A thin spherical conducting shell of radius `r_(1)` carries a charge `Q`. Concentric with it is another thin metallic spherical shell of radius `r_(2) (r_(2) gt r_(1))`. Calculate electric field at distance `r` when (i) `r lt r_(1)` ,(ii) `r_(1) lt r lt r_(2)` and (iii) `r gt r_(2)`.
What will be the field in above cases if outer shell `(a)` is given charge `q` and `(b)` is earthed ?

Explanation

We know that electric field inside a conductor is zero and for external point , whole charge is assumed to be concentrated at centre. (i) `r lt r_(1) , E = 0`
(ii) `r_(1) lt r lt r_(2) , E = (1)/(4pi in_(0)) (Q)/(r^(2))`
(iii) `r gt r_(2) , E = (1)/(4 pi in_(0)) (Q)/(r^(2))`
(a)
(i) `r lt r_(1) , E = 0`
(ii) `r_(1) lt r lt r_(2) , E = (1)/(4 pi in_(0)) (Q)/(r^(2))`
(iii) `r gt r_(2) , E = (1)/(4 pi in_(0)) ((Q + q))/(r^(2))`
(b)
(i) `r lt r_(1) , E_(0)`
(ii) `r_(1) lt r lt r_(2) , E = (1)/(4 pi in_(0)) (Q)/(r^(2))`
(iii) Due to eathing , charge on inner surface on outer shell is `-Q`. Therefore,
`r gt r_(2) , E = 0`