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Component of the quadrupole Q_ij 
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#1
May1212, 01:13 PM

P: 6

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
May1212, 09:59 PM

P: 4,663

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\theta1 \right)=6\sin\theta\cos\theta=3\sin\left(2\theta \right) [/itex]



#3
May1312, 12:14 AM

P: 6

Thank you for commenting, but how does this translate to the i and j ?



#4
May1312, 03:51 PM

P: 4,663

Component of the quadrupole Q_ij
http://www.cems.uvm.edu/~oughstun/Le...tipoles%29.pdf which is a plot of the equipotential lines of V(r,θ,φ) of a linear electric quadrupole. 


#5
May1312, 04:00 PM

P: 6

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. 


#6
May1412, 09:17 PM

P: 4,663

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



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