- #1

Zatman

- 86

- 0

## Homework Statement

Evaluate ∫∫

**r.n**dS where

**r**=(x,y,z) and

**n**is a normal unit vector to the surface S, which is a sphere of radius a centred on the origin.

**2. The attempt at a solution**

I decided to use polar coordinates. The radius of the sphere is clearly constant, a. So a surface element is dS = a

^{2}dθdø.

**r**= a(sinθcosø, sinθsinø, cosθ)

**n**= (sinθcosø, sinθsinø, cosθ)

**r.n**= a

therefore, ∫∫

**r.n**dS = ∫∫a

^{3}dθdø

where θ varies from 0 to 2π, and ø varies from 0 to π.

This gives an answer of 2π

^{2}a

^{3}. Is this correct? I'm not so sure.