Draw a circle to reprresent the disc of radius R. Draw to circles inside with radii r and r+dr.

Now assume that the charges are distrubuted uniformly over the disc of radius R.

Then charges inside the circle of radiusr q1 = R ^ 2 this can be cosidered concentrated at the centre for all calculation

the charges inside the circular strip of radius r and width dr = 2r dr

 

then the potential energy of the sysem = integral from 0 to R (q1 q2) / 4re

where e is the permitivity of free space.

I don't know whether you got the idea or whether you approve this. Please check it if you find it iteresting and see whether you get the same answer or not.

Anyway thank you for that interesting question.

best wishes

suresan