Vector Calculus II: Flux Integrals

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SUMMARY

The discussion focuses on calculating the flux of the vector field F = 2i + 3j through a disk of radius 5 in the plane y = 2. The key steps involve determining the area vector of the surface and performing a dot product with the vector field F. The area vector is defined as the unit normal multiplied by the area element of the planar surface. The original poster successfully solved the problem after clarifying these concepts.

PREREQUISITES
  • Understanding of vector fields and their representation
  • Knowledge of surface integrals in vector calculus
  • Familiarity with calculating area vectors and normal vectors
  • Proficiency in performing dot products of vectors
NEXT STEPS
  • Study the concept of surface integrals in vector calculus
  • Learn how to calculate area vectors for different surfaces
  • Explore the application of the Divergence Theorem in flux calculations
  • Review examples of flux integrals in various coordinate systems
USEFUL FOR

Students and educators in mathematics, particularly those studying vector calculus, as well as professionals applying these concepts in physics or engineering contexts.

Tylerdhamlin
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Homework Statement




F = 2i + 3j through a disk of radius 5 in the plane y = 2 oriented in the direction of increasing y.
Calculate the flux of the vector field through the surface.


Homework Equations





The Attempt at a Solution



I know that I need to calculate the area vector of the surface and then dot that with F, However, I'm in a bit of a brain slump and can't figure out how to calculate the Area Vector.
 
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Well, in the simple case of a planar (flat) area, the area vector is the unit normal multiplied by the usual area element in that plane.
 
Yes. Shortly after the post, I was able to solve this problem. Anyways, thank you for your help.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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