A Sphere of radius `R_0` carries a volume charge density proportional to the distance (x) from the origin, `rho=alphax` where `alpha` is a positive constant. (a) Calculate the total charge in the sphere of radius `R_0`. (b) The sphere is shaved off so as to reduce its radius. What should be the radius (R) of the remaining sphere so that it contains half the charge of the original sphere? (c) Find the electric field at a point inside the sphere at a distance r lt R. Give your answer for original sphere of radius `R_0` as well as for the smaller sphere of radius R that was left after shaving off the original sphere.

Answer

(a). `pialphaR_(0)^(4)`
(b). `(R_(0))/((2)^(1//4))`