A point charge `q` si located at a distance `r` from the centre `O` of an uncharged conducting conducting spherical layer whose inside and outside radii are equal to `R_(1)` and `R_(2)` respectively. Find the potentail at the point `O` if `r lt R_(1)`.

Explanation

As the sphere has conducting layers, charge `-q` is induced on the inner surface of the sphere `q` and consequently charge `+q` and consequently chagre `+q` is induced on the outer layer as the sphere as a whole is uncharged.
Hence, the potentail at `O` is given by,
`varphi_(0) = (q)/(4pi epsilon_(0) r) + (-q)/(4pi epsilon_(0) R_(1)) + (q)/(4pi epsilon_(0) R_(2))`
It should be noticed that the potentail can be found in such a simple way only at `O`, since all the induced charges are at the same distance from this point, and their distribution, (which is unknown to us), does not play any role.