Total Charge (Spheres and Potential)

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Homework Help Overview

The discussion revolves around a problem involving a conducting sphere and a concentric spherical shell with a surface charge distribution. The participants are exploring the implications of the potential and charge distribution in this electrostatic context.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to apply the integral for charge calculation but are uncertain about the limits and expressions for the area element. Questions arise regarding the nature of the area element and the contributions of the inner sphere's charge.

Discussion Status

The discussion is ongoing, with participants clarifying their understanding of the problem setup and the necessary calculations. Some guidance has been offered regarding the need to compute charges individually before summing them.

Contextual Notes

There is a focus on the geometry of the problem, particularly the implications of spherical coordinates and the definitions of area elements in this context. Participants are also navigating the assumptions related to the charge distribution and potential.

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Homework Statement


A conducting sphere of radius a, at potential V0, is surrounded by a thin concentric spherical shell of radius b over which someone has glued a surface charge. sigma = kcos(theta) where k is a constant

i know V(r, theta) and induced surface charge on the conductor


Homework Equations



Q = integral (sigma) da

The Attempt at a Solution


trying to use equation 1 but I'm not sure first off the limits on r for each
 
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da is the infinitesimal area element of the surface...the entire surface is at r=b...what is your expression for da?
 
but what about the charge coming from the inner sphere at Vo my da is going to rdrdtheta
 
why is there a dr term in your da, isn't r constant over a spherical surface?

Are you trying to compute the total charge on the outer shell, or the conductor, or both?
 
trying to find the charge for both
 
Well, you'll have to compute the charge of each individually and then add them up.
 

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