Is Multiplying Divergence by Area Correct in Divergence Theorem Problems?

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Homework Help Overview

The discussion revolves around the application of the Divergence Theorem in relation to a vector field and the surface of a sphere. The original poster attempts to connect the divergence of a vector field with the area of a sphere, questioning the correctness of their approach.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between divergence and surface area, with the original poster initially suggesting a multiplication of divergence by area. Others clarify that volume should be considered instead of area.

Discussion Status

The discussion has highlighted a misunderstanding regarding the use of area versus volume in the context of the Divergence Theorem. Some participants have provided corrective feedback, leading to a reevaluation of the original poster's calculations.

Contextual Notes

There is an emphasis on the need to correctly apply the Divergence Theorem, with specific reference to the geometric properties of the sphere involved in the problem.

joemama69
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Homework Statement



F = xi + yj + zk, s = x^2 + y^2 + z^2

Homework Equations





The Attempt at a Solution



div F = 1+1+1=3

area of sphere = 4pi

i can just multiply them to get 12pi as an answer right?
 
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No. You want the volume of the sphere, not the area.
 
ooooops

V of sphere = 4/3 pi r^3 where r = 1, V = 4/3 pi

so i got 4pi
 
Correct.
 

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