1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Component of the quadrupole Q_ij
  1. Electric Quadrupole (Replies: 2)

Loading...