The energy needed to construct a charged hollow spherical shell with finite thickness

[Avital]

Homework Statement

I am trying to solve the relevant integral

Relevant Equations

I found that the energy needed to create a shell with radius R and charge Q is U=kQ^2/2R

So in the probleme is given a sphere with inner radius of r1 and outher radius r2 and elecric charge density p.

i tried to devide the sphere to shells with radius dr. And got that the charge for each shell is 4piR^2*p*dr
when plugin this expression to the work needed to create one shell i get dr^2.

so first of all how in general i can deal with dr^2 in integrals and secondly i guess that the way iam solving it is not taking into acount the shells created before so what is the right approach. Thanks.

 

[haruspex]

Consider the work done in adding a thin shell of charge q to an existing thick shell of charge density p.