Surface Integrals: Why Dot ds with Normal?

[likephysics]

Homework Statement

This is not a HW prob. Just a question.
When doing surface integrals, why should the area element ds be dotted with the normal. I don't get it .
$$\oint$$A.n ds

Homework Equations

The Attempt at a Solution

 

[gabbagabbahey]

Homework Statement

This is not a HW prob. Just a question.
When doing surface integrals, why should the area element ds be dotted with the normal. I don't get it .
$$\oint$$A.n ds

It doesn't have to be, in general. There are other types of surface integrals as well. The type you've listed above is designed to determine the flux of the vector field A through the surface you are integrating over. The dot product is there because, by definition of flux, you are only concerned with the component of A that is perpendicular to the surface at each point on the surface.

 

[likephysics]

Ok. Thanks. I can live with it now.