Flux & Divergence Theorem

Posted on 2006-11-30
Last Modified: 2008-03-03
Suppose F is a vector field with div F = 10. Find the flush F out of a cylinder of height a and radius a, centered on z-axis and with base in the xy-plane.

By the divergence theorem:

  /                       /
 | div(F) dV = 10 | dV  = 10 * (volume of cone radius a & height a)
 /W                    /W

First, is this part right?
Second, Is there a way to calculate the flux however without knowing the volume of a cone with radius a and height a?

Question by:BrianGEFF719
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LVL 19

Author Comment

ID: 18051758
so the answer would be (10 * a^3 *pi)/3
LVL 84

Expert Comment

ID: 18051767
Do you mean cone or cylinder?
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Expert Comment

ID: 18051774
Can you integrate to find the volume?
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LVL 84

Accepted Solution

ozo earned 500 total points
ID: 18051784
You can integrate the area of circular slices d height, but after you do so you will know the volume of a cone with radius a and height a
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Author Comment

ID: 18051793
So there is no way around working with the volume of the cylinder?
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Expert Comment

ID: 18051816
or cone, whichever.
you don't need to start knowing the volume, but after you find the flux, you will know the volume by the divergence theorem

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