A solid non conducting sphere of radius R and uniform volume density `rho` has centre at origin. Find out electric field intensity in vector form at following positions :
(i) (R, 0, 0) (ii) (0, 0, R/2) (iii) (R, R, R)

Explanation

For uniformly charged non-conducting sphere, electric field inside the sphere :
`vec(E)=k (Qvec(r))/R^(3)=(rho vec(r))/(3 epsi_(0)) ("for "r lt R)`
and electric field outside the sphere
`vec(E)_(0) =(KQ)/r^(2). hat(r) =1/(4piepsi_(0)). (rho 4/3pi R^(3))/r^(2) hat(r)=(rho R^(3))/(3 epsi_(0) r^(2)). hat(r) ("for "r ge R)`
(i) (R, 0, 0) means it is at the surface `vec(r)=R hat(r)` and `hat(r)=hat(i)`
`:. vec(E)_(0) =(rho R^(3))/(3 epsi_(0) R^(2)) (hat(i))=(rho R)/(3 epsi_(0)). hat(i)`
(ii) `(0, 0, R/2)`
means point is inside the sphere
`vec(r)=R/2 hat(k)" "implies" "vec(E)=(rho R)/(6 epsi_(0)) hat(k)`
(iii) For position (R, R, R)
`vec(r)=R (hat(i)+hat(j)+hat(k))implies" "hat(r)=(hat(i)+hat(j)+hat(k))/sqrt(3), r=Rsqrt(3)`
means point (R, R, R) is outside the sphere
`:. vec(E)=(rhoR^(3))/(3 epsi_(0) (3R^(2))). ((hat(i)+hat(j)+hat(k)))/sqrt(3)=(rho R)/(9sqrt(3) epsi_(0)) (hat(i)+hat(j)+hat(k))`