# Problem with solving laplace equation with a charged ring

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1. Oct 10, 2016

### throwaway128

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
∇V=0

3. 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.

2. Oct 10, 2016

### haruspex

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

3. Oct 10, 2016

### haruspex

Don't forget the induced charge on the sphere.

4. Oct 10, 2016

### throwaway128

It is everywhere in 3D.

5. Oct 11, 2016

### haruspex

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