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Energy of an electric quadrupole in an Electric Field

by karanmohan
Tags: electric, energy, field, quadrupole
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karanmohan
#1
Mar24-10, 03:39 PM
P: 9
Hello, I have tried to look for related threads but could not find any. Please excuse me if this is a repetition. I was curious about the energy of an electric quadrupole moment in an electro-magnetic field.

Basically, i am trying to follow first order perturbation theory and derive the matrix element of an atom interacting with a field in Bohm's Quantum Theory book - upon expansion, we get terms that "look" like an electric dipole, magnetic dipole and so on.

For example, the energy of an electric dipole in an electric field is E dotted with d (dipole moment). Likewise, that of a magnetic dipole would mu (magnetic moment) dotted with B. I am looking for a similar expression for the quadrupole.

Any help, as well as references are greatly appreciated. Thanks again!
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Naty1
#2
Mar24-10, 03:50 PM
P: 5,632
I can't answer your question directly, but this may help:

http://en.wikipedia.org/wiki/Electri...pole_Radiation
karanmohan
#3
Mar24-10, 08:44 PM
P: 9
hmm....thanks for the link friend, but it doesnt give me enough detail unfortunately :(

clem
#4
Mar25-10, 07:24 AM
Sci Advisor
P: 1,256
Energy of an electric quadrupole in an Electric Field

[tex]U_Q = -\frac{1}{3}\bf[Q]:[{\nabla} E][/tex].
karanmohan
#5
Mar25-10, 10:55 AM
P: 9
thanks a lot clem, that really helps alot...do you have reference by any chance?
clem
#6
Mar27-10, 05:54 AM
Sci Advisor
P: 1,256
Section 2.4 of Franklin's "Classical Electromagnetism" discusses electric quadrupoles.
JJfortherear
#7
Sep27-12, 05:00 PM
P: 14
What does the operation : signify? I assume it yields a scalar here, since the expression is for energy, but how is it defined? Thank you
SiggyYo
#8
Dec10-12, 02:26 PM
P: 5
Quote Quote by JJfortherear View Post
What does the operation : signify? I assume it yields a scalar here, since the expression is for energy, but how is it defined? Thank you
What clem said about Franklin's "Classical Electromagnetism" are wise words in this context :P

Quote Quote by clem View Post
Section 2.4 of Franklin's "Classical Electromagnetism" discusses electric quadrupoles.
Meir Achuz
#9
Dec12-12, 12:43 PM
Sci Advisor
HW Helper
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P: 1,991
Quote Quote by clem View Post
[tex]U_Q = -\frac{1}{3}\bf[Q]:[{\nabla} E][/tex].
That is a misprint.
The correct equation is
[tex]U_Q = -\frac{1}{3}\bf[Q]:[{\nabla}\nabla E][/tex]
[tex]=-\frac{1}{3}[(\bf[Q]\cdot\nabla)\cdot\nabla] E[/tex].


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