Flux in vector field question

Pyroadept

1. The problem statement, all variables and given/known data
Consider the vector field:
F = r/r³

where r = xi + yj + zk

Compute the flux of F out of a sphere of radius a centred at the origin.

2. Relevant equations



3. The attempt at a solution
Hi everyone,

I have: flux = [tex]\int[/tex]F.dA

I can't use Gauss' Law, because the field will not be defined at the origin.

Instead, I want to use F.n, where n is the normal vector to the sphere.

Is it correct that the normal vector is the div of the equation of the sphere?

ie. n = div (x^2 + y^2 + z^2 = a^2)

= 2x i + 2y j + 2z k

and then F.n = 2/r

Is this correct so far?
Thanks for any help

dacruick

Looks good. the divergence is how fast the field falls off, so it has to be in the direction of the normal vector.