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Calculating Divergence With Spherical Coords

  1. Sep 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Calculate div v.

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

    2. Relevant equations

    3. 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.
  2. jcsd
  3. Sep 12, 2010 #2


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    What you've shown is not a vector. I'm guessing you omitted putting hats on some of the symbols, like [tex]\hat r[/tex]. But if you have the formula for a gradient in spherical coordinates, just use it. Find the functions in front of [tex]\hat r[/tex], [tex]\hat \theta[/tex] and [tex]\hat \phi[/tex] and use it.
  4. Sep 12, 2010 #3
  5. Sep 12, 2010 #4


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    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.
  6. Sep 12, 2010 #5
    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?

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