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Divergence in plane polars

  1. Apr 30, 2010 #1
    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. jcsd
  3. Apr 30, 2010 #2
    Solved it :)
     
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