Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Legendre Expansion solution to sphere of potential V with charge q outside

  1. Oct 24, 2012 #1
    Hi,

    It seems that there is no much examples of this particular case.

    OK, we all know how to write the general solution to Laplace equation in spherical coordinates in terms of Legendre polynomials (when there is azimuthal symmetry).

    There are a lot of cases here but I would like to know how to attack the problem of a sphere held at potential V with a charge 1 outside a distance d.

    I know you will have an image charge inside the sphere a distance d*a^2 from sphere's center.

    But how to account for this system of image charge and original charge? Can we simply add a term (outside the sum of Legendre Polynomial) ?

    Thanks in advance
     
  2. jcsd
  3. Oct 25, 2012 #2

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You can put an image charge, q"=V/a+qa/d, at the center of the sphere of radius a.
    You don't need Legendre polynomials for this.
    The original image charge should be at d'=a^2/d.
     
  4. Oct 28, 2012 #3
    I understand the image charge method.

    What I seek is the solution utilizing Legendre Polynomials.

    Again, I understand Legendre Polynomial solution as applied to different cases, but not this one.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Legendre Expansion solution to sphere of potential V with charge q outside
Loading...