#5 A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume p. (a.) Using Gauss's law, derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of the charge density p. (b.) What is the electric field at a point outside the volume in terms of the charge per unit length in the cylinder? (c.) Compare the answers to part (a) and (b) for r = R. (d.) Graph the electric-field magnitude as a function of r from r = 0 to r = 3R.