How to Find the Potential Within a Grounded Conducting Hollow Sphere?

[m0nk3y]

Homework Statement

A grounded conducting hollow sphere of radius a contains a ring of radius b and charge per unit length $$\Lambda$$. The ring is coaxil to the z axis, and with the sphere lies a distance d about the center of the sphere such that d^2 + b^2 < a^2. Find the potential within the sphere along the z-axis

Homework Equations

d^2 + b^2 < a^2.

The Attempt at a Solution

Honestly I don't know where to start. Reading Griffiths chapter 3.3 I attempted using the separation of variables but had no idea had to proceed. So now I am attempting on using the law of cosines and concentrating on the part where the radius of the charged ring and the center of the sphere make a triangle. However, i doubt this is right. Any help to push me in the right direction to solving this problem is greatly appreciated!

Thanks

 

[michalll]

The ring inducts an equivalent charge on the sphere, the very problem is to compute the charge distribution. But the inducted charges negates themselves so it would be enough to compute the potential only for the ring.

 

[pam]

The ring inducts an equivalent charge on the sphere, the very problem is to compute the charge distribution. But the inducted charges negates themselves so it would be enough to compute the potential only for the ring.

That is not correct. The potential due only to the ring is not equipotential at the surface.
This problem has to be done using a Green's function for the sphere.