Question

A solid conducting sphere having charge Q is surrounded by an uncharged concentric conducting hollow spherical shell . Let the potential difference between the surface of the solid sphere and the hollow sphere be V . The shell is now given a charge -3Q , what is the new potential differened?

Answer 1

In case of a charged conducting sphere
Vinside=Vcentre=Vsurface=14πϵ0.qR,Voutside=14πϵ0.qr
If a and b are the radii of sphere and spherical shell respectively, then potential at their surface will be
Vsphere=14πϵ0.Qa and Vshell=14πϵ0.Qb
∴V=Vsphere−Vshell=14πϵ0.[Qa−Qb]
Now when the shell is given charge (–3Q), then the potential will be
V′sphere=14πϵ0[Qa+(−3Q)b]
∴V′sphere−V′shell=14πϵ0[Qa−Qb]=V