Potential inside a grounded conducting sphere

In summary, the conversation discusses solving for the potential inside a hollow, grounded, conducting sphere with a point charge q at the center. The recommended method is to use the Method of Images and place an image charge outside the sphere at a distance r from the center. If q is exactly at the center, the image charge approaches infinity and the solution needs to be modified. One suggestion is to distribute q over 100 small charges on a spherical shell around the center to create 100 evenly distributed image charges far away. The use of Green functions is also mentioned as a possible method.
  • #1
shinobi20
267
19

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

 
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  • #2
Well, what happens to the image charge if q approaches the center ?
 
  • #3
The image charge approaches infinity. But how will I modify the solution?
 
  • #4
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.
 
  • #5
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:
 

1. What is the potential inside a grounded conducting sphere?

The potential inside a grounded conducting sphere is zero. This is because a grounded conducting sphere has a constant potential, and when it is connected to a ground, the potential is equalized, resulting in a potential of zero inside the sphere.

2. How is the potential inside a grounded conducting sphere affected by its shape and size?

The potential inside a grounded conducting sphere is not affected by its shape or size. As long as the sphere is perfectly conducting and grounded, the potential inside will always be zero.

3. Can the potential inside a grounded conducting sphere be changed?

No, the potential inside a grounded conducting sphere cannot be changed. This is because the potential is determined by the grounding connection, and as long as the sphere remains grounded, the potential will remain at zero.

4. How does the potential inside a grounded conducting sphere differ from that of a charged conducting sphere?

The potential inside a grounded conducting sphere is always zero, while the potential inside a charged conducting sphere can vary depending on the amount of charge and the distance from the center. Additionally, the potential inside a charged conducting sphere is affected by its shape and size, unlike a grounded conducting sphere.

5. Why is the potential inside a grounded conducting sphere important in electrostatics?

The potential inside a grounded conducting sphere is important in electrostatics because it helps us understand the behavior of electric fields and charges. It also serves as a reference point for determining the potential outside the sphere and in other parts of the system.

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