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Evaluate: ∇(∇ . r(hat)/r) where r is a position vector

  1. Oct 12, 2016 #1
    1. The problem statement, all variables and given/known data
    ∇ . r = 3, ∇ x r = 0

    2. Relevant equations


    3. The attempt at a solution
    So far I've gotten up to ∇(∇^2 r)
     
  2. jcsd
  3. Oct 12, 2016 #2

    kuruman

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    Homework Helper
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    Hi Dave-o and welcome to PF. :welcome:


    You need to provide more details about what the problem is, the relevant equations and your attempt at a soluton before we can help you.
     
  4. Oct 12, 2016 #3
    1. The problem statement, all variables and given/known data

    Not using any Cartesian or any other coordinates but rather the facts that (see equations, r^ is the position vector)..
    Evaluate:
    ∇( ∇ . (r^ / r))

    2. Relevant equations

    ∇ . r^ = 3, ∇ x r^ = 0, ∇r = r^ / r

    3. The attempt at a solution
    From the 3rd equation I got ∇( ∇ . ∇r) => ∇(∇^2 r)

    I don't know where to go from there
     
  5. Oct 12, 2016 #4

    kuruman

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    Are you allowed to use vector analysis identities? What comes to mind is ## \vec{\nabla} \cdot (\phi \vec{A})=\phi \vec{\nabla} \cdot \vec{A}+\vec{A} \cdot \vec{\nabla}\phi##. You can use this to find the term in parentheses and then take its gradient. You should also be allowed to use the expression for the gradient of 1/r.
     
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