An uncharged conductor of inner radius `R_(1)` and outer radius `R_(2)` constains a point charge q at the centre as shown in figure

(i) Find `vec(E)` and V at points A, B and C
(ii) If a pint charge Q is kept out side the sphere at a distance `'r' ( gt gt R_(2))` from centre then find out resultant force on charge Q and charge q.

Explanation

At point A :

`V_(A)=(Kq)/(OA)+(Kq)/R_(2)+(K(-q))/R_(1), vec(E)_(A)=(Kq)/(OA^(3)) vec(OA)`
Note : Electric field at 'A' due to -q od `S_(1)` and `+q` of `S_(2)` is zero individually because they are uniformly distributed
at point B : `V_(B)=(Kq)/(OB)+(K(-q))/(OB)+(Kq)/R_(2)=(Kq)/R_(2), E_(B) =0`
At point C : `V_(C)=(Kq)/(OC), vec(E)_(C)=(Kq)/(OC^(3)) vec(OC)`
(ii) Force on point charge Q:
(Note : Here, force on 'Q' will be only due to 'q' of `S_(2)` (see result (iii))
`vec(F)_(0)=(KqQ)/r^(2) hat(r)` (r = distance of 'Q' from centre 'O')
Force on point charge q :
`vec(F)_(0)=0` (using result (iii) & charge on `S_(1)` uniform)