# Divergence in plane polars

1. Apr 30, 2010

### Kate2010

1. The problem statement, all variables and given/known data

I have to prove the divergence formula for plane polars. The question goes something like:

Find the divergence of the vector field F(r,t) = Frer + Ftet where r and t are polar coordinates and er = (cos t, sin t, 0) and et = (- sin t, cos t, 0)
(t is theta in the question but t was easier to type)

2. Relevant equations

x=rcost
y=rsint
Divergence formula in cartesian coordinates

3. The attempt at a solution

F(r,t) = (Frcost - Ftsint, Frsint + Ftcost, 0)

Could I partially differentiate the first bit with respect to r and the second bit with respect to t, just ignoring the 0 at the end? This does not seem right, I'm not sure if it is even possible.

Or I feel like the chain rule might come into it somewhere?

I really don't know where to start.

2. Apr 30, 2010

Solved it :)