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Monopole and dipole momnts

  1. Oct 28, 2006 #1
    Two point charges 3q and iq are spearated by distance a as in the diagram. Find the monopole, dipole moments and the approximate potential at large (in spherical coords including both dipole and monopole contributions)

    monopole moment is sum of charges [itex]3q \hat{k} + qa \hat{k} = q(a+2) \hat{k}[/itex]

    dipole moment is (assume that the origin is located half way between the two cahrges

    [tex] p= 3q \frac{a}{2} \hat{k} + (-q}\frac{a}{2} \hat{k} = 2qa \hat{k}[/tex]

    [tex] \overline{p} = p + qa\hat{k} [/tex]
    [tex] \overline{p} = qa \hat{k} [/tex]
    is this correct???

    where di i got wrong? with the transofmration of coordinates? With the way i calculated p?? When i calculate the potential the dipole moment will point radially in the z direction hence [itex] \hat{k} = \hat{r} \cos\theta [/tex]

    thank you for your help and responses!
    Last edited: Oct 28, 2006
  2. jcsd
  3. Oct 28, 2006 #2

    Meir Achuz

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    1. You seem to mean q and 2q in the first line. There should be no \hat k and no a in the monopole moment.
    2. The usual convention for a charged object is to pick the origin so that the dipole moment is zero. I have not seen the diagram, so maybe you are told where to pick the origin.
  4. Oct 28, 2006 #3

    here is the diagram

    pick a zer dipole moment... how in this case

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  5. Oct 28, 2006 #4
    but isnt hte dipole moment a vector?/
  6. Oct 30, 2006 #5

    Meir Achuz

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    For your diagram, the charge is 3q-q=2q.
    With the origin given at the postionf of the -q charge, the dipole moment is
    [tex]{\bf p}=3q{\bf\hat z}[/tex].
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