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Find the electrostatic interaction energy between the dipole

  1. Mar 8, 2016 #1
    1. The problem statement, all variables and given/known data

    Consider the following pair of dipoles in one dimension.
    One of the dipoles: -ve dipole positioned at (-D/2, 0) and +ve (+D/2, 0), with the origin between them.
    Other dipole: -ve dipole positioned at (r-d/2, 0) and +ve at (r+d/2, 0), with (r, 0) being the centre.

    Show that the total electrostatic interaction energy between the dipoles, when r is much greater than both d and D, is given by,


    V = – [1/2(Pi)*(epsilon nought)](QD)(qd)/r^3.


    2. Relevant equations


    3. The attempt at a solution

    I have attempted this question by considering a point x between the dipoles and finding the Electrostatic potential caused by each of the ends of the dipole. This ended up with 4 terms in a summation and I'm struggling to see how the correct answer is a multiplication? I believe some of the terms can be taken as zero when they are squared (in the limit where r>>d and D) but I'm not sure how to get to this step.

    I would appreciate a push in the right direction, thanks in advance.
     
  2. jcsd
  3. Mar 8, 2016 #2
    Hint : You can use the field of one of the dipoles to find the potential developed for each charge on the other dipole ( to get to the appropriate distance from fromer dipole), and then add the two potentials thus obtained.

    Hope this helps.
     
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