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

[NT123]

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.

 

[gneill]

Ignoring the test charge, what does Gauss' Law say about the field inside the spherical shell?