(a) A charge +Q is placed on a large spherical conducting shell of radius R. Another small conducting sphere of radius r carrying charge 'q' is introduced inside the large shell and is placed at its centre. Find the potential difference between two points, one lying on the sphere and the other on the shell.
(b) How would the charge between the two flow if they are connected by a conducting wire ? Name the device which works on this fact.

Explanation

(a) Potential inside conducting spherical shell of radius R carrying charge Q is
`=1/(4pi epsi_(0)).Q/R`
When a small sphere of radius r, carrying some charge q is introduced into the large sphere and place it at the centre.
`:.` Potential due to small sphere of radius r carrying charge q
`=1/(4pi epsi_(0))q/r` at surface of small sphere
`=1/(4 pi epsi_(0)). q/R` at large shell of radius R.
`:.` Total potential is given by
`V*R)=1/(4pi epsi_(0)) (Q/R+q/R)`
and `V(r)=1/(4pi epsi_(0))(Q/R+q/r)`
`:.`Potential difference `=V(r) =1/(4pi epsi_(0))(Q/R+q/r)`
`:.` Potential difference `=V(r)-V(R)`
`1/(4pi epsi_(0))(Q/R+q/r)-1/(4pi epsi_(0))(Q/R+q/R)=2/(4 pi epsi_(0))(q/r-q/R)`
`=1/(4pi epsi_(0))(q/r-q/R)=q/(4 pi epsi_(0))(1/r-1/R)`
(b) When both spheres are connected by a consucting wire then the charge q on smaller spher will flow onto the larger sphere having charge Q.
Van de Graaff generator work on this fact that charge given to a hollow conductor is transferred to outer surface and is distributed uniformly over it.