Find V and E at point r where : (Q is a point charge kept at the centre of the non-conducting neutral thick sphere of inner radius 'a' and outer radius 'b') (dielectric constant `=in_(r)`)

(i) `0 lt r lt a " " (ii) a le r lt b " " (iii) r ge b`

Explanation

`-q` and `+q` charge will induce on inner and outer surface respectively
`E (0ltrlta)=(KQ)/(r^(2))`
`E(r ge b)=(KQ)/(r^(2))`
`E(a le r lt b) = (KQ)/(r^(2))-(Kq)/(r^(2))=(KQ)/(in_(r)r^(2))`
`q=Q.(1-(1)/(in_(r))) , V(r ge b) = (KQ)/(r)`
`(a le r le b) V_(A)=V_(P)+underset(b) overset(r)int (KQ)/(in_(r)r^(2))(-dr)=(KQ)/(b)+(KQ)/(in_(r))((1)/(r)-(1)/(b))`
`V(r le a) " " V_(B)=5V_(c)+ underset(a)overset(r)int (KQ)/(r^(2))(-dr)=(kQ)/(b)+(kQ)/(in_(r))((1)/(a)-(1)/(b))+kQ((1)/(r)-(1)/(a))`