Figure (a) shows a shall of radius R having charge `q_(1)` uniformly distributed over it. A point charge q is placed at the centre of shell. Find amount of work required to increase the radius of shell from R to `R_(1)` as shown in figure (b).

Explanation

Work `=U_(i)-U_(f)`
`U_(1)=SE_(q)+SE_(q_(1))+IE=SE_(q)+(Kq_(1)^(2))/(2R)+(Kq_(1)q)/( R )`
`U_(f)=SE_(q)+(Kq_(1)^(2))/(2R_(1))+(Kq_(1)q)/(R_(1))`
work done `=U_(i)-U_(f)`
`=(Kq_(1)^(2))/(2R)+(Kq_(1)q)/( R )-(Kq_(1)^(2))/(2R_(1))-(Kq_(1)q)/(R_(1))`
(Try this problem yourself using the energy density formula)