Problem with solving laplace equation with a charged ring

[throwaway128]

Homework Statement

A ring charge of total charge Q and radius a is concentric with a grounded conducting sphere of radius b, b < a.
Determine the potential everywhere. The ring is located in the equatorial plane, so both the sphere and the ring have their center at the same spot.

Homework Equations

∇V=0

The Attempt at a Solution

Well the region r < b is V = 0.
At first I thought about using the Laplace equatio for he next zone (b < r < a) making it zero on the surface of the sphere and Q/4πε on the ring, but then I am at a draw and don't know what to do next.

 

[haruspex]

Determine the potential everywhere.

Everywhere in 3D, or just in the equatorial plane?

 

[haruspex]

Q/4πε on the ring,

Don't forget the induced charge on the sphere.

 

[throwaway128]

Everywhere in 3D, or just in the equatorial plane?

It is everywhere in 3D.

 

[haruspex]

This one looks beyond me. The method of images might be applicable.