A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression, , 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.
(b) Show that the magnitude of the electric field inside ( r < R ) the sphere is .
Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr.
