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Homework Help: Magnetic quadrupole?

  1. Feb 11, 2012 #1
    1. The problem statement, all variables and given/known data

    By analogy with an electric quadrupole, one can devise a simple model for a magnetic quadrupole
    that consists of two small parallel loops with currents circulating in opposite senses and that are
    separated by a small distance. Consider two magnetic dipoles of equal dipole moments +/-m0 z-hat
    located at z = +/-a. In this case, the total dipole moment is zero. Show that, at large distances,
    the vector potential is given approximately by [itex]A_{\phi} = 6 \mu_0 m_0 a sin(\theta)cos(\theta)/(4 \pi r^3)[/itex].

    2. Relevant equations

    Multipole Expansion + Taylor Expansion?

    3. The attempt at a solution

    I think that what I need to do is to perform a multipole expansion to get the field for a single dipole. Then, superpose the two. Finally, I think I need to Taylor expand that result. Is this the correct way of going about doing things? What do I do with the radius of each dipole? (I can't get the radius of the dipole to go away!)
  2. jcsd
  3. Feb 13, 2012 #2
    Simply expand the general vector potential till the quadrupole term. You will get an integral which has to be evaluated according to the given configuration.
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