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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!

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# Component of the quadrupole Q_ij

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