Homework Help: Vectorcalculus problem

1. Mar 8, 2007

Kolahal Bhattacharya

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

I am to show
int{A . grad(phi)}dV=0 where A is a solinoidal field and normal component of A at the boundary vanishes.
I expressed A as curl F and suspect that the (curl F).(grad phi)=0
So,I am done.Is it correct?

2. Relevant equations

3. The attempt at a solution

2. Mar 8, 2007

Dick

You aren't supposed to show the integrand vanishes. In general, it doesn't. You need to find something whose divergence is A.grad(phi) and then argue that integrating that something over the boundary vanishes.

3. Mar 8, 2007

Kolahal Bhattacharya

I hyope i got it.I took the divergence of (phi A),and what comes out is that the given integral transforms to Int{phi A}.dS where I can apply the additional condition

4. Mar 8, 2007

Dick

Yes. That's it.