Solving Surface Integral Questions w/Check Solutions

[c.francis]

Surface Integral Question and Solution Check

Hi everyone, this is my first post and I was hoping someone could help me check my solution to this problem (which could be completely wrong) and help me get unstuck at part 3. Any help would be greatly appreciated.

Homework Statement

Calculate $$\int$$r.ds (a surface integral) where the surface is 1. The square 0<x,y<a at z=b. 2. The surface of sphere whose radius is R centered at origin 3. The same surface centered at x=a, y=0, z=o.

Homework Equations

The Attempt at a Solution

Well for the first one, I got the surface element to be 1k, and so r.dS would have to b (right because for position vector r to touch surface its z component would b?).Then integrating you get ab^2.

For 2, I figure that $$\hat{r}$$ and r are in same direction so r.ds=R so after integrating surface element R^2sin$$\vartheta$$*R gives 4R^3$$\pi$$.

For 3, all I know is the surface element is the same as the previously (so I think) but I don't know how to evaluate the dot product.

Thanks guys

 

[c.francis]

I just wanted to add that I assumed that the mystery vector r must be touching the same point that the vector "tracing" out the shape is touching. Is that not conceptually correct?