Potential inside a grounded conducting sphere

Click For Summary

Homework Help Overview

The discussion revolves around a problem from electrodynamics concerning the potential inside a grounded conducting sphere with a point charge located within it. The original poster is particularly interested in the implications of placing the charge at the center of the sphere.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the behavior of the image charge as the point charge approaches the center of the sphere and question how this affects the solution. There is also discussion about using the Green function in this context.

Discussion Status

Participants are actively engaging with the problem, raising questions about the nature of the image charge and its implications for the solution. Some suggest alternative approaches, such as distributing the charge over multiple smaller charges, indicating a productive exploration of the topic.

Contextual Notes

There is an emphasis on the method of images and the potential complexities introduced when the charge is centered within the sphere. Participants express uncertainty regarding the application of Green functions in this scenario.

shinobi20
Messages
277
Reaction score
20

Homework Statement


Hi, I'm currently answering a problem in Jackson's electrodynamics. The question is:
Given a point charge q inside a hollow. grounded, conducting sphere of inner radius a. Find the potential inside.

This can be solved by placing an image charge outside the sphere, and placing q a distance say, r from the center. I'm just wondering, what if the charge is exactly at the center of the sphere? What changes in the solution would happen?

Homework Equations


Method of Images

The Attempt at a Solution

 
Physics news on Phys.org
Well, what happens to the image charge if q approaches the center ?
 
The image charge approaches infinity. But how will I modify the solution?
 
BvU said:
Well, what happens to the image charge if q approaches the center ?
How is the Green function to be used here? I think this is a possible way but I'm not sure.
 
shinobi20 said:
The image charge approaches infinity. But how will I modify the solution?
Very good. Now imagine q is distributed over 100 little charges that are evenly distributed on a small spherical shell around the center. That gives 100 image charges evenly distributed very far away, right ?

See where I am going ?

How is the Green function to be used here? I think this is a possible way but I'm not sure.
I'm not much good with these (very useful) functions, so I try to wiggle around them :smile:
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
13
Views
4K
Replies
7
Views
4K
  • · Replies 49 ·
2
Replies
49
Views
7K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
4
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 29 ·
Replies
29
Views
4K
  • · Replies 7 ·
Replies
7
Views
6K