Show all work an infinitely long, solid cylindrical charge insulator of radius r carries a volumetric charge density of p in electrostatic equilibrium. a) draw an appropriate gaussian surface for inside the cylinder. label r and r. b) draw an appropriate gaussian surface for outside the cylinder. label r and r c) derive an equation for the electric field as a function of the radial position inside the cylinder using electric flux and a gaussian surface of variable radius. d) derive an equation for the electric field as a function of the radial position outside the cylinder e) multiply your result from part b with some test charge. is this result consistent with coulomb's law? (consider when coulomb's law applies.) f) sketch a graph of your electric field as a function of radius from parts a and b. g) redraw the graph if it was a conductor of the same shape and size, carrying the same total charge.