Problem with solving laplace equation with a charged ring

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Homework Help Overview

The problem involves determining the electric potential due to a ring charge placed in the presence of a grounded conducting sphere. The setup includes a ring of total charge Q and radius a, which is concentric with a grounded sphere of radius b, where b is less than a. The ring is positioned in the equatorial plane.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the Laplace equation in the region between the sphere and the ring, noting the boundary conditions. Questions arise regarding the extent of the potential determination, whether it is needed in 3D or just in the equatorial plane. There is also mention of the method of images as a potential approach.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and the methods that could be applied. Some guidance has been offered regarding boundary conditions, but no consensus has been reached on the approach to take.

Contextual Notes

Participants note the importance of considering the induced charge on the sphere and clarify the regions where the potential is defined. The distinction between 3D potential and potential in the equatorial plane is also under consideration.

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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