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)ltR`, so point lies inside the sphere so
`vec(E)=(rho vec( r ))/(3 in_(0))=(rho)/(3in_(0))[( R )/(2)hati]`
(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)piR^(3)rho)/(R^(3))[(R)/(sqrt(2))hati+(R)/(sqrt(2))hatj]`
`=(rho)/(3epsilon_(0))[(R)/(sqrt(2))hati+(R)/(sqrt(2))hatj]`
(iii) The point is outside the sphere
so, `vec(E)=(KQ)/(r^(3))vec(r)=(K(4)/(3)piR^(3)rho)/((sqrt(2)R)^(3))[Rhati+Rhatj]=(rho)/(6sqrt(2)epsilon_(0))[Rhati+Rhatj]`