Work to construct a conducting sphere

[ClCripper]

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I need to find the work it would take an applied force to assemble a conducting sphere of radius R and charge Q at constant kinetic energy from infinity.

Tried:
Since the Electric Field inside the conductor is zero I figured it wouldn't take any work to build the whole sphere until we got to the surface. Then the work that it would take would be the work required to build a spherical shell with no thickness. This seems like it is not an integral to me.
I am using:
W(applied)=QV
since V=Vf-Vi and Vi=0
and Vf=kQ/R

Solution:
I come up with
W(applied)=(kQ^2)/R

The correct answer should be (kQ^2)/(2R)

What am I doing wrong?

 

[Dick]

You've computed the work it would take to bring a charge Q in from infinity to a sphere whose charge is already Q. I think it is an integral problem. If there is no charge on the sphere initially then the charges you bring in first take very little work.