Gce Model Questions Vol1 2021 Physics Question 45

A thin conducting spherical shell has inner radius \(a=0.10\;\text{m}\) and outer radius \(b=0.15\;\text{m}\). Initially it is uncharged. A point charge \(+Q\) with \(Q=5.0\;\mu\text{C}\) is placed at the centre of the cavity. The shell is then connected to ground, allowing charge to flow, and subsequently disconnected (so it remains isolated). After this, a second point charge \(-q\) with \(q=2.0\;\mu\text{C}\) is placed at a distance \(r=0.20\;\text{m}\) from the centre, along a radial line outside the shell. (a) State the final charge on the inner and outer surfaces of the shell, (b) find the electric potential at the position of the second charge, and (c) calculate the work required to bring the second charge from infinity to this position, assuming the shell stays isolated after grounding.