How Is Work Calculated When Moving a Charge Near a Conducting Shell?

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SUMMARY

The work done to move a test charge q from the origin to the edge of a spherical conducting shell, also with charge q and radius R, is calculated using the equation W = ∫(F·ds). The initial assumption that the forces cancel at the origin is correct; however, the force outside the shell must be considered. The correct expression for the work done is derived from Gauss' Law, which indicates that the electric field inside the shell is zero, leading to the conclusion that no work is done in moving the charge within the shell's interior.

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  • Familiarity with Gauss' Law
  • Knowledge of work-energy principles in physics
  • Basic calculus for evaluating integrals
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Homework Statement

Find the work done to move a test charge with charge q from the origin to the edge of a spherical conducting shell which surrounds it, also of charge q. (Shell is of radius R).



Homework Equations

W = int(F.ds) where W = work done, F = force



The Attempt at a Solution

I would have thought that at the origin the force cancels out since there is an equal amount from each radial direction. Beyond this however I am not sure what to do... I tried the overall answer

(1/4*pi*epsilon0)*(q^2)/R where R is the radius of the shell, but that was incorrect. Any help would be appreciated.
 
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Ignoring the test charge, what does Gauss' Law say about the field inside the spherical shell?
 

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