Register to reply

Component of the quadrupole Q_ij

by ellocomateo
Tags: component, quadrupole
Share this thread:
ellocomateo
#1
May12-12, 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!
Phys.Org News Partner Physics news on Phys.org
Engineers develop new sensor to detect tiny individual nanoparticles
Tiny particles have big potential in debate over nuclear proliferation
Ray tracing and beyond
Bob S
#2
May12-12, 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\theta-1 \right)=6\sin\theta\cos\theta=3\sin\left(2\theta \right) [/itex]
ellocomateo
#3
May13-12, 12:14 AM
P: 6
Thank you for commenting, but how does this translate to the i and j ?

Bob S
#4
May13-12, 03:51 PM
P: 4,663
Component of the quadrupole Q_ij

Quote Quote by ellocomateo View Post
Thank you for commenting, but how does this translate to the i and j ?
Perhaps you and I are looking at different slides and/or files. I am looking at slide 12 of the file
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.
ellocomateo
#5
May13-12, 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.
Bob S
#6
May14-12, 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 four-fold symmetry indicates it is a quadrupole field.


Register to reply

Related Discussions
Quadrupole-quadrupole interaction? Quantum Physics 9
What is a quadrupole? Atomic, Solid State, Comp. Physics 2
Electric field problem Introductory Physics Homework 18
Quadrupole-quadrupole interaction? Differential Geometry 0