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Thread: Quadrupole moments?

  1. #1
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    Quadrupole moments?

    Does anybody know how to calculate quadrupole moments? I have the formula and I should get a number, but I get 0...

    I've got a system of 4 charges, q at (a,b), -q at (-a,b), q at (-a,-b) and -q at (a,-b). I've tried plugging everything in and it doesn't work, does anyone know if there's a direction component in this or if it's just purely scalars... though I'm not sure that will help either. :?

    If nobody knows what I'm talking about then just carry on with your lives...

  2. #2
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    Quote Originally Posted by dakini
    Does anybody know how to calculate quadrupole moments? I have the formula and I should get a number, but I get 0...

    I've got a system of 4 charges, q at (a,b), -q at (-a,b), q at (-a,-b) and -q at (a,-b). I've tried plugging everything in and it doesn't work, does anyone know if there's a direction component in this or if it's just purely scalars... though I'm not sure that will help either. :?

    If nobody knows what I'm talking about then just carry on with your lives...
    There should be something like a direction component... a moment is a directional quantity applied around an axis, so it's a cross product of a vector relative to the origin and the quantity measured at the point defined by that vector.

    http://www.chem.ubc.ca/faculty/burne...is/node37.html

    Take equation 51, and let each of alpha and beta be a different point in space, and let the i's correspond to each of your charges. If you're unfamiliar with the notation, it helps to try the dipole case with just two charges first, then with three, then move on to quadrupole.

    Note that quadrupole moment is symmetric, so you only have to do half the work. Since you have no monopole or dipole moments, you can pick any origin you want, too. I'd use two of the point charge locations for alpha and beta, just so stuff cancels nicely.

    Would you care to detail exactly what you've been trying? It'll be easier to help if we can see what you are doing.... Give the formula you're using, anyway?

    Edit: fixed confused muddlings. Might still be stuff wrong. It's been a while....
    Last edited by snarkophilus; 2005-Oct-14 at 12:33 AM.

  3. #3
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    The formula I've been using is: Qij=sum(3xixj-deltaijr^2)qn

    i and j are used to denote entries in the matrix and n is used to denote the number of the charge. xi and xj are the two axes in question for each entry (x,y,z) the delta is the delta-kroenicker fucntion (I think that's what it's called, it's =1 when i=j and 0 otherwise) qn is the charge...I know it looks terrible computers suck for writing math.

    edit: Now that I look at the link you gave me, it's that equation... without the 1/2 in front
    Last edited by dakini; 2005-Oct-14 at 03:26 AM. Reason: didn't look at link first

  4. #4
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    you equation seems right


    maybe the quadripole moment is 0?
    My travel blog Mostly about riding a motorcycle across the US and Europe. Also has cool things that happen in between.

  5. #5
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    Quote Originally Posted by crosscountry
    that seems to be the dipole moment.



    if I read it right.
    The equation I gave?

    I think I did a bad job expressing it... look at the link snarkophilus gave and equation 51, it's that but without a half out in front.

  6. #6
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    Quote Originally Posted by crosscountry
    you equation seems right


    maybe the quadripole moment is 0?
    The quadropole moment shouldn't be 0 though, it's a quadropole...

    I think moving the origin is in order... I wasn't sure if that was allowed, as my text kinda glosses over multipoles, which is somewhat frustrating.

  7. #7
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    the moment will change based on what origin you choose.


    that only goes for the second term. If there is no net charge and no dipole moments, then the quadrupole doesn't change with the origin.


    if the dipole exists then the quadrupole does change.
    My travel blog Mostly about riding a motorcycle across the US and Europe. Also has cool things that happen in between.

  8. #8
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    Quadruple moments: The moment I met my wife, the moment we married, the moment she filed for divorce, and the moment it was final.

    For more moments: She robbed me of my youth, my health, my wealth, and half my retirement!

    Oh. "Quadrupole," not "quadruple."

    Sorry - I'm still a little touchy about the issue...

  9. #9
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    you should use smilies in your posts. that would help lighten the mood
    My travel blog Mostly about riding a motorcycle across the US and Europe. Also has cool things that happen in between.

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