
Replies
4
Views
2K
Divergence of ##\vec{x}/\vert\vec{x}\vert^3##
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Solenoidal and irrotational vector field
    • Calculus and Beyond Homework Help
Replies
1
Views
2K
Finding Div and Curl of a Vector Field then evaluating a point
    • Calculus and Beyond Homework Help
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top