Divergence of (r^-2)r̂ × ẑ in cylindrical coordinates

[sm1t]

Homework Statement

$$\nabla$$ of (r^-2)rhat x zhat

Homework Equations

$$\nabla$$(AxB) = B($$\nabla$$xA) - A($$\nabla$$xB)


Using cylindrical coordinates and curl in cylindrical with the above equation, I get zero?
But I think I am wrong?
Any help?

 

[quantumdude]

I didn't get zero. Let's see what you did, then we can tell you where you're going wrong.

 

[sm1t]

I am using the formula for curl in spherical, I konw I said cylindrical.
Taking the first cross product, zhat($$\nabla$$ x r^2 rhat) I use the ffact its in the rhat direction, so in the curl formula, sub r^2 for all r direction components. However they are then partially differentiated and I get zero, as the r^2 has no phi or theta components does it?

 

[quantumdude]

I am using the formula for curl in spherical, I konw I said cylindrical.

You should be using cylindrical. "z" isn't a spherical coordinate.