1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Difficulty with the Laplacian

  1. Jun 23, 2015 #1
    1. The problem statement, all variables and given/known data
    Given: |r|=√(x^2+y^2+z^2) r=xi+yj+zk

    (i)Find the partial derivative with respect to x of |r|.
    (ii) Find the Laplacian of |r|.

    2. Relevant equations


    3. The attempt at a solution
    For (i) I got x/|r|
    but then for (ii) I got 2/r which I don't think is correct
     
  2. jcsd
  3. Jun 23, 2015 #2

    Zondrina

    User Avatar
    Homework Helper

    If ##| \vec r(x, y, z) | = \sqrt{x^2 + y^2 + z^2}##, then:

    $$| \vec r(x, y, z) |_x = \frac{\partial}{\partial x} (x^2 + y^2 + z^2)^{\frac{1}{2}} = \frac{1}{2} (x^2 + y^2 + z^2)^{- \frac{1}{2}} \cdot \frac{\partial}{\partial x} (x^2 + y^2 + z^2)$$

    What is the definition of the Laplacian?
     
  4. Jun 23, 2015 #3

    RUber

    User Avatar
    Homework Helper

    Part i) is the warm up for part ii).
    What did you do to get x/|r|?

    If ##\frac{\partial}{\partial x } |r| = \frac{x}{|r|} ##, then what is ##\frac{\partial}{\partial x } \frac{x}{|r|} ##?

    I think 2/|r| is right.
     
  5. Jun 23, 2015 #4

    Zondrina

    User Avatar
    Homework Helper

    If you clean up the computation in the second post:

    $$\frac{1}{2} (x^2 + y^2 + z^2)^{- \frac{1}{2}} \cdot \frac{\partial}{\partial x} (x^2 + y^2 + z^2) = \frac{x}{\sqrt{x^2 + y^2 + z^2}} = \frac{x}{| \vec r |}$$

    It is, but it would be nice if the OP showed some of the work.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Difficulty with the Laplacian
  1. Laplacian Translation (Replies: 1)

  2. Laplacian Help (Replies: 2)

  3. Is this the laplacian? (Replies: 1)

  4. Laplacian calculation (Replies: 4)

Loading...