- #1
Divergence Theorem Homework: Volume & Surface Integral
- Thread starter athrun200
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Homework Help Overview
The discussion revolves around applying the divergence theorem in the context of a volume and surface integral problem. Participants are examining the relationship between given points and the surfaces they may define, particularly in relation to a cube.
Discussion Character
- Conceptual clarification, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants are attempting to apply the divergence theorem to transition from a volume integral to a surface integral. There is uncertainty regarding whether the four points provided can form a valid surface, with some suggesting that they do not define a cube.
Discussion Status
The discussion is exploring different interpretations of the problem, particularly the nature of the surface defined by the points. Some participants have offered clarifications regarding the definition of surfaces and the implications of the problem statement, but there is no explicit consensus on the interpretation of the points or the surface they define.
Contextual Notes
There is a noted ambiguity regarding the relationship between the four points and the surface they are supposed to represent, with participants questioning whether they imply a cube or another geometric shape. The original problem statement is referenced but not fully detailed in the posts.
- #2
Office_Shredder
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Don't confuse a surface with a plane. The surface of the cube is all six of its sides
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LCKurtz
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athrun200 said:Homework Statement
Homework Equations
The Attempt at a Solution
I can get the answer after applying divergence theorem to have a volume integral.
But how about about the surface integral?
It seems the 4 points given can't form a surface.
Those four points don't form a cube either. The problem doesn't imply that they do either. But the problem says a cube includes those four vertices, and that is enough to determine the cube. Presumably you knew that otherwise how did you apply the divergence theorem? It's the surface of that cube you need to use.
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HallsofIvy
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I don't believe that Office Shredder meant to imply that it was a cube- he was only giving that as an example. His point was what you said- that every solid has a surface (not necessarily smooth) as boundary. Here, the surface is made of four planes.
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LCKurtz
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HallsofIvy said:
If you are addressing that to me, I was neither quoting nor replying to Office Shredder. The original post clearly refers to the cube containing those four vertices, not a tetrahedron, and the OP was apparently missing that when trying to figure out the surface.
- #6
hunt_mat
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Well, you know that a cube has 6 sides that are the same, so from the the information given you should be able to construct the cube from that.
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