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 inside a hollow sphere = 0
`:.` Force on charge q.
`F=qE=qxx0=0`
(ii) Net electric field at centre of sphere
`vec(E)_("net")+vec(E)_(1)+vec(E)_(2)`
`E_(1)=` field due to sphere = 0
`E_(2)=` field due to this charge `=(Kq)/r^(2)`
`:. E_("net")=(Kq)/r^(2)`
(iii) Electric field at B due to charge on sphere, `vec(E)_(1)=(KQ)/r_(1)^(2) hat(r)_(1)` ans due to charge q at A, `vec(E)_(2)=(Kq)/r_(2)^(2) hat(r)_(2)`
So, `vec(E)_("net")=vec(E)_(1)+vec(E)_(2)=(KQ)/r_(1)^(2) hat(r)_(1)+(Kq)/r_(2)^(2) hat(r)_(2)` where `r_(1)=CB` and `r_(2)=AB`