A small conducting spherical shell with inner radius `a` and outer radius `b` is concentric with a larger conducting spherical shell with inner radius `c` and outer radius `d` ( as shown in Fig . 2.121). The inner shell has a total charge ` + 2 q`, and the outer shell has a total charge ` + 4 q`. Calculate the electric field in terms of `q` and the distance `r` from the common center of the two shells for

`b lt r lt c`

Explanation

Charge distribution
(a) Total charge on inner shell `= 2q`
Total charge on outer shell `= 4q`
Charge distribution :
(i) Charge on inner surface of inner shell `= 0`
(ii) Charge on outer surface of inner shell `= 2q`
(iii) Charge on inner surface of outer shell `= -2q` (facing surfaces have equal and opposite charges)
(iv) Charge on outer surface of outer shell `= 6q`
(total charge on outer shell is `4q`)
(b) To calculate electric field , draw a sphere with centre `O` through that point where electric field is required. Assume charge to be concentrated at centre and apply formula of point charge.
(i) `r lt a` , enclosed charge `= 0 , E = 0`
(ii) `a lt r lt b` , enclosed charged `= 0 , E = 0` or electric inside conductor `= 0`
(iii) `b lt r lt c` , enclosed charge `= 2q , E = (1)/(4 pi in_(0)) .(2q)/(r^(2))`
(iv) `c lt r lt d` , enclosed charge `= 0 , E = 0`, or electric field inside conductor `= 0`
(v) `r gt d`, enclosed charge `= 6 q , E = (1)/(4 pi in_(0)) . (6q)/(r^(2))`