Finding Curl from a vector field picture

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SUMMARY

The discussion centers on calculating the curl of a vector field from a visual representation, specifically at a designated point marked in red. The user expresses difficulty in transitioning from mathematical calculations of curl and divergence to practical analysis of vector field images. A suggested method involves visualizing a loop in the xy-plane around the point of interest and performing a line integral to determine the net result for each axis, while being mindful of the sign conventions.

PREREQUISITES
  • Understanding of vector calculus concepts, specifically curl and divergence.
  • Familiarity with line integrals and their application in vector fields.
  • Ability to interpret graphical representations of vector fields.
  • Knowledge of sign conventions in vector calculus.
NEXT STEPS
  • Study the mathematical definition and computation of curl in vector fields.
  • Learn how to perform line integrals in two-dimensional spaces.
  • Explore visual tools or software for analyzing vector fields, such as MATLAB or Python's Matplotlib.
  • Review examples of curl calculations from graphical representations in vector calculus textbooks.
USEFUL FOR

Students in physics or engineering courses, educators teaching vector calculus, and anyone seeking to enhance their skills in analyzing vector fields visually.

sjrrkb
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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
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 +-.
 

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