Electrostatic equilibrium and Gauss' law

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Homework Help Overview

The problem involves a conducting spherical shell with a net charge and a point charge placed at its center, focusing on determining the surface charge density on both the inner and outer surfaces of the shell using Gauss' law.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply Gauss' law to find the electric field and surface charge density at the inner surface of the shell, questioning whether their reasoning is correct. Other participants discuss the implications of the net charge on the shell and how it affects charge distribution.

Discussion Status

Some participants have offered insights into the charge distribution on the inner and outer surfaces, while others are exploring the implications of the net charge on the shell. There is an acknowledgment of the need to reconsider the original poster's approach based on the presence of the net charge.

Contextual Notes

The original poster expresses uncertainty about their reasoning and mentions a learning curve with the equation editor, indicating a possible lack of familiarity with the concepts involved.

Kenny Lee
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A conducting spherical shell of ineer radius a and outer radius b carries a net charge Q. A point charge q is placed at the center of this shell. Determine the surface charge densit on (a) the ineer surface of the shell and (b) the outer surface of the shell.

I'm not sure of my reasoning. For part (a), I argued that at the inner surface
E = q/ (4*pi*a^2*epsilon) from Gauss' law.

And equated that to the formula for electric field, right outside a conductor in electro-static equilibrium i.e.
E = (surface charge density)/ epsilon.

So I get q/ (4*pi*a^2). Is that correct? If not, what would the correct method be.

Any advice pls. Thanks.

PS I apologize for the ugly equations. Still learning how to use the equation editor...
 
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Last edited by a moderator:
A charge q would induced an equal and opposite charge on the inner surface of a 'conducting' sphere, and the same charge on the outer surface. The areas are different.

However, the sphere also has a net charge Q. How would this be distributed.

And then think of superposition.
 
Thanks. So my answer was wrong? Yea, come to think of it, I only accounted for the charge q and not the sphere...I'll have another go at it.
 

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