Solution to Peculiar Problem: Can Closed Integral be Evaluated?

[Kolahal Bhattacharya]

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?

 

[Dick]

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?

 

[Kolahal Bhattacharya]

OK,there is no cross product.This actually appeared in the exam I appeared yesterday.

 

[Dick]

I'll think about this, but let me know what the answer is when you find out.

 

[Kolahal Bhattacharya]

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).

 

[Dick]

Hmm. Ok. I'll keep thinking about it. But I'm having trouble thinking about dS as a vector separate from n.