# Peculiar problem

1. Mar 12, 2007

### Kolahal Bhattacharya

1. The problem statement, all variables and given/known data

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. Relevant equations

3. The attempt at a solution

I do not want to evaluate this.I just want to know if it is done.And how?

2. Mar 12, 2007

### 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?

3. Mar 12, 2007

### Kolahal Bhattacharya

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

4. Mar 13, 2007

### Dick

5. Mar 13, 2007

### 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).

6. Mar 13, 2007

### Dick

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