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!

Solving potential of electron inside the nucleus

  1. Nov 6, 2016 #1
    1. The problem statement, all variables and given/known data
    I want to derive the following equation. It is the potential energy of an electron inside a nucleus assumed to be a uniformly charged sphere of R.


    2. Relevant equations

    V'(r) =( -Ze2/4∏ε0R)(3/2 - (1/2)(r/R)^2)

    3. The attempt at a solution
    I get E = Ze2r/(4∏ε0R3)

    But I am having problem in integration limits and hence going towards final required result!
     
    Last edited by a moderator: Nov 6, 2016
  2. jcsd
  3. Nov 6, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Something went wrong with the formatting.

    The electric field should be linear with the distance - right. You can check if the electric field at the border of the nucleus agrees with the electric field of a point-charge. If yes, your result is right.
     
  4. Nov 16, 2016 #3
    First, Electrical field is not linearly dependent on distance! And I am not trying to find the field at the nucleus border but inside it. Can you help please to reach the desired formula?
     
  5. Nov 16, 2016 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Inside a homogeneously charged sphere, it is proportional to the radius, its magnitude is proportional to the distance to the center.

    If your formula reproduces this relationship and agrees at the boundary, then it is right. Hence the suggestion to check if it fits at the boundary.
     
  6. Nov 17, 2016 #5
    Yup! You are right... But How to drive it mathematically?
     
  7. Nov 17, 2016 #6

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    The shell theorem should help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted