A solid insulating sphere of radius R has a non-uniform charge density that varies with r according to the expression 1 = Ar 2, where A is a constant and r < R is measured from the center of the sphere.
(a) Show that the magnitude of the electric field outside (r > R) the sphere is E = AR 5/5/ 0r 2.
(b) Show that the magnitude of the electric field inside (r , R) the sphere is E = Ar 3/5/0. (Suggestion: The total charge Q on the sphere is equal to the integral of 1 dV, where r extends from 0 to R; also, the charge q within a radius r , R is less than Q. To evaluate the integrals, note that the volume element dV for a spherical shell of radius r and thickness dr is equal to 4(r 2dr.)