Question

A metal spherical shell has an inner radius `R_(1)` and outer radius `R_(2)`. A charge Q is placed at the center of the spherical cavity. What will be surface charge density on (i) the inner surface, and (ii) the outer surface ?

Answer 1

When a chare `+Q` is placed at the center of spherical cavity, shown in Fig, charge induced on the inner surface of shell `= -Q` and charge induced on the outer surface of the shell `= +Q`.
`:.` Surface charge density on the inner surface `= (-Q)/(4pi R_(1)^(2))`, and
Surface charge density on the outer surface `= (+Q)/(4pi R_(2)^(2))`