Calculating Divergence With Spherical Coords

[maherelharake]

Homework Statement

Calculate div v.

v= r sin(θ) r + r sin(2θ) cos(φ) θ + r cos(2θ) φ.

Homework Equations

The Attempt at a Solution

I've never had to do a problem like this using spherical coords, so I am not sure where to start. I have the general formula though.

 

[Dick]

What you've shown is not a vector. I'm guessing you omitted putting hats on some of the symbols, like $$\hat r$$. But if you have the formula for a gradient in spherical coordinates, just use it. Find the functions in front of $$\hat r$$, $$\hat \theta$$ and $$\hat \phi$$ and use it.

 

[maherelharake]

What I have so far is attached (as 6B). Am I on the right track?


http://i77.photobucket.com/albums/j72/maherelharake/photo-25.jpg

 

[Dick]

What I have so far is attached (as 6B). Am I on the right track?


http://i77.photobucket.com/albums/j72/maherelharake/photo-25.jpg

Some parts are right. You got some extra hats hanging around. The divergence should be a scalar, right? It shouldn't have any vector parts. And you haven't expanded your derivatives yet.

 

[maherelharake]

Thank you for responding.
I was still working on it, I just wanted to see if I was on the right track. What about now?