Solution to Peculiar Problem: Can Closed Integral be Evaluated?

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Homework Help Overview

The discussion revolves around evaluating a closed integral involving a vector field F and a scalar differential dS, with a focus on whether it can be approached using the divergence theorem or its corollaries. Participants are exploring the implications of the notation and the relationships between the components involved.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the feasibility of evaluating the integral without a clear relationship between F and the normal vector n. There is also discussion about the absence of a cross product and the implications of treating dS as a vector.

Discussion Status

The conversation is ongoing, with participants sharing their thoughts and observations. Some have expressed uncertainty about the notation and its implications, while others are considering different interpretations of the integral. No consensus has been reached yet.

Contextual Notes

One participant mentioned that this integral appeared in an exam, indicating a potential constraint on the context of the problem. There is also a note about misreading the question, which may affect the understanding of the integral's evaluation.

Kolahal Bhattacharya
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Homework Statement



Can anyone say if this can at all be evaluated?
closed integral{F dS} using divrgence theorem/any of its corollary?
here F is a vector and dS is a scalar and there is no dot sign between them.

2. Homework Equations



The Attempt at a Solution



I do not want to evaluate this.I just want to know if it is done.And how?
 
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I don't think so, unless F has some special relation with the normal vector n. Is it a cross product with n, as in a problem you posted before?
 
OK,there is no cross product.This actually appeared in the exam I appeared yesterday.
 
I'll think about this, but let me know what the answer is when you find out.
 
I misread the question and worked as int{F.dS}...it's easy.
This observation may yield something-
Note that FdS=F(n dot dS).Using triple product rules, we have nx(FxdS)=F(n dot dS)-dS(n dot F) => FdS=F(n dot dS)=nx(FxdS)+dS(n dot F).
 
Hmm. Ok. I'll keep thinking about it. But I'm having trouble thinking about dS as a vector separate from n.
 

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