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 charges hollow sphere = 0 So 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`