Problem with solving laplace equation with a charged ring

AI Thread Summary
The discussion focuses on solving the Laplace equation for a charged ring located in the equatorial plane of a grounded conducting sphere. The potential is zero in the region inside the sphere (r < b) and requires further analysis in the region between the sphere and the ring (b < r < a). The challenge lies in applying the Laplace equation with boundary conditions, specifically the induced charge on the sphere and the potential due to the ring. Participants suggest that the method of images may be a useful approach to find the potential throughout the three-dimensional space. The overall consensus indicates that the problem is complex and requires careful consideration of the boundary conditions.
throwaway128
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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.
 
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throwaway128 said:
Determine the potential everywhere.
Everywhere in 3D, or just in the equatorial plane?
 
throwaway128 said:
Q/4πε on the ring,
Don't forget the induced charge on the sphere.
 
haruspex said:
Everywhere in 3D, or just in the equatorial plane?
It is everywhere in 3D.
 
This one looks beyond me. The method of images might be applicable.
 

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