Figure shows a uniformly charged thin non-conducting sphere of total charge Q and radius R. If point charge q is situated at point 'A' which is at a distance `r lt R` from centre of the sphere, then find out following :
(i) Force acting on charge q.
(ii) Electric field at centre of sphere.
(iii) Electric field at point B.

Explanation

(i) Electric field at the centre of the uniformly charged hollow sphere = 0
Sp force on charge q = 0
(ii) Electric field at A
`vec(E)_(A) = vec(E)_("sphere") + vec(E)_(q) = 0 + (Kq)/(r^(2)) , r = CA`
E due to sphere = 0, because point lies inside the charged hollow sphere.
(iii) Electric field `vec(E)_(B)` at point `B = vec(E)_("sphere") + vec(E)_(q)`
`= (KQ)/(r^(2)).hat(r ) + (Kq)/(r^(2)).hat(r ) = (K(Q + q))/(r^(2)).hat(r ) , r = CB`
Note :
Here we can also assume that the total charge of sphere is concentrated at the centre, for calculation of electric field at B.