Help finding direction of area vector on curved surfaces

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SUMMARY

The discussion focuses on determining the direction of area vectors on curved surfaces, specifically cylindrical and spherical geometries, as well as a bent rectangular rod forming a circular ring. The area vector direction is defined by the normal to the surface, which for a cylindrical surface is the radial direction. Understanding this concept is crucial for accurately applying surface integrals in physics and engineering contexts.

PREREQUISITES
  • Understanding of vector calculus
  • Familiarity with surface integrals
  • Knowledge of cylindrical and spherical coordinates
  • Basic principles of geometry related to curves
NEXT STEPS
  • Study the concept of surface normals in vector calculus
  • Learn about surface integrals in cylindrical coordinates
  • Explore applications of area vectors in electromagnetism
  • Investigate the geometry of curved surfaces in differential geometry
USEFUL FOR

Students and professionals in physics, engineering, and mathematics, particularly those working with vector calculus and surface integrals on curved geometries.

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Homework Statement


I understand how to determine the direction on rectangular surfaces, however when it comes to a cylinder or sphere or, in the case of the problem i am working on now, for a long rod that has been bent around in a circle i.e a a rectangular ring, I don't know what to do.
 
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The direction of the area vector is given by the normal to the surface. At the curved side of a circular cylinder, that is simply the radial direction.
 

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