Can someone help explain me a problem?

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Homework Help Overview

The problem involves a sphere of radius R with a uniformly distributed charge Q on its surface, and it asks how large a sphere would need to be to contain 90 percent of the energy stored in the electrostatic field of this charge distribution.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of the sphere in question, debating whether it is a solid sphere or a hollow one, and how this affects the interpretation of the problem. There are attempts to clarify the meaning of the "sphere" that contains the energy, with some suggesting it could refer to a Gaussian surface.

Discussion Status

The discussion is exploring various interpretations of the problem, particularly regarding the type of sphere and the implications for calculating the energy. Some participants express confusion about the setup, while others provide insights that may help clarify the problem's requirements.

Contextual Notes

There is uncertainty about whether the sphere is considered solid or hollow, and participants are questioning the implications of these assumptions on the energy calculations. The original poster has derived a formula related to energy but is seeking further clarification on the problem's specifics.

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Homework Statement



A sphere of radius R has a charge Q distributed uniformly over its surface. How large
a sphere contains 90 percent of the energy stored in the electrostatic field of this charge
distribution?

Homework Equations



U= 1/8pi integral E^2dv.


The Attempt at a Solution



I was able to derive that the energy to assemble a shell is Q^2/2R. The problem is idk what kind of sphere they are talking about? Do they mean a hollow sphere or one with a charge density?
 
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I think they mean solid sphere because otherwise they would say hollow sphere in the question.

So you have to compute the energy in the initial sphere, take 90% of it and then use it to get a new radius, right?
 
I guess it is a solid one. The thing that confused me was that the initial sphere has to be hollow because there is no charge density on the inside just on the surface. Thus I know I can treat that as a shell.
 
Solid or hollow the charge is on the surface only.
 
It could be that they mean what size of a spherical volume of space surrounding the charged sphere contains 90% of the energy of the field. So the "sphere" would be insubstantial, like a Gaussian surface, a designated boundary.
 
Last edited:
I think I understand now thanks a lot gneill I'll post my answer tmr. I'm pretty tired from working all day.
 

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