Charged ring inside a conducting sphere.

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A thin charged (charge=Q) ring of radius a centered on the z axis lies in the x-y plane. The potential outside the ring is given. Now the ring is placed inside a grounded conducting spherical shell of radius b > a. What is the potential inside the ring and between the ring and the sphere. I'd like to solve this problem without using the method of images. Any thoughts? Thanks
 
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