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Homework Help: Force on electric dipole

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that a line of charge density [tex]\lambda[/tex] exerts an attractive force on an electric dipole with magnitude F = [tex]\frac{2\lambda p}{4\pi\epsilon_{0}r^{2}}[/tex]. Assume that r is much larger than the charge separation in the dipole.


    2. Relevant equations

    I need to show that the magnitude, F = [tex]\frac{2\lambda p}{4\pi\epsilon_{0}r^{2}}[/tex]

    p = qs => assume s is very small at end of calculations

    F = Fon -q + Fon +q = 0

    Fon -q = -qE
    Fon +q = +qE

    3. The attempt at a solution

    I am not sure if I am doing this correct?

    F = Fon -q + Fon +q
    F = -qE + +qE

    = [tex]\frac{pE}{s} + \frac{pE}{s}[/tex]

    = [tex]\frac{p}{s}\frac{1}{4\pi\epsilon_{0}}\frac{2\lambda}{r} + \frac{p}{s}\frac{1}{4\pi\epsilon_{0}}\frac{2\lambda}{r}[/tex]
  2. jcsd
  3. Jan 19, 2009 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper

    There are 2 problems here:

    • A "-" sign got lost from the -qE term, when you went on to the next step.
    • The distance to the +q charge is not r.

    Hope that helps. :smile:
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