Energy of an electric quadrupole in an Electric Field

  1. Mar 24, 2010 #1
    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!
  2. jcsd
  3. Mar 24, 2010 #2
  4. Mar 24, 2010 #3
    hmm....thanks for the link friend, but it doesnt give me enough detail unfortunately :(
  5. Mar 25, 2010 #4


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    [tex]U_Q = -\frac{1}{3}\bf[Q]:[{\nabla} E][/tex].
  6. Mar 25, 2010 #5
    thanks a lot clem, that really helps you have reference by any chance?
  7. Mar 27, 2010 #6


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    Section 2.4 of Franklin's "Classical Electromagnetism" discusses electric quadrupoles.
  8. Sep 27, 2012 #7
    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
  9. Dec 10, 2012 #8
    What clem said about Franklin's "Classical Electromagnetism" are wise words in this context :P

  10. Dec 12, 2012 #9

    Meir Achuz

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    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].
    Last edited: Dec 12, 2012
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