## Homework Statement

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 $A_{\phi} = 6 \mu_0 m_0 a sin(\theta)cos(\theta)/(4 \pi r^3)$.

## Homework Equations

Multipole Expansion + Taylor Expansion?

## 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!)

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.