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

Explanation

(i) At `(R//2, 0, 0)` : Distance of point from centre `=sqrt((R//2)^(2)+0^(2)+0^(2))=R//2 lt R`, so point lies inside the sphere, so `vec(E)=(p vec(r))/(3 epsi_(0))=rho/(3 epsi_(0)) [R/2 hat(i)]`
(ii) At `(R/sqrt(2), R/sqrt(2), 0)` distance of point from centre `=sqrt((R//sqrt(2))^(2)+(R//sqrt(2))^(2)+0^(2))=R=R`, so point lies at the surface of sphere, therefore
`vec(E)=(KQ)/R^(3) vec(r) =(k 4/3 pi R^(2) rho)/R^(3) =[R/sqrt(2) hat(i) +R/sqrt(2)hat(j)]=rho/(3 epsi_(0))[R/sqrt(2) hat(i) +R/sqrt(2)hat(j)]`
(ii) The point is outside the sphere
So, `vec(E)=(KQ)/r^(3) vec(r) =(K4/3 pi R^(3) rho)/((sqrt(2) R)^(3)) [Rhat(i)+Rhat(j)]=rho/(6sqrt(2) epsi_(0)) [Rhat(i)+Rhat(j)]`