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!

Potential Energy

  1. Sep 11, 2011 #1
    Consider 4 charges all of magnitude q located at the following positions:
    r1 = (+1; +1; 0) ; r2 = (-1; +1; 0) ; r3 = (-1;-1; 0) ; r4 = (+1;-1; 0)

    We now want to study the stability of such an equilibrium con guration against
    small displacements. Show that near the origin the potential energy felt by the test particle may be written as
    V (x; y; z) = V0 + Ax^2 + By^2 + Cz^2 + ...

    Where a test charge e is at the origin.

    I'm a bit confused about how to arrive at this derivation. In general we have E=-[itex]\nabla[/itex]V, so if we have the electric field at the origin, we can get the potential. However it does not turn out to be the above. Any help on getting me started?
     
    Last edited: Sep 11, 2011
  2. jcsd
  3. Sep 11, 2011 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Expand V as a Taylor series about the origin. You should find the first-order terms vanish.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Potential Energy
  1. Potential Energy (Replies: 0)

  2. Potential Energy (Replies: 15)

  3. Potential energy (Replies: 1)

  4. Potential energy (Replies: 4)

Loading...