Is There a Relationship Between Dipole and Wire Interaction Energy?

[Diracobama2181]

Homework Statement

A sphere of radius R carries a charge q that is distributed uniformly over the
surface of the sphere. The sphere spins at constant angular velocity ω.
(a) Calculate the magnetic moment m of this sphere and determine the leading
term of the multipole expansion of the vector potential A at large distances
r : i.e., r >> R.
(b) Calculate the interaction energy between this sphere and an infinite straight
wire carrying a steady current I. The angle between the direction of the
current and the angular velocity vector ω is θ while the distance ρ between the wire and the sphere is much greater than the sphere radius: i.e.,
ρ >>R. Consider the case when ω is perpendicular to ˆe_ρ.

Relevant Equations

$$m=\int I da$$
$$A_{dip}=\frac{\mu_0}{4\pi}\frac{msin\theta}{r^2}$$ (from Griffiths)

Part a was not much of a problem. I got that $$m=QR\omega \hat{z}$$. From that, I get $$A_{dip}=\frac{\mu_0}{4\pi}\frac{QR\omega}{r^2}\hat{\phi}$$ (using $$\theta=\frac{pi}{2}$$.
My problem occurs in part b. I know there is a potential energy relation for two dipoles, but what would I use for a dipole and a wire? More specifically, is there a relationship between A and the interaction energy? Any suggestions or further readings on this subject would be appreciated. Thank you.

 

[Abhishek11235]

Try using approximation r>>R. The magnetic field is approximately constant over the surface. Or you can be more exact if you Taylor expand the magnetic field due to wire at large distance. After that use:

$U= -m.B$