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Component of the quadrupole Q_ij

  1. May 12, 2012 #1
    Hello,

    I do not manage to visualize the link between the component of the quadrupole Q_ij and the spatial distribution of the electric quadrupole field.

    I was told to imagine the Q_ij as an ellipsoid, which I understand (the ellipsoid "radius" in a given direction being the strength of the quadrupole along this direction). Yet what is the link between the Q_ij and the usual representation in Slide 12 of this file?:
    cems.uvm.edu/~oughstun/LectureNotes141/Topic_09%20%28ElectrostaticMultipoles%29.pdf

    In particular, I want to find out when does the gradient \nabla_k Q_ij equal zero? When i,j =! k ?

    Pleeeease, help!
     
  2. jcsd
  3. May 12, 2012 #2
    Re: Quadrupole

    The azimuthal gradient of V(r,θ,[itex]\varphi[/itex]) in slide 11 is proportional to [itex] \frac{d}{d\theta}\left(3\cos^2\theta-1 \right)=6\sin\theta\cos\theta=3\sin\left(2\theta \right) [/itex]
     
  4. May 13, 2012 #3
    Re: Quadrupole

    Thank you for commenting, but how does this translate to the i and j ?
     
  5. May 13, 2012 #4
    Re: Quadrupole

    Perhaps you and I are looking at different slides and/or files. I am looking at slide 12 of the file
    www.cems.uvm.edu/~oughstun/LectureNotes141/Topic_09%20%28ElectrostaticMultipoles%29.pdf [Broken]
    which is a plot of the equipotential lines of V(r,θ,φ) of a linear electric quadrupole.
     
    Last edited by a moderator: May 6, 2017
  6. May 13, 2012 #5
    Re: Quadrupole

    We are looking on the same graph, but I still do not see how I should label the axes.
    There is no information whatsoever on this point. Or at least I do not see it.
     
  7. May 14, 2012 #6
    Re: Quadrupole

    The plot is a combination of the gradient and the equipotential lines of V(r,θ,φ) using r and z as axes. The four-fold symmetry indicates it is a quadrupole field.
     
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