How do I use F and the divergence theorem to find the flux and plot it?

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SUMMARY

The discussion focuses on using the divergence theorem to calculate the flux of a vector field F in spherical coordinates. Participants emphasize the importance of applying the divergence operator correctly in spherical coordinates and integrating over the surface area of a sphere, which is given by the formula 4πr². Tools such as MATLAB and FreeMat are recommended for visualizing the results. The conversation highlights common pitfalls in calculations and the need for clarity in plotting the function values.

PREREQUISITES
  • Understanding of the divergence theorem
  • Familiarity with spherical coordinates
  • Knowledge of vector calculus
  • Basic skills in MATLAB or FreeMat for plotting
NEXT STEPS
  • Review the divergence operator in spherical coordinates
  • Practice integrating vector fields over spherical surfaces
  • Learn how to use MATLAB for 3D plotting of vector fields
  • Explore the mathematical properties of flux in vector calculus
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Students in physics or engineering courses, educators teaching vector calculus, and anyone interested in applying the divergence theorem to solve problems involving flux in spherical coordinates.

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Homework Statement



Capture.JPG


Homework Equations



∇.F(r)

The Attempt at a Solution



I keep trying to plug F into the divergence theorem but end up with very ugly answers that I know are not right.

Is there a simple way to do this question? Also, how the heck would I plot this for for the specified function values! thanks! help with the flux would be appreciated to.
 
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Your starting equation should be the equation for the divergence of an arbitrary vector in spherical coordinates. What is that equation?

Chet
 
Can you show us your approach and what you did to get ugly answers for the divergence?

Did you use spherical coordinates? and the spherical variant of the divergence operator?

http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates

For plotting you could use MATLAB or FreeMat (a free clone of MATLAB).

For the flux you have to integrate over the whole surface of the sphere. If you recall the surface of a sphere
is 4*pi*r^2 which might help you with the eventual solution.

http://en.wikipedia.org/wiki/Sphere
 

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