Finding Divergence of Vector Fields on a Sphere

[aligshah88]

Homework Equations

Hey guys I had a slight problem trying to find divergence of vector fields for the following equation:

F(x,y,z)=(yzi-xzj-xyk)/(x^2 + y^2 + z^2)

So I want to know if its possible of substitute (x^2 + y^2 + z^2) for 1 since that is the equation of a sphere? If not could some one please help me solve this question...Thanks :)

 

[Dick]

No, you can't put x^2+y^2+z^2 to be 1. You do the problem just like you usually do divergence problems. Start by finding the derivative with respect to x of the i component. So find d/dx y*z/(x^2+y^2+z^2). What do you get?