1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Integration and Laplacian in polar coordinates

  1. Apr 13, 2014 #1
    1. The problem statement, all variables and given/known data
    I have a function y that is axisymmetric, so that y=y(r).

    I want to solve for r such that ∇2y(r) = Z.

    Can anyone tell me if I'm following the right procedure? I'm not sure since there are two "∂/∂r"s present...


    2. Relevant equations
    2 = (1/r)(∂/∂r)(r*(∂/∂r)) + (1/r2)*(∂2/∂θ2)
    --> The terms involving theta become zero since y is a function of r only


    3. The attempt at a solution
    2y = (1/r)(∂/∂r)(r*(∂y/∂r)) = Z
    (∂/∂r)(r*(∂y/∂r)) = Zr
    integrate with respect to r: r(∂y/∂r) = (1/2)Z*r2 + C
    (∂y/∂r) = (1/2)Zr + C/r
    integrate with respect to r again: y = (1/4)Z*r2 + Cln(r) + K
     
  2. jcsd
  3. Apr 13, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Looks fine to me. If you substitute that back into the original equation you do get Z, right? That's a good way to check.
     
    Last edited: Apr 13, 2014
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted