Question

Doing a flux integral, not allowed to use divergence theorem. The surface is the upper hemisphere of radius 1, bounded below by the disk of radius 1 at z=0. When doing the disk part of the integral, do you take the normal to be (0,0,-1) to point outwards rather than inwards so get F dot n = (0,0,-F3) or use the formula F dot n = ( - partial df/dx * F, - partial df/dy * F2, F3) giving (0,0,F3)? I hope it's the first one otehr wise I'm in trouble. Need to know for tomorrow

Answer 1

It's been a while since I've done these, but take a look at Example 2 on Paul's Online Notes http://tutorial.math.lamar.edu/Classes/CalcIII/SurfIntVectorField.aspx

I believe he is confirming that when working with the bottom disk (on the plane z=0) you use \(\overrightarrow{n} = -\overrightarrow{k}\).

Answer 2

Good that's what I wanted to hear, thanks :)

Answer 3

From what I remember, you always want the normal to point away from the interior of the surface.