A point charge q is located at the center O of an uncharged spherical capacitor provided with a small orifice. The inside and outside radii of the capacitor are `a and b`, respectively (Fig. 3.116). What amount of work has to be performed to slowly transfer the charge q bit by from the point O through the orifice to infinity ?
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Explanation

Because of q, charges will induce on the outer and inner surface of the layer. Those are +q and -q respectively.

Potential at the centre `=(q)/(4pi in_(0)) [(1)/(r_(1)) -(1)/(r_(2))]`
Work done in transferring q from centre to infinity.
`intVdq=int (q)/(4pi in_(0)) [(1)/(r_(1))-(1)/(r_(2))] dq=(q^(2))/(8pi in_(0)) ((1)/(r_(1))-(1)/(r_(2)))`
We can do this even by finding the difference in electric potential energy of the system.