A non-conducting hollow sphere having inner and outer radii a and b respectively is made ofa material having di-electric constant K and has uniformly distributed charge over its entire solid volume. Volume density of charge is `rho` . Calculate potential at a distance r from its centre when :

(a) `r gt b`,
(b) `r lt a`,
(c) `a lt r lt b`

Answer

[(a) `V_(1) = (p(b^(3)-a^(3)))/(3 epsilon_(0)r)`;
(b) `V_(f) = (p(b^(3)-a^(3)))/(3 epilson_(0)b) + (p)/(3 epsilon_(0)K) [((b^(2)-a^(2))/(2))-(a^(3)(b-a))/(ab)]`
(c) `V =(p(b^(2)-a^(2)))/(3epsilon_(0)b)+(p)/(3epsilon_(0)K) [((b^(2)-a^(2))/(2))-a^(3)((b-r))/(rb)]`