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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?