Answer: Calc III: Find Div(F) in Terms of r

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SUMMARY

The discussion focuses on calculating the divergence of the vector field F, defined as F = r/R^p, where r = xi + yj + zk and R = |r|. The key steps include expressing F in terms of Cartesian coordinates (x, y, z), computing the divergence of F manually, and substituting r to simplify the expression. The user successfully identifies the divergence in terms of r, demonstrating that the process is manageable with the right substitutions.

PREREQUISITES
  • Understanding of vector calculus concepts, specifically divergence.
  • Familiarity with Cartesian coordinates and vector notation.
  • Knowledge of the gradient operator and its application in vector fields.
  • Basic proficiency in manipulating algebraic expressions involving vectors.
NEXT STEPS
  • Study the properties of divergence in vector fields.
  • Learn about the gradient operator and its applications in physics.
  • Explore the implications of vector field transformations in three-dimensional space.
  • Investigate advanced topics in vector calculus, such as curl and Laplacian operators.
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Students and professionals in mathematics, physics, and engineering who are working with vector calculus and need to understand divergence in the context of vector fields.

craig16
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Homework Statement



Let r = x i + y j + z k and R = |r|. Let F = r/R^p.

find div(F) in terms of r.. i can't figure out how to express it in therms of r

Homework Equations



div(F) = the gradient added together
 
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First: express F in terms of x,y,z
Second: Compute the divergence of F by hand
Third: try to identify r in div F
 
hahaha sweet.. i figured it out. I was thinkin it was just too complicated but when you replace all the stuff with r it works out nicely.

thanks!
 

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